p= 0.05 num clusters= 5
linkage completed in  10.879576921463013
silhouette_score of the clusters -0.026993756649087115
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 2: 1, 3: 1, 6: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 2, 3, 6, 7, 10, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 5: 1, 10: 1, 13: 1, 15: 1, 19: 1} [1, 2, 5, 10, 13, 15, 19]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 5: 1, 6: 1, 10: 1, 15: 2, 17: 2, 100: 1} [2, 3, 5, 6, 10, 100, 15, 17]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 6: 3, 7: 2, 10: 3, 11: 6, 12: 7, 13: 4, 14: 5, 20: 5, 23: 5, 29: 10, 33: 9, 84: 12, 100: 0} [3, 100, 1, 5, 7, 6, 10, 13, 14, 20, 23, 11, 12, 33, 29, 84]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.021153121827976115), 3: np.float64(0.020630849389167986), 4: np.float64(0.04044320575657124), 59: np.float64(0.04044320575657124), 40: np.float64(0.04044320575657124), 84: np.float64(0.04044320575657124), 0: np.float64(0.04044320575657124)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.09396227352671953), 3: np.float64(0.06654984212744788), 4: np.float64(0.08522845452457264), 59: np.float64(0.11325235745531465), 40: np.float64(0.11325235745531465), 84: np.float64(0.11325235745531465), 0: np.float64(0.11325235745531465)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10672017709431149), 3: np.float64(0.0913818581995159), 4: np.float64(0.11006047059664066), 59: np.float64(0.13808437352738268), 40: np.float64(0.13808437352738268), 84: np.float64(0.13808437352738268), 0: np.float64(0.13808437352738268)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.11746872276085493), 3: np.float64(0.1018650213279849), 4: np.float64(0.12956412883763824), 59: np.float64(0.15758803176838024), 40: np.float64(0.15758803176838024), 84: np.float64(0.15758803176838024), 0: np.float64(0.15758803176838024)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12046128983639276), 3: np.float64(0.10465961887475804), 4: np.float64(0.13255669591317606), 59: np.float64(0.16058059884391807), 40: np.float64(0.16058059884391807), 84: np.float64(0.16058059884391807), 0: np.float64(0.16058059884391807)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.14823608584737621), 3: np.float64(0.13107982209991056), 4: np.float64(0.17051769606594885), 59: np.float64(0.19854159899669088), 40: np.float64(0.19854159899669088), 84: np.float64(0.19854159899669088), 0: np.float64(0.19854159899669088)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.21438200045632616), 3: np.float64(0.19463996802533556), 4: np.float64(0.23097797709577228), 59: np.float64(0.26468751360564086), 40: np.float64(0.26468751360564086), 84: np.float64(0.26468751360564086), 0: np.float64(0.26468751360564086)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2313810011600232), 3: np.float64(0.21876513457471936), 4: np.float64(0.25510314364515607), 59: np.float64(0.28881268015502465), 40: np.float64(0.28881268015502465), 84: np.float64(0.28881268015502465), 0: np.float64(0.28881268015502465)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.24605039759091207), 3: np.float64(0.2327190960994466), 4: np.float64(0.27312847205403284), 59: np.float64(0.3068380085639014), 40: np.float64(0.3068380085639014), 84: np.float64(0.3068380085639014), 0: np.float64(0.3068380085639014)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.24881736999837226), 3: np.float64(0.23686726165468583), 4: np.float64(0.275895444461493), 59: np.float64(0.3096049809713616), 40: np.float64(0.3096049809713616), 84: np.float64(0.3096049809713616), 0: np.float64(0.3096049809713616)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.29343636422082553), 3: np.float64(0.2772401971822918), 4: np.float64(0.3076970585114811), 59: np.float64(0.3414065950213497), 40: np.float64(0.3414065950213497), 84: np.float64(0.3414065950213497), 0: np.float64(0.3414065950213497)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.342986756397554), 3: np.float64(0.3859098595673312), 4: np.float64(0.40602543524279955), 59: np.float64(0.39095698719807814), 40: np.float64(0.39095698719807814), 84: np.float64(0.39095698719807814), 0: np.float64(0.39095698719807814)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.37162821917358635), 3: np.float64(0.4080946157713258), 4: np.float64(0.4282101914467941), 59: np.float64(0.4131417434020727), 40: np.float64(0.4131417434020727), 84: np.float64(0.4131417434020727), 0: np.float64(0.4131417434020727)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.39659887685369116), 3: np.float64(0.43068900119325165), 4: np.float64(0.44244718282638795), 59: np.float64(0.42737873478166655), 40: np.float64(0.42737873478166655), 84: np.float64(0.42737873478166655), 0: np.float64(0.42737873478166655)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3987693758679518), 3: np.float64(0.4384160071076878), 4: np.float64(0.4446176818406486), 59: np.float64(0.4295492337959272), 40: np.float64(0.4295492337959272), 84: np.float64(0.4295492337959272), 0: np.float64(0.4295492337959272)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5011207125872221), 3: np.float64(0.5181273082930605), 4: np.float64(0.45700515425972), 59: np.float64(0.4419367062149986), 40: np.float64(0.4419367062149986), 84: np.float64(0.4419367062149986), 0: np.float64(0.4419367062149986)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5109792735283509), 3: np.float64(0.746065815602611), 4: np.float64(0.634523842244525), 59: np.float64(0.4517952671561274), 40: np.float64(0.4517952671561274), 84: np.float64(0.4517952671561274), 0: np.float64(0.4517952671561274)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5921379139573358), 3: np.float64(0.7594977088644468), 4: np.float64(0.6479557355063608), 59: np.float64(0.4652271604179632), 40: np.float64(0.4652271604179632), 84: np.float64(0.4652271604179632), 0: np.float64(0.4652271604179632)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6488645249881375), 3: np.float64(0.8036764379562221), 4: np.float64(0.6515246674818453), 59: np.float64(0.46879609239344777), 40: np.float64(0.46879609239344777), 84: np.float64(0.46879609239344777), 0: np.float64(0.46879609239344777)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6494465664501172), 3: np.float64(0.8209341891843438), 4: np.float64(0.652106708943825), 59: np.float64(0.4693781338554275), 40: np.float64(0.4693781338554275), 84: np.float64(0.4693781338554275), 0: np.float64(0.4693781338554275)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7980706750900125), 3: np.float64(0.9110792678469016), 4: np.float64(0.6531528714833345), 59: np.float64(0.4704242963949369), 40: np.float64(0.4704242963949369), 84: np.float64(0.4704242963949369), 0: np.float64(0.4704242963949369)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7983940994637856), 3: np.float64(1.1931360561139794), 4: np.float64(0.8242289613473915), 59: np.float64(0.4707477207687099), 40: np.float64(0.4707477207687099), 84: np.float64(0.4707477207687099), 0: np.float64(0.4707477207687099)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.9416556976158001), 3: np.float64(1.196217456421977), 4: np.float64(0.8273103616553891), 59: np.float64(0.4738291210767075), 40: np.float64(0.4738291210767075), 84: np.float64(0.4738291210767075), 0: np.float64(0.4738291210767075)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.0151141842423037), 3: np.float64(1.2407722807770418), 4: np.float64(0.8274576994590754), 59: np.float64(0.4739764588803938), 40: np.float64(0.4739764588803938), 84: np.float64(0.4739764588803938), 0: np.float64(0.4739764588803938)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.015142233129076), 3: np.float64(1.2613539874564075), 4: np.float64(0.8274857483458478), 59: np.float64(0.4740045077671662), 40: np.float64(0.4740045077671662), 84: np.float64(0.4740045077671662), 0: np.float64(0.4740045077671662)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.1805926434273954), 3: np.float64(1.339507227418611), 4: np.float64(0.8275650182937431), 59: np.float64(0.47408377771506155), 40: np.float64(0.47408377771506155), 84: np.float64(0.47408377771506155), 0: np.float64(0.47408377771506155)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.1806074485001787), 3: np.float64(1.6483134644182507), 4: np.float64(0.9734347559301876), 59: np.float64(0.4740985827878448), 40: np.float64(0.4740985827878448), 84: np.float64(0.4740985827878448), 0: np.float64(0.4740985827878448)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.3394641255546078), 3: np.float64(1.6487956849091792), 4: np.float64(0.9739169764211161), 59: np.float64(0.4745808032787733), 40: np.float64(0.4745808032787733), 84: np.float64(0.4745808032787733), 0: np.float64(0.4745808032787733)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.4200892793622741), 3: np.float64(1.6868803108775206), 4: np.float64(0.9739250204659146), 59: np.float64(0.47458884732357176), 40: np.float64(0.47458884732357176), 84: np.float64(0.47458884732357176), 0: np.float64(0.47458884732357176)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.4200902695775663), 3: np.float64(1.7076243695857674), 4: np.float64(0.9739260106812068), 59: np.float64(0.47458983753886397), 40: np.float64(0.47458983753886397), 84: np.float64(0.47458983753886397), 0: np.float64(0.47458983753886397)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.5984421739684076), 3: np.float64(1.7732363685049326), 4: np.float64(0.9739332300192055), 59: np.float64(0.4745970568768627), 40: np.float64(0.4745970568768627), 84: np.float64(0.4745970568768627), 0: np.float64(0.4745970568768627)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.598442873986957), 3: np.float64(2.105682698364099), 4: np.float64(1.0962334000672926), 59: np.float64(0.47459775689541206), 40: np.float64(0.47459775689541206), 84: np.float64(0.47459775689541206), 0: np.float64(0.47459775689541206)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.7598423967641423), 3: np.float64(2.105741111234568), 4: np.float64(1.0962918129377617), 59: np.float64(0.47465616976588115), 40: np.float64(0.47465616976588115), 84: np.float64(0.47465616976588115), 0: np.float64(0.47465616976588115)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.8466538596448872), 3: np.float64(2.1376772636864114), 4: np.float64(1.096292289871244), 59: np.float64(0.47465664669936347), 40: np.float64(0.47465664669936347), 84: np.float64(0.47465664669936347), 0: np.float64(0.47465664669936347)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.846653888122271), 3: np.float64(2.1584270928221083), 4: np.float64(1.0962923183486277), 59: np.float64(0.4746566751767473), 40: np.float64(0.4746566751767473), 84: np.float64(0.4746566751767473), 0: np.float64(0.4746566751767473)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.036312819359966), 3: np.float64(2.212765286389085), 4: np.float64(1.0962928933876934), 59: np.float64(0.47465725021581295), 40: np.float64(0.47465725021581295), 84: np.float64(0.47465725021581295), 0: np.float64(0.47465725021581295)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.036312846223154), 3: np.float64(2.566242293854516), 4: np.float64(1.1975657516063247), 59: np.float64(0.47465727707900046), 40: np.float64(0.47465727707900046), 84: np.float64(0.47465727707900046), 0: np.float64(0.47465727707900046)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.1980314746057537), 3: np.float64(2.566247522457416), 4: np.float64(1.1975709802092247), 59: np.float64(0.4746625056819005), 40: np.float64(0.4746625056819005), 84: np.float64(0.4746625056819005), 0: np.float64(0.4746625056819005)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.2903357433590896), 3: np.float64(2.592693138225919), 4: np.float64(1.197571003304857), 59: np.float64(0.4746625287775328), 40: np.float64(0.4746625287775328), 84: np.float64(0.4746625287775328), 0: np.float64(0.4746625287775328)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.2903357439800915), 3: np.float64(2.613443134499907), 4: np.float64(1.197571003925859), 59: np.float64(0.4746625293985348), 40: np.float64(0.4746625293985348), 84: np.float64(0.4746625293985348), 0: np.float64(0.4746625293985348)}
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 3, 5, 6, 7, 14, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 14: 0, 16: 0, 100: 0} [4, 5, 6, 7, 9, 14, 16, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 4: 1, 6: 1, 10: 1, 13: 1, 14: 1, 18: 2} [1, 2, 4, 6, 10, 13, 14, 18]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 4: 2, 6: 1, 10: 1, 12: 2, 23: 4, 100: 1} [2, 3, 6, 10, 100, 4, 12, 23]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 4: 5, 5: 2, 6: 3, 7: 2, 9: 10, 10: 3, 12: 7, 13: 4, 14: 5, 15: 6, 21: 9, 24: 8, 31: 12, 34: 14, 41: 13, 100: 0} [3, 100, 1, 5, 7, 6, 10, 13, 4, 14, 15, 12, 24, 21, 9, 31, 41, 34]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.03709591037813351), 3: np.float64(0.021424537731199084), 4: np.float64(0.03709591037813351), 59: np.float64(0.03709591037813351), 40: np.float64(0.03709591037813351), 84: np.float64(0.03709591037813351), 0: np.float64(0.03709591037813351)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10592385954200928), 3: np.float64(0.09025248689507485), 4: np.float64(0.07887821539487888), 59: np.float64(0.10592385954200928), 40: np.float64(0.10592385954200928), 84: np.float64(0.10592385954200928), 0: np.float64(0.10592385954200928)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.1202527222218363), 3: np.float64(0.11694169799916383), 4: np.float64(0.09285329719460704), 59: np.float64(0.13261307064609826), 40: np.float64(0.13261307064609826), 84: np.float64(0.13261307064609826), 0: np.float64(0.13261307064609826)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.1308878568969284), 3: np.float64(0.12731425026353738), 4: np.float64(0.10226987278978478), 59: np.float64(0.15469450501243742), 40: np.float64(0.15469450501243742), 84: np.float64(0.15469450501243742), 0: np.float64(0.15469450501243742)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.1340354953963151), 3: np.float64(0.13005468036399034), 4: np.float64(0.10454125019239825), 59: np.float64(0.15784214351182413), 40: np.float64(0.15784214351182413), 84: np.float64(0.15784214351182413), 0: np.float64(0.15784214351182413)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.16994382631422236), 3: np.float64(0.15860469485654716), 4: np.float64(0.14044958111030553), 59: np.float64(0.1937504744297314), 40: np.float64(0.1937504744297314), 84: np.float64(0.1937504744297314), 0: np.float64(0.1937504744297314)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.23605619365011254), 3: np.float64(0.2247170621924373), 4: np.float64(0.19852537709496487), 59: np.float64(0.2598628417656216), 40: np.float64(0.2598628417656216), 84: np.float64(0.2598628417656216), 0: np.float64(0.2598628417656216)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2552407522942497), 3: np.float64(0.24958036712793738), 4: np.float64(0.21677429377332763), 59: np.float64(0.2847261467011216), 40: np.float64(0.2847261467011216), 84: np.float64(0.2847261467011216), 0: np.float64(0.2847261467011216)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.26958901152386183), 3: np.float64(0.26322885349750835), 4: np.float64(0.22804360819346486), 59: np.float64(0.3045971316962916), 40: np.float64(0.3045971316962916), 84: np.float64(0.3045971316962916), 0: np.float64(0.3045971316962916)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2723894403937131), 3: np.float64(0.26721547581891686), 4: np.float64(0.2308048415227999), 59: np.float64(0.30739756056614287), 40: np.float64(0.30739756056614287), 84: np.float64(0.30739756056614287), 0: np.float64(0.30739756056614287)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3051240546566606), 3: np.float64(0.31480779024123134), 4: np.float64(0.26353945578574745), 59: np.float64(0.3401321748290904), 40: np.float64(0.3401321748290904), 84: np.float64(0.3401321748290904), 0: np.float64(0.3401321748290904)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3636118893418554), 3: np.float64(0.3732956249264262), 4: np.float64(0.36736244767457793), 59: np.float64(0.3986200095142852), 40: np.float64(0.3986200095142852), 84: np.float64(0.3986200095142852), 0: np.float64(0.3986200095142852)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3953683948107797), 3: np.float64(0.39354742894977207), 4: np.float64(0.3960969220889242), 59: np.float64(0.4188718135376311), 40: np.float64(0.4188718135376311), 84: np.float64(0.4188718135376311), 0: np.float64(0.4188718135376311)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4191689660191502), 3: np.float64(0.41508307634973507), 4: np.float64(0.41091328135634847), 59: np.float64(0.4335211690686916), 40: np.float64(0.4335211690686916), 84: np.float64(0.4335211690686916), 0: np.float64(0.4335211690686916)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4211772792838775), 3: np.float64(0.42223029004118584), 4: np.float64(0.41447450134126135), 59: np.float64(0.43552948233341887), 40: np.float64(0.43552948233341887), 84: np.float64(0.43552948233341887), 0: np.float64(0.43552948233341887)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.44081359538555226), 3: np.float64(0.5484123934311371), 4: np.float64(0.4341108174429361), 59: np.float64(0.45516579843509364), 40: np.float64(0.45516579843509364), 84: np.float64(0.45516579843509364), 0: np.float64(0.45516579843509364)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.46835571631770423), 3: np.float64(0.5759545143632891), 4: np.float64(0.7236080918500245), 59: np.float64(0.4827079193672456), 40: np.float64(0.4827079193672456), 84: np.float64(0.4827079193672456), 0: np.float64(0.4827079193672456)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5413659043427259), 3: np.float64(0.5823303984370694), 4: np.float64(0.7804684834561019), 59: np.float64(0.4890838034410258), 40: np.float64(0.4890838034410258), 84: np.float64(0.4890838034410258), 0: np.float64(0.4890838034410258)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5925034897150382), 3: np.float64(0.622156389969407), 4: np.float64(0.7971329727545741), 59: np.float64(0.4918642868902453), 40: np.float64(0.4918642868902453), 84: np.float64(0.4918642868902453), 0: np.float64(0.4918642868902453)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5929083099285175), 3: np.float64(0.6375488576402425), 4: np.float64(0.8004664040163422), 59: np.float64(0.49226910710372457), 40: np.float64(0.49226910710372457), 84: np.float64(0.49226910710372457), 0: np.float64(0.49226910710372457)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.5975521378880086), 3: np.float64(0.8536858898832956), 4: np.float64(0.8051102319758333), 59: np.float64(0.4969129350632157), 40: np.float64(0.4969129350632157), 84: np.float64(0.4969129350632157), 0: np.float64(0.4969129350632157)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.6011793276629035), 3: np.float64(0.8573130796581905), 4: np.float64(1.2380970933264648), 59: np.float64(0.5005401248381105), 40: np.float64(0.5005401248381105), 84: np.float64(0.5005401248381105), 0: np.float64(0.5005401248381105)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7007218708351276), 3: np.float64(0.8576794501478012), 4: np.float64(1.2984726977061871), 59: np.float64(0.5009064953277212), 40: np.float64(0.5009064953277212), 84: np.float64(0.5009064953277212), 0: np.float64(0.5009064953277212)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7698495068181368), 3: np.float64(0.8996074808049506), 4: np.float64(1.3057427651153402), 59: np.float64(0.5010125618153933), 40: np.float64(0.5010125618153933), 84: np.float64(0.5010125618153933), 0: np.float64(0.5010125618153933)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7698619477254529), 3: np.float64(0.919309645849578), 4: np.float64(1.3067283955341322), 59: np.float64(0.5010250027227094), 40: np.float64(0.5010250027227094), 84: np.float64(0.5010250027227094), 0: np.float64(0.5010250027227094)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.770601021573529), 3: np.float64(1.1588752027611209), 4: np.float64(1.3074674693822084), 59: np.float64(0.5017640765707856), 40: np.float64(0.5017640765707856), 84: np.float64(0.5017640765707856), 0: np.float64(0.5017640765707856)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.7709409243993514), 3: np.float64(1.1592151055869433), 4: np.float64(1.760178052427274), 59: np.float64(0.5021039793966079), 40: np.float64(0.5021039793966079), 84: np.float64(0.5021039793966079), 0: np.float64(0.5021039793966079)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8807176476843649), 3: np.float64(1.1592387904600714), 4: np.float64(1.8120329047766202), 59: np.float64(0.502127664269736), 40: np.float64(0.502127664269736), 84: np.float64(0.502127664269736), 0: np.float64(0.502127664269736)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.9596850548677853), 3: np.float64(1.1965403523701998), 4: np.float64(1.8144852487433207), 59: np.float64(0.5021348360046737), 40: np.float64(0.5021348360046737), 84: np.float64(0.5021348360046737), 0: np.float64(0.5021348360046737)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.9596853935230042), 3: np.float64(1.2170952859000383), 4: np.float64(1.814678621937388), 59: np.float64(0.5021351746598925), 40: np.float64(0.5021351746598925), 84: np.float64(0.5021351746598925), 0: np.float64(0.5021351746598925)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(0.9597763283076066), 3: np.float64(1.4605496771924242), 4: np.float64(1.8147695567219904), 59: np.float64(0.502226109444495), 40: np.float64(0.502226109444495), 84: np.float64(0.502226109444495), 0: np.float64(0.502226109444495)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(0.9598015699412613), 3: np.float64(1.4605749188260788), 4: np.float64(2.2693681069200626), 59: np.float64(0.5022513510781497), 40: np.float64(0.5022513510781497), 84: np.float64(0.5022513510781497), 0: np.float64(0.5022513510781497)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.0780438505935064), 3: np.float64(1.460576681869793), 4: np.float64(2.3128670110492475), 59: np.float64(0.5022531141218637), 40: np.float64(0.5022531141218637), 84: np.float64(0.5022531141218637), 0: np.float64(0.5022531141218637)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.164301995791164), 3: np.float64(1.4923092801215923), 4: np.float64(2.3136244381343083), 59: np.float64(0.5022535714882342), 40: np.float64(0.5022535714882342), 84: np.float64(0.5022535714882342), 0: np.float64(0.5022535714882342)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.1643020048530006), 3: np.float64(1.51302658225205), 4: np.float64(2.3136570906946674), 59: np.float64(0.5022535805500709), 40: np.float64(0.5022535805500709), 84: np.float64(0.5022535805500709), 0: np.float64(0.5022535805500709)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.1643102944052557), 3: np.float64(1.7569768449385197), 4: np.float64(2.3136653802469223), 59: np.float64(0.5022618701023259), 40: np.float64(0.5022618701023259), 84: np.float64(0.5022618701023259), 0: np.float64(0.5022618701023259)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.1643116886863618), 3: np.float64(1.7569782392196258), 4: np.float64(2.7684070145602853), 59: np.float64(0.502263264383432), 40: np.float64(0.502263264383432), 84: np.float64(0.502263264383432), 0: np.float64(0.502263264383432)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.2900395151080921), 3: np.float64(1.7569783488615536), 4: np.float64(2.8044286399289162), 59: np.float64(0.5022633740253598), 40: np.float64(0.5022633740253598), 84: np.float64(0.5022633740253598), 0: np.float64(0.5022633740253598)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.3821695210434146), 3: np.float64(1.7833740374967813), 4: np.float64(2.8046528545640723), 59: np.float64(0.5022633967239332), 40: np.float64(0.5022633967239332), 84: np.float64(0.5022633967239332), 0: np.float64(0.5022633967239332)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
empirical probabilities from test set: {2: 0.272, 3: 0.242, 4: 0.248, 59: 0.07, 40: 0.068, 84: 0.052, 0: 0.048}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(1.382169521238396), 3: np.float64(1.8041189289842918), 4: np.float64(2.8046579621016545), 59: np.float64(0.5022633969189146), 40: np.float64(0.5022633969189146), 84: np.float64(0.5022633969189146), 0: np.float64(0.5022633969189146)}
err dic= {2: np.float64(1.110169521238396), 3: np.float64(1.5621189289842918), 4: np.float64(2.5566579621016547), 59: np.float64(0.43226339691891463), 40: np.float64(0.43426339691891463), 84: np.float64(0.45026339691891465), 0: np.float64(0.45426339691891465)} 

err list= [np.float64(1.110169521238396), np.float64(1.5621189289842918), np.float64(2.5566579621016547), np.float64(0.43226339691891463), np.float64(0.43426339691891463), np.float64(0.45026339691891465), np.float64(0.45426339691891465)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: np.float64(0.13748223350253808), 3: np.float64(0.10631895093062604), 4: np.float64(0.11342935702199661), 59: np.float64(0.03844966159052453), 40: np.float64(0.04806387478849407), 84: np.float64(0.05433460236886634), 0: np.float64(0.21638240270727582)} 

err MNL list= [np.float64(0.13748223350253808), np.float64(0.10631895093062604), np.float64(0.11342935702199661), np.float64(0.03844966159052453), np.float64(0.04806387478849407), np.float64(0.05433460236886634), np.float64(0.21638240270727582)]
sampled assortment [2, 7, 1, 45, 87, 59] number: 1
#  Learning probs for MM model, A = [2, 7, 1, 45, 87, 59]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 2: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 10: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 6, 7, 10, 14, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 10: 0, 11: 0, 100: 0} [3, 4, 5, 6, 9, 10, 11, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 14: 1, 16: 1, 19: 1} [1, 2, 3, 4, 5, 6, 14, 16, 19]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 10: 1, 15: 1, 100: 1} [2, 3, 4, 5, 6, 7, 10, 15, 100]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 6: 2, 7: 2, 10: 2, 11: 5, 12: 6, 13: 4, 14: 4, 15: 6, 20: 6, 23: 7, 26: 10, 72: 13, 73: 13, 90: 13, 100: 0} [3, 100, 1, 5, 6, 7, 10, 13, 14, 11, 12, 15, 20, 23, 26, 72, 73, 90]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.02551219428473207), 7: np.float64(0.023182126005281807), 1: np.float64(0.026158038557892716), 45: np.float64(0.04228691028802371), 87: np.float64(0.04228691028802371), 59: np.float64(0.04228691028802371), 0: np.float64(0.04228691028802371)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.09047647999901798), 7: np.float64(0.08814641171956772), 1: np.float64(0.09112232427217862), 45: np.float64(0.10725119600230962), 87: np.float64(0.10725119600230962), 59: np.float64(0.10725119600230962), 0: np.float64(0.10725119600230962)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10640614242501958), 7: np.float64(0.11404389448432142), 1: np.float64(0.10745524802240791), 45: np.float64(0.13314867876706332), 87: np.float64(0.13314867876706332), 59: np.float64(0.13314867876706332), 0: np.float64(0.13314867876706332)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.11845765962768448), 7: np.float64(0.12473439462833846), 1: np.float64(0.1266568445530714), 45: np.float64(0.15235027529772682), 87: np.float64(0.15235027529772682), 59: np.float64(0.15235027529772682), 0: np.float64(0.15235027529772682)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12159829701916003), 7: np.float64(0.12716767949949795), 1: np.float64(0.1292703727245342), 45: np.float64(0.15549091268920237), 87: np.float64(0.15549091268920237), 59: np.float64(0.15549091268920237), 0: np.float64(0.15549091268920237)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.1553011226864424), 7: np.float64(0.15506327015095658), 1: np.float64(0.16470117921474814), 45: np.float64(0.1922336069869635), 87: np.float64(0.1922336069869635), 59: np.float64(0.1922336069869635), 0: np.float64(0.1922336069869635)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.22026540840072822), 7: np.float64(0.22002755586524242), 1: np.float64(0.22966546492903395), 45: np.float64(0.2571978927012493), 87: np.float64(0.2571978927012493), 59: np.float64(0.2571978927012493), 0: np.float64(0.2571978927012493)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.24177052210402442), 7: np.float64(0.243554992232472), 1: np.float64(0.2522731693895892), 45: np.float64(0.2807253290684789), 87: np.float64(0.2807253290684789), 59: np.float64(0.2807253290684789), 0: np.float64(0.2807253290684789)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.25858496453893265), 7: np.float64(0.25682984160039846), 1: np.float64(0.2700053110290222), 45: np.float64(0.2984574707079119), 87: np.float64(0.2984574707079119), 59: np.float64(0.2984574707079119), 0: np.float64(0.2984574707079119)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2613744862651347), 7: np.float64(0.25999253124993216), 1: np.float64(0.2736450127484783), 45: np.float64(0.30124699243411396), 87: np.float64(0.30124699243411396), 59: np.float64(0.30124699243411396), 0: np.float64(0.30124699243411396)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3132189097453194), 7: np.float64(0.29591033504416464), 1: np.float64(0.3309419618431767), 45: np.float64(0.32598219834183545), 87: np.float64(0.32598219834183545), 59: np.float64(0.32598219834183545), 0: np.float64(0.32598219834183545)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.37818319545960505), 7: np.float64(0.3608746207584503), 1: np.float64(0.39590624755746234), 45: np.float64(0.3909464840561211), 87: np.float64(0.3909464840561211), 59: np.float64(0.3909464840561211), 0: np.float64(0.3909464840561211)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4131576098329767), 7: np.float64(0.3784991967553405), 1: np.float64(0.43455895319963966), 45: np.float64(0.4085710600530113), 87: np.float64(0.4085710600530113), 59: np.float64(0.4085710600530113), 0: np.float64(0.4085710600530113)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4426931962926526), 7: np.float64(0.3972218865761292), 1: np.float64(0.44865729794354675), 45: np.float64(0.4226694047969184), 87: np.float64(0.4226694047969184), 59: np.float64(0.4226694047969184), 0: np.float64(0.4226694047969184)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4446966088103696), 7: np.float64(0.40186949385940607), 1: np.float64(0.454742628071685), 45: np.float64(0.4246728173146354), 87: np.float64(0.4246728173146354), 59: np.float64(0.4246728173146354), 0: np.float64(0.4246728173146354)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5293808145470735), 7: np.float64(0.43770182399147145), 1: np.float64(0.5634793006296268), 45: np.float64(0.4283595152079577), 87: np.float64(0.4283595152079577), 59: np.float64(0.4283595152079577), 0: np.float64(0.4283595152079577)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5943451002613592), 7: np.float64(0.5026661097057572), 1: np.float64(0.6284435863439125), 45: np.float64(0.49332380092224337), 87: np.float64(0.49332380092224337), 59: np.float64(0.49332380092224337), 0: np.float64(0.49332380092224337)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6574867116556247), 7: np.float64(0.5061727006507326), 1: np.float64(0.7095190202247696), 45: np.float64(0.49683039186721883), 87: np.float64(0.49683039186721883), 59: np.float64(0.49683039186721883), 0: np.float64(0.49683039186721883)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.7292394839437228), 7: np.float64(0.5324353606166267), 1: np.float64(0.7136659337739711), 45: np.float64(0.5009773054164204), 87: np.float64(0.5009773054164204), 59: np.float64(0.5009773054164204), 0: np.float64(0.5009773054164204)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.7296505060558272), 7: np.float64(0.5390324861234036), 1: np.float64(0.7257636977066725), 45: np.float64(0.5013883275285247), 87: np.float64(0.5013883275285247), 59: np.float64(0.5013883275285247), 0: np.float64(0.5013883275285247)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.8159195020118649), 7: np.float64(0.5540043605548728), 1: np.float64(0.8679972263413352), 45: np.float64(0.5015197277729823), 87: np.float64(0.5015197277729823), 59: np.float64(0.5015197277729823), 0: np.float64(0.5015197277729823)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.8808837877261506), 7: np.float64(0.6189686462691586), 1: np.float64(0.932961512055621), 45: np.float64(0.566484013487268), 87: np.float64(0.566484013487268), 59: np.float64(0.566484013487268), 0: np.float64(0.566484013487268)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.9417338317844491), 7: np.float64(0.6190836850651076), 1: np.float64(1.0332862740175777), 45: np.float64(0.5665990522832169), 87: np.float64(0.5665990522832169), 59: np.float64(0.5665990522832169), 0: np.float64(0.5665990522832169)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.0439087998316965), 7: np.float64(0.6345327636661484), 1: np.float64(1.03351146468792), 45: np.float64(0.5668242429535593), 87: np.float64(0.5668242429535593), 59: np.float64(0.5668242429535593), 0: np.float64(0.5668242429535593)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.0439231961827176), 7: np.float64(0.6393984845191867), 1: np.float64(1.0493237620797764), 45: np.float64(0.5668386393045803), 87: np.float64(0.5668386393045803), 59: np.float64(0.5668386393045803), 0: np.float64(0.5668386393045803)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.1205772257526079), 7: np.float64(0.6444384495081953), 1: np.float64(1.2116003439526624), 45: np.float64(0.5668459951966341), 87: np.float64(0.5668459951966341), 59: np.float64(0.5668459951966341), 0: np.float64(0.5668459951966341)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.1855415114668937), 7: np.float64(0.709402735222481), 1: np.float64(1.2765646296669482), 45: np.float64(0.6318102809109198), 87: np.float64(0.6318102809109198), 59: np.float64(0.6318102809109198), 0: np.float64(0.6318102809109198)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.237425909625651), 7: np.float64(0.7094080012379239), 1: np.float64(1.3864039014309761), 45: np.float64(0.6318155469263628), 87: np.float64(0.6318155469263628), 59: np.float64(0.6318155469263628), 0: np.float64(0.6318155469263628)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.3498343212625912), 7: np.float64(0.7156940830057507), 1: np.float64(1.3864150027500228), 45: np.float64(0.6318266482454095), 87: np.float64(0.6318266482454095), 59: np.float64(0.6318266482454095), 0: np.float64(0.6318266482454095)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.3498349334134052), 7: np.float64(0.7186786492136881), 1: np.float64(1.4041773757880154), 45: np.float64(0.6318272603962235), 87: np.float64(0.6318272603962235), 59: np.float64(0.6318272603962235), 0: np.float64(0.6318272603962235)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.4150376717982296), 7: np.float64(0.7202349920985338), 1: np.float64(1.5814167947052524), 45: np.float64(0.6318276353494967), 87: np.float64(0.6318276353494967), 59: np.float64(0.6318276353494967), 0: np.float64(0.6318276353494967)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.4800019575125152), 7: np.float64(0.7851992778128195), 1: np.float64(1.646381080419538), 45: np.float64(0.6967919210637824), 87: np.float64(0.6967919210637824), 59: np.float64(0.6967919210637824), 0: np.float64(0.6967919210637824)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.5235028976010871), 7: np.float64(0.785199526802375), 1: np.float64(1.7646288953831886), 45: np.float64(0.6967921700533379), 87: np.float64(0.6967921700533379), 59: np.float64(0.6967921700533379), 0: np.float64(0.6967921700533379)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.6399930267618001), 7: np.float64(0.7874564925817462), 1: np.float64(1.7646294763951718), 45: np.float64(0.6967927510653211), 87: np.float64(0.6967927510653211), 59: np.float64(0.6967927510653211), 0: np.float64(0.6967927510653211)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.639993053167128), 7: np.float64(0.7891695414596853), 1: np.float64(1.7836662954905933), 45: np.float64(0.6967927774706489), 87: np.float64(0.6967927774706489), 59: np.float64(0.6967927774706489), 0: np.float64(0.6967927774706489)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.6942292751317276), 7: np.float64(0.7896302441042026), 1: np.float64(1.9729693108640707), 45: np.float64(0.6967927924750004), 87: np.float64(0.6967927924750004), 59: np.float64(0.6967927924750004), 0: np.float64(0.6967927924750004)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.7591935608460134), 7: np.float64(0.8545945298184883), 1: np.float64(2.0379335965783563), 45: np.float64(0.7617570781892861), 87: np.float64(0.7617570781892861), 59: np.float64(0.7617570781892861), 0: np.float64(0.7617570781892861)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.7952152976615463), 7: np.float64(0.8545945393734538), 1: np.float64(2.163661811987996), 45: np.float64(0.7617570877442515), 87: np.float64(0.7617570877442515), 59: np.float64(0.7617570877442515), 0: np.float64(0.7617570877442515)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.9132110493074799), 7: np.float64(0.855348662943191), 1: np.float64(2.1636618369448617), 45: np.float64(0.7617571127011175), 87: np.float64(0.7617571127011175), 59: np.float64(0.7617571127011175), 0: np.float64(0.7617571127011175)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.913211050222012), 7: np.float64(0.8562848574023176), 1: np.float64(2.1834756379130744), 45: np.float64(0.7617571136156496), 87: np.float64(0.7617571136156496), 59: np.float64(0.7617571136156496), 0: np.float64(0.7617571136156496)}
#  Learning probs for MM model, A = [2, 7, 1, 45, 87, 59]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 6, 7, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 7, 9, 10, 11, 12, 15, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 4: 1, 6: 1, 10: 1, 13: 1, 14: 1, 17: 2, 19: 1} [1, 2, 4, 6, 10, 13, 14, 19, 17]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 4: 2, 6: 1, 7: 2, 10: 1, 16: 2, 17: 2, 23: 2, 100: 1} [2, 3, 6, 10, 100, 4, 7, 16, 17, 23]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 6: 3, 7: 2, 10: 3, 12: 5, 13: 5, 14: 5, 15: 4, 16: 8, 20: 8, 23: 9, 24: 8, 71: 13, 100: 0} [3, 100, 1, 5, 7, 6, 10, 15, 12, 13, 14, 16, 20, 24, 23, 71]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.041516383423224876), 7: np.float64(0.01732487754614376), 1: np.float64(0.019093205337731855), 45: np.float64(0.041516383423224876), 87: np.float64(0.041516383423224876), 59: np.float64(0.041516383423224876), 0: np.float64(0.041516383423224876)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10924161131129065), 7: np.float64(0.06572351021775051), 1: np.float64(0.08681843322579763), 45: np.float64(0.10924161131129065), 87: np.float64(0.10924161131129065), 59: np.float64(0.10924161131129065), 0: np.float64(0.10924161131129065)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12517127373729225), 7: np.float64(0.09162099298250422), 1: np.float64(0.10315135697602693), 45: np.float64(0.13513909407604435), 87: np.float64(0.13513909407604435), 59: np.float64(0.13513909407604435), 0: np.float64(0.13513909407604435)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.1384626313856337), 7: np.float64(0.10314411284336862), 1: np.float64(0.1219384614741859), 45: np.float64(0.1539261985742033), 87: np.float64(0.1539261985742033), 59: np.float64(0.1539261985742033), 0: np.float64(0.1539261985742033)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.14159356619980423), 7: np.float64(0.10563037515237876), 1: np.float64(0.12454752509432308), 45: np.float64(0.15705713338837385), 87: np.float64(0.15705713338837385), 59: np.float64(0.15705713338837385), 0: np.float64(0.15705713338837385)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.18118913161206315), 7: np.float64(0.12642859943445423), 1: np.float64(0.14977147375095262), 45: np.float64(0.19665269880063277), 87: np.float64(0.19665269880063277), 59: np.float64(0.19665269880063277), 0: np.float64(0.19665269880063277)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2460262358379064), 7: np.float64(0.19215597407939516), 1: np.float64(0.2146085779767959), 45: np.float64(0.261489803026476), 87: np.float64(0.261489803026476), 59: np.float64(0.261489803026476), 0: np.float64(0.261489803026476)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.26753134954120256), 7: np.float64(0.21568341044662476), 1: np.float64(0.23721628243735113), 45: np.float64(0.2850172393937056), 87: np.float64(0.2850172393937056), 59: np.float64(0.2850172393937056), 0: np.float64(0.2850172393937056)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2863617518043267), 7: np.float64(0.2299038274451757), 1: np.float64(0.25435611858501617), 45: np.float64(0.3021570755413706), 87: np.float64(0.3021570755413706), 59: np.float64(0.3021570755413706), 0: np.float64(0.3021570755413706)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.28912810459013133), 7: np.float64(0.23319850849308846), 1: np.float64(0.25797967360808016), 45: np.float64(0.3049234283271752), 87: np.float64(0.3049234283271752), 59: np.float64(0.3049234283271752), 0: np.float64(0.3049234283271752)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3238834018991756), 7: np.float64(0.2617450825299994), 1: np.float64(0.2996566130259476), 45: np.float64(0.3396787256362195), 87: np.float64(0.3396787256362195), 59: np.float64(0.3396787256362195), 0: np.float64(0.3396787256362195)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.38124674083546223), 7: np.float64(0.3723150489122823), 1: np.float64(0.35701995196223424), 45: np.float64(0.3970420645725061), 87: np.float64(0.3970420645725061), 59: np.float64(0.3970420645725061), 0: np.float64(0.3970420645725061)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4162211552088339), 7: np.float64(0.3899396249091725), 1: np.float64(0.3956726576044115), 45: np.float64(0.41466664056939634), 87: np.float64(0.41466664056939634), 59: np.float64(0.41466664056939634), 0: np.float64(0.41466664056939634)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.44962160330163936), 7: np.float64(0.4094390098870861), 1: np.float64(0.4088426909902678), 45: np.float64(0.42783667395525266), 87: np.float64(0.42783667395525266), 59: np.float64(0.42783667395525266), 0: np.float64(0.42783667395525266)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4515719445055518), 7: np.float64(0.41443290111308995), 1: np.float64(0.4148470937447017), 45: np.float64(0.4297870151591651), 87: np.float64(0.4297870151591651), 59: np.float64(0.4297870151591651), 0: np.float64(0.4297870151591651)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.46881178427928394), 7: np.float64(0.4610143471889755), 1: np.float64(0.5260664488001554), 45: np.float64(0.44702685493289723), 87: np.float64(0.44702685493289723), 59: np.float64(0.44702685493289723), 0: np.float64(0.44702685493289723)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.4993844340078663), 7: np.float64(0.7323284488174826), 1: np.float64(0.5566390985287378), 45: np.float64(0.4775995046614796), 87: np.float64(0.4775995046614796), 59: np.float64(0.4775995046614796), 0: np.float64(0.4775995046614796)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5625260454021317), 7: np.float64(0.735835039762458), 1: np.float64(0.637714532409595), 45: np.float64(0.48110609560645506), 87: np.float64(0.48110609560645506), 59: np.float64(0.48110609560645506), 0: np.float64(0.48110609560645506)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6403424108727714), 7: np.float64(0.7597235842221413), 1: np.float64(0.6411235504235304), 45: np.float64(0.48451511362039046), 87: np.float64(0.48451511362039046), 59: np.float64(0.48451511362039046), 0: np.float64(0.48451511362039046)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6407037583006046), 7: np.float64(0.7672061483570224), 1: np.float64(0.6525842491494835), 45: np.float64(0.4848764610482236), 87: np.float64(0.4848764610482236), 59: np.float64(0.4848764610482236), 0: np.float64(0.4848764610482236)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.6432149002528476), 7: np.float64(0.8069670103852286), 1: np.float64(0.8442676773600624), 45: np.float64(0.4873876030004666), 87: np.float64(0.4873876030004666), 59: np.float64(0.4873876030004666), 0: np.float64(0.4873876030004666)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.6488933971003197), 7: np.float64(1.227646029300395), 1: np.float64(0.8499461742075345), 45: np.float64(0.49306609984793864), 87: np.float64(0.49306609984793864), 59: np.float64(0.49306609984793864), 0: np.float64(0.49306609984793864)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7097434411586182), 7: np.float64(1.227761068096344), 1: np.float64(0.9502709361694913), 45: np.float64(0.49318113864388763), 87: np.float64(0.49318113864388763), 59: np.float64(0.49318113864388763), 0: np.float64(0.49318113864388763)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.81647225837387), 7: np.float64(1.2390111278616402), 1: np.float64(0.9504251607733817), 45: np.float64(0.493335363247778), 87: np.float64(0.493335363247778), 59: np.float64(0.493335363247778), 0: np.float64(0.493335363247778)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.8164836997621545), 7: np.float64(1.2452642698119591), 1: np.float64(0.9648648118816403), 45: np.float64(0.49334680463606245), 87: np.float64(0.49334680463606245), 59: np.float64(0.49334680463606245), 0: np.float64(0.49334680463606245)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8167073901602652), 7: np.float64(1.266759833123713), 1: np.float64(1.186250796579333), 45: np.float64(0.49357049503417316), 87: np.float64(0.49357049503417316), 59: np.float64(0.49357049503417316), 0: np.float64(0.49357049503417316)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8174165371490891), 7: np.float64(1.7172549511907698), 1: np.float64(1.1869599435681568), 45: np.float64(0.49427964202299707), 87: np.float64(0.49427964202299707), 59: np.float64(0.49427964202299707), 0: np.float64(0.49427964202299707)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8693009353078465), 7: np.float64(1.7172602172062128), 1: np.float64(1.2967992153321848), 45: np.float64(0.49428490803844005), 87: np.float64(0.49428490803844005), 59: np.float64(0.49428490803844005), 0: np.float64(0.49428490803844005)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.9844051468357249), 7: np.float64(1.720874424391275), 1: np.float64(1.2968055315895968), 45: np.float64(0.4942912242958519), 87: np.float64(0.4942912242958519), 59: np.float64(0.4942912242958519), 0: np.float64(0.4942912242958519)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.9844056149682103), 7: np.float64(1.725459180311255), 1: np.float64(1.3129684350071897), 45: np.float64(0.49429169242833737), 87: np.float64(0.49429169242833737), 59: np.float64(0.49429169242833737), 0: np.float64(0.49429169242833737)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(0.9844243016374342), 7: np.float64(1.735379145644503), 1: np.float64(1.5469550363278224), 45: np.float64(0.4943103790975612), 87: np.float64(0.4943103790975612), 59: np.float64(0.4943103790975612), 0: np.float64(0.4943103790975612)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(0.9844940463351216), 7: np.float64(2.1897106774583786), 1: np.float64(1.5470247810255098), 45: np.float64(0.49438012379524865), 87: np.float64(0.49438012379524865), 59: np.float64(0.49438012379524865), 0: np.float64(0.49438012379524865)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.0279949864236935), 7: np.float64(2.189710926447934), 1: np.float64(1.6652725959891603), 45: np.float64(0.4943803727848041), 87: np.float64(0.4943803727848041), 59: np.float64(0.4943803727848041), 0: np.float64(0.4943803727848041)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.145731978684458), 7: np.float64(2.1907226045713624), 1: np.float64(1.6652728619123218), 45: np.float64(0.4943806387079656), 87: np.float64(0.4943806387079656), 59: np.float64(0.4943806387079656), 0: np.float64(0.4943806387079656)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.1457319980363172), 7: np.float64(2.1939564340903592), 1: np.float64(1.6827889356340286), 45: np.float64(0.4943806580598249), 87: np.float64(0.4943806580598249), 59: np.float64(0.4943806580598249), 0: np.float64(0.4943806580598249)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.1457335191016298), 7: np.float64(2.198216845345687), 1: np.float64(1.922520919052137), 45: np.float64(0.4943821791251376), 87: np.float64(0.4943821791251376), 59: np.float64(0.4943821791251376), 0: np.float64(0.4943821791251376)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.1457386513302028), 7: np.float64(2.6529360519742484), 1: np.float64(1.92252605128071), 45: np.float64(0.4943873113537107), 87: np.float64(0.4943873113537107), 59: np.float64(0.4943873113537107), 0: np.float64(0.4943873113537107)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.1817603881457357), 7: np.float64(2.652936061529214), 1: np.float64(2.0482542666903494), 45: np.float64(0.49438732090867626), 87: np.float64(0.49438732090867626), 59: np.float64(0.49438732090867626), 0: np.float64(0.49438732090867626)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.3002477968903254), 7: np.float64(2.653198607359371), 1: np.float64(2.0482542757754003), 45: np.float64(0.494387329993727), 87: np.float64(0.494387329993727), 59: np.float64(0.494387329993727), 0: np.float64(0.494387329993727)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
empirical probabilities from test set: {2: 0.272, 7: 0.215, 1: 0.245, 45: 0.088, 87: 0.051, 59: 0.078, 0: 0.051}
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.025 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.05 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.1 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.25 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.5 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  0.75 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  1 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

beta is  1.25 

learned probs for this beta: {2: np.float64(1.3002477975390394), 7: np.float64(2.6554105262665555), 1: np.float64(2.066792353624645), 45: np.float64(0.494387330642441), 87: np.float64(0.494387330642441), 59: np.float64(0.494387330642441), 0: np.float64(0.494387330642441)}
err dic= {2: np.float64(1.0282477975390394), 7: np.float64(2.4404105262665556), 1: np.float64(1.821792353624645), 45: np.float64(0.40638733064244104), 87: np.float64(0.443387330642441), 59: np.float64(0.416387330642441), 0: np.float64(0.443387330642441)} 

err list= [np.float64(1.0282477975390394), np.float64(2.4404105262665556), np.float64(1.821792353624645), np.float64(0.40638733064244104), np.float64(0.443387330642441), np.float64(0.416387330642441), np.float64(0.443387330642441)]
results for assortment [2, 7, 1, 45, 87, 59] :

err MNL dic= {2: np.float64(0.1376952803294267), 7: np.float64(0.07948104740787668), 1: np.float64(0.10615510505754408), 45: np.float64(0.022547988596769097), 87: np.float64(0.0575418646394256), 59: np.float64(0.03027790096082779), 0: np.float64(0.21296367859782495)} 

err MNL list= [np.float64(0.1376952803294267), np.float64(0.07948104740787668), np.float64(0.10615510505754408), np.float64(0.022547988596769097), np.float64(0.0575418646394256), np.float64(0.03027790096082779), np.float64(0.21296367859782495)]
sampled assortment [1, 2, 5, 13, 46, 71] number: 2
#  Learning probs for MM model, A = [1, 2, 5, 13, 46, 71]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 12: 1, 100: 1} [8, 1, 3, 5, 6, 7, 10, 12, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 14: 1, 100: 0} [3, 4, 5, 6, 7, 9, 11, 100, 14]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 4: 1, 5: 1, 6: 1, 10: 1, 13: 1, 19: 1} [1, 2, 4, 5, 6, 10, 13, 19]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 4: 1, 6: 1, 10: 1, 100: 1} [2, 4, 6, 10, 100]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 6: 3, 7: 2, 10: 3, 12: 7, 13: 2, 14: 4, 15: 5, 20: 5, 24: 7, 28: 11, 35: 12, 38: 10, 52: 9, 76: 13, 87: 10, 100: 0} [3, 100, 1, 5, 7, 13, 6, 10, 14, 15, 20, 12, 24, 52, 38, 87, 28, 35, 76]
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.024157136459499847), 2: np.float64(0.039366773330393595), 5: np.float64(0.023008996888531627), 13: np.float64(0.039366773330393595), 46: np.float64(0.039366773330393595), 71: np.float64(0.039366773330393595), 0: np.float64(0.039366773330393595)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.09249188594418474), 2: np.float64(0.10770152281507848), 5: np.float64(0.06775049998042164), 13: np.float64(0.10770152281507848), 46: np.float64(0.10770152281507848), 71: np.float64(0.10770152281507848), 0: np.float64(0.10770152281507848)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.10680938205125143), 2: np.float64(0.12166551868372767), 5: np.float64(0.08104843743830367), 13: np.float64(0.12006483879054156), 46: np.float64(0.14363727434539159), 71: np.float64(0.14363727434539159), 0: np.float64(0.14363727434539159)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.12545411715675778), 2: np.float64(0.1285471080506896), 5: np.float64(0.09969317254381002), 13: np.float64(0.1387095738960479), 46: np.float64(0.16228200945089793), 71: np.float64(0.16228200945089793), 0: np.float64(0.16228200945089793)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.12799586544461086), 2: np.float64(0.13188887585257883), 5: np.float64(0.10217216484283417), 13: np.float64(0.14107176210161376), 46: np.float64(0.16562377725278715), 71: np.float64(0.16562377725278715), 0: np.float64(0.16562377725278715)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.16090108250074908), 2: np.float64(0.16813230192477432), 5: np.float64(0.13204981742571711), 13: np.float64(0.17731518817380926), 46: np.float64(0.20186720332498265), 71: np.float64(0.20186720332498265), 0: np.float64(0.20186720332498265)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.2265521626061138), 2: np.float64(0.23378338203013904), 5: np.float64(0.19289333679352622), 13: np.float64(0.24296626827917397), 46: np.float64(0.26751828343034734), 71: np.float64(0.26751828343034734), 0: np.float64(0.26751828343034734)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.24561535859651118), 2: np.float64(0.25191685498122907), 5: np.float64(0.20934942042038931), 13: np.float64(0.2572044526092537), 46: np.float64(0.29880463779753735), 71: np.float64(0.29880463779753735), 0: np.float64(0.29880463779753735)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.26391669079321256), 2: np.float64(0.2608588618010208), 5: np.float64(0.2276507526170907), 13: np.float64(0.27550578480595506), 46: np.float64(0.31710596999423873), 71: np.float64(0.31710596999423873), 0: np.float64(0.31710596999423873)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.2673427185211667), 2: np.float64(0.26363454354741905), 5: np.float64(0.23090969100107603), 13: np.float64(0.2784680917084225), 46: np.float64(0.319881651740637), 71: np.float64(0.319881651740637), 0: np.float64(0.319881651740637)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.3226709976143788), 2: np.float64(0.29220480174241464), 5: np.float64(0.27673012093288607), 13: np.float64(0.3070383499034181), 46: np.float64(0.3484519099356326), 71: np.float64(0.3484519099356326), 0: np.float64(0.3484519099356326)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.3811717119596389), 2: np.float64(0.35070551608767475), 5: np.float64(0.38047583486132674), 13: np.float64(0.3655390642486782), 46: np.float64(0.4069526242808927), 71: np.float64(0.4069526242808927), 0: np.float64(0.4069526242808927)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.41182393360401714), 2: np.float64(0.3784407931774399), 5: np.float64(0.40339595109700904), 13: np.float64(0.38277462886698166), 46: np.float64(0.42802156441818295), 71: np.float64(0.42802156441818295), 0: np.float64(0.42802156441818295)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.4291676071387973), 2: np.float64(0.3931287519687586), 5: np.float64(0.42073962463178927), 13: np.float64(0.4001183024017618), 46: np.float64(0.4453652379529631), 71: np.float64(0.4453652379529631), 0: np.float64(0.4453652379529631)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.43447505984533974), 2: np.float64(0.3947921179877031), 5: np.float64(0.4255420064351251), 13: np.float64(0.40410500381610565), 46: np.float64(0.4470286039719076), 71: np.float64(0.4470286039719076), 0: np.float64(0.4470286039719076)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.5583705683325936), 2: np.float64(0.4027760841237889), 5: np.float64(0.5057266672674419), 13: np.float64(0.41208896995219146), 46: np.float64(0.4550125701079934), 71: np.float64(0.4550125701079934), 0: np.float64(0.4550125701079934)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.5895251525237017), 2: np.float64(0.43393066831489713), 5: np.float64(0.7735491621207926), 13: np.float64(0.4432435541432997), 46: np.float64(0.4861671542991016), 71: np.float64(0.4861671542991016), 0: np.float64(0.4861671542991016)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.6504577031985688), 2: np.float64(0.48138498649502165), 5: np.float64(0.8036853549694153), 13: np.float64(0.45835003394625806), 46: np.float64(0.4888739737969108), 71: np.float64(0.4888739737969108), 0: np.float64(0.4888739737969108)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.6625766849007018), 2: np.float64(0.5274210962822237), 5: np.float64(0.8158043366715483), 13: np.float64(0.47046901564839105), 46: np.float64(0.5009929554990438), 71: np.float64(0.5009929554990438), 0: np.float64(0.5009929554990438)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.6713736515670755), 2: np.float64(0.5276012331500045), 5: np.float64(0.8226554211999731), 13: np.float64(0.4748504169824689), 46: np.float64(0.5011730923668246), 71: np.float64(0.5011730923668246), 0: np.float64(0.5011730923668246)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.8403011629205603), 2: np.float64(0.5280030434913532), 5: np.float64(0.8957188581397448), 13: np.float64(0.47525222732381756), 46: np.float64(0.5015749027081733), 71: np.float64(0.5015749027081733), 0: np.float64(0.5015749027081733)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.8459492446850319), 2: np.float64(0.5336511252558247), 5: np.float64(1.3165803675529157), 13: np.float64(0.480900309088289), 46: np.float64(0.5072229844726448), 71: np.float64(0.5072229844726448), 0: np.float64(0.5072229844726448)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9304327313478804), 2: np.float64(0.5848929501562656), 5: np.float64(1.3372714581820462), 13: np.float64(0.48590940574063934), 46: np.float64(0.5073311515243881), 71: np.float64(0.5073311515243881), 0: np.float64(0.5073311515243881)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9339494316470915), 2: np.float64(0.6825427483609987), 5: np.float64(1.3407881584812573), 13: np.float64(0.4894261060398505), 46: np.float64(0.5108478518235993), 71: np.float64(0.5108478518235993), 0: np.float64(0.5108478518235993)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9451387248092169), 2: np.float64(0.6825486003494239), 5: np.float64(1.3475748078445993), 13: np.float64(0.49217675556068224), 46: np.float64(0.5108537038120244), 71: np.float64(0.5108537038120244), 0: np.float64(0.5108537038120244)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.135134189311114), 2: np.float64(0.6825718983500394), 5: np.float64(1.4014628533396245), 13: np.float64(0.4922000535612978), 46: np.float64(0.51087700181264), 71: np.float64(0.51087700181264), 0: np.float64(0.51087700181264)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.135831269268876), 2: np.float64(0.6832689783078013), 5: np.float64(1.8520303735930532), 13: np.float64(0.4928971335190597), 46: np.float64(0.5115740817704019), 71: np.float64(0.5115740817704019), 0: np.float64(0.5115740817704019)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.236617389566334), 2: np.float64(0.7308769705168529), 5: np.float64(1.8640136052556944), 13: np.float64(0.49424531665719307), 46: np.float64(0.5115822393346404), 71: np.float64(0.5115822393346404), 0: np.float64(0.5115822393346404)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.2373083510820133), 2: np.float64(0.8454812014227765), 5: np.float64(1.8647045667713738), 13: np.float64(0.49493627817287245), 46: np.float64(0.5122732008503198), 71: np.float64(0.5122732008503198), 0: np.float64(0.5122732008503198)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.250346052772625), 2: np.float64(0.8454814683338687), 5: np.float64(1.8708631409746337), 13: np.float64(0.49648893463463184), 46: np.float64(0.512273467761412), 71: np.float64(0.512273467761412), 0: np.float64(0.512273467761412)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.456313223541582), 2: np.float64(0.8454829586039698), 5: np.float64(1.908888518855171), 13: np.float64(0.49649042490473294), 46: np.float64(0.5122749580315131), 71: np.float64(0.5122749580315131), 0: np.float64(0.5122749580315131)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.456380809107008), 2: np.float64(0.8455505441693959), 5: np.float64(2.3632330054626145), 13: np.float64(0.49655801047015896), 46: np.float64(0.5123425435969392), 71: np.float64(0.5123425435969392), 0: np.float64(0.5123425435969392)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.5696775132154237), 2: np.float64(0.8872300723633662), 5: np.float64(2.369670599457358), 13: np.float64(0.4968925518973061), 46: np.float64(0.5123430876888471), 71: np.float64(0.5123430876888471), 0: np.float64(0.5123430876888471)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.5697816334719026), 2: np.float64(1.0053553508244923), 5: np.float64(2.369774719713837), 13: np.float64(0.49699667215378507), 46: np.float64(0.512447207945326), 71: np.float64(0.512447207945326), 0: np.float64(0.512447207945326)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.5843457417052815), 2: np.float64(1.0053553620021085), 5: np.float64(2.3751325557118927), 13: np.float64(0.4978246832118854), 46: np.float64(0.5124472191229422), 71: np.float64(0.5124472191229422), 0: np.float64(0.5124472191229422)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.80233537475582), 2: np.float64(1.0053554401158908), 5: np.float64(2.4011425320924427), 13: np.float64(0.49782476132566766), 46: np.float64(0.5124472972367244), 71: np.float64(0.5124472972367244), 0: np.float64(0.5124472972367244)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.8023402586121964), 2: np.float64(1.0053603239722673), 5: np.float64(2.8558632289541834), 13: np.float64(0.4978296451820442), 46: np.float64(0.512452181093101), 71: np.float64(0.512452181093101), 0: np.float64(0.512452181093101)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.9254395929331725), 2: np.float64(1.0406288737455232), 5: np.float64(2.859165613139272), 13: np.float64(0.49790929277230994), 46: np.float64(0.5124522091365721), 71: np.float64(0.5124522091365721), 0: np.float64(0.5124522091365721)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.9254511283963953), 2: np.float64(1.1593096609661855), 5: np.float64(2.859177148602495), 13: np.float64(0.4979208282355329), 46: np.float64(0.512463744599795), 71: np.float64(0.512463744599795), 0: np.float64(0.512463744599795)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.9412505814058598), 2: np.float64(1.1593096613390446), 5: np.float64(2.8637037676774737), 13: np.float64(0.49834475465965383), 46: np.float64(0.512463744972654), 71: np.float64(0.512463744972654), 0: np.float64(0.512463744972654)}
#  Learning probs for MM model, A = [1, 2, 5, 13, 46, 71]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 16: 3, 100: 1} [8, 1, 2, 3, 4, 5, 6, 7, 10, 100, 16]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 4: 1, 5: 1, 6: 1, 10: 1, 12: 1, 14: 1, 19: 1} [1, 2, 4, 5, 6, 10, 12, 14, 19]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 5: 1, 6: 1, 10: 1, 14: 2, 20: 4, 21: 1, 100: 1} [2, 3, 5, 6, 10, 21, 100, 14, 20]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 6: 3, 7: 2, 9: 10, 10: 2, 13: 5, 14: 3, 15: 5, 16: 8, 23: 7, 41: 10, 44: 11, 56: 11, 57: 13, 71: 10, 100: 0} [3, 100, 1, 5, 7, 10, 6, 14, 13, 15, 23, 16, 9, 41, 71, 44, 56, 57]
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.02835030448352165), 2: np.float64(0.02765033297179995), 5: np.float64(0.02573409777898181), 13: np.float64(0.04056631619142398), 46: np.float64(0.04056631619142398), 71: np.float64(0.04056631619142398), 0: np.float64(0.04056631619142398)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.09668505396820654), 2: np.float64(0.09598508245648484), 5: np.float64(0.07047560087087182), 13: np.float64(0.10890106567610887), 46: np.float64(0.10890106567610887), 71: np.float64(0.10890106567610887), 0: np.float64(0.10890106567610887)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.11275780968655229), 2: np.float64(0.1116610004221975), 5: np.float64(0.08540638733230366), 13: np.float64(0.1376687006397362), 46: np.float64(0.1376687006397362), 71: np.float64(0.1376687006397362), 0: np.float64(0.1376687006397362)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.13181923800469098), 2: np.float64(0.12366758496174672), 5: np.float64(0.09684266120206075), 13: np.float64(0.15673012895787491), 46: np.float64(0.15673012895787491), 71: np.float64(0.15673012895787491), 0: np.float64(0.15673012895787491)}
learned probs (dictionary) for beta: 0.025 

probs= {1: np.float64(0.1343733899026829), 2: np.float64(0.12704046841042332), 5: np.float64(0.09933375086499825), 13: np.float64(0.1589433536022391), 46: np.float64(0.1601030124065515), 71: np.float64(0.1601030124065515), 0: np.float64(0.1601030124065515)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.1729778899603738), 2: np.float64(0.16376220478343845), 5: np.float64(0.131205781157278), 13: np.float64(0.19314378692149264), 46: np.float64(0.19430344572580505), 71: np.float64(0.19430344572580505), 0: np.float64(0.19430344572580505)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.23862897006573852), 2: np.float64(0.22941328488880317), 5: np.float64(0.1920493005250871), 13: np.float64(0.2587948670268574), 46: np.float64(0.25995452583116974), 71: np.float64(0.25995452583116974), 0: np.float64(0.25995452583116974)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.26046686815425), 2: np.float64(0.2501861361198432), 5: np.float64(0.21091014215934992), 13: np.float64(0.2838644692884036), 46: np.float64(0.28502412809271593), 71: np.float64(0.28502412809271593), 0: np.float64(0.28502412809271593)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.27786078711717593), 2: np.float64(0.26684140070653367), 5: np.float64(0.2260352827580295), 13: np.float64(0.3012583882513295), 46: np.float64(0.30241804705564185), 71: np.float64(0.30241804705564185), 0: np.float64(0.30241804705564185)}
learned probs (dictionary) for beta: 0.05 

probs= {1: np.float64(0.2813282464622562), 2: np.float64(0.26968410066190696), 5: np.float64(0.2293336321153298), 13: np.float64(0.30387177972745577), 46: np.float64(0.30526074701101513), 71: np.float64(0.30526074701101513), 0: np.float64(0.30526074701101513)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.3428631230532276), 2: np.float64(0.3253631595156429), 5: np.float64(0.27165502100683014), 13: np.float64(0.32498794864340386), 46: np.float64(0.3263769159269632), 71: np.float64(0.3263769159269632), 0: np.float64(0.3263769159269632)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.4013638373984877), 2: np.float64(0.383863873860903), 5: np.float64(0.3754007349352708), 13: np.float64(0.38348866298866396), 46: np.float64(0.3848776302722233), 71: np.float64(0.3848776302722233), 0: np.float64(0.3848776302722233)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.43707377917155754), 2: np.float64(0.41617556537306194), 5: np.float64(0.4021490267188248), 13: np.float64(0.40023368172146834), 46: np.float64(0.4016226490050277), 71: np.float64(0.4016226490050277), 0: np.float64(0.4016226490050277)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.45032615582654584), 2: np.float64(0.44487499410221143), 5: np.float64(0.4259377147147338), 13: np.float64(0.41348605837645663), 46: np.float64(0.414875025660016), 71: np.float64(0.414875025660016), 0: np.float64(0.414875025660016)}
learned probs (dictionary) for beta: 0.1 

probs= {1: np.float64(0.4558096527822918), 2: np.float64(0.44666009488060054), 5: np.float64(0.43089938794197896), 13: np.float64(0.41665048507990904), 46: np.float64(0.4166601264384051), 71: np.float64(0.4166601264384051), 0: np.float64(0.4166601264384051)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.5631288284909481), 2: np.float64(0.5302403529610799), 5: np.float64(0.4746087494855839), 13: np.float64(0.41899828624672425), 46: np.float64(0.4190079276052203), 71: np.float64(0.4190079276052203), 0: np.float64(0.4190079276052203)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.5942834126820563), 2: np.float64(0.561394937152188), 5: np.float64(0.7424312443389347), 13: np.float64(0.4501528704378325), 46: np.float64(0.45016251179632855), 71: np.float64(0.45016251179632855), 0: np.float64(0.45016251179632855)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.6616513942795111), 2: np.float64(0.6138611739742258), 5: np.float64(0.7759192770825519), 13: np.float64(0.45225980764705503), 46: np.float64(0.4522694490055511), 71: np.float64(0.4522694490055511), 0: np.float64(0.4522694490055511)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.6645954172824812), 2: np.float64(0.6769072477273854), 5: np.float64(0.8169030883145422), 13: np.float64(0.45520383065002507), 46: np.float64(0.45521347200852114), 71: np.float64(0.45521347200852114), 0: np.float64(0.45521347200852114)}
learned probs (dictionary) for beta: 0.25 

probs= {1: np.float64(0.674276706124513), 2: np.float64(0.6771386532599988), 5: np.float64(0.8244428836458569), 13: np.float64(0.45780712434622467), 46: np.float64(0.45544487754113455), 71: np.float64(0.45544487754113455), 0: np.float64(0.45544487754113455)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.8120753048977294), 2: np.float64(0.7607177282813942), 5: np.float64(0.8467684056632474), 13: np.float64(0.45788132539322435), 46: np.float64(0.45551907858813423), 71: np.float64(0.45551907858813423), 0: np.float64(0.45551907858813423)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.8177233866622009), 2: np.float64(0.7663658100458657), 5: np.float64(1.2676299150764183), 13: np.float64(0.4635294071576958), 46: np.float64(0.4611671603526057), 71: np.float64(0.4611671603526057), 0: np.float64(0.4611671603526057)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9048903241046216), 2: np.float64(0.8192352301179469), 5: np.float64(1.2890561704294443), 13: np.float64(0.46360125394081386), 46: np.float64(0.46123900713572374), 71: np.float64(0.46123900713572374), 0: np.float64(0.46123900713572374)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9049992220020516), 2: np.float64(0.9017302679170732), 5: np.float64(1.3247666431431675), 13: np.float64(0.463710151838244), 46: np.float64(0.46134790503315387), 71: np.float64(0.46134790503315387), 0: np.float64(0.46134790503315387)}
learned probs (dictionary) for beta: 0.5 

probs= {1: np.float64(0.9173765189341663), 2: np.float64(0.9017376121331465), 5: np.float64(1.332273853216862), 13: np.float64(0.4645462679681416), 46: np.float64(0.46135524924922716), 71: np.float64(0.46135524924922716), 0: np.float64(0.46135524924922716)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.0764279246743174), 2: np.float64(0.9768681763712341), 5: np.float64(1.3420784463230144), 13: np.float64(0.46454962719704407), 46: np.float64(0.46135860847812965), 71: np.float64(0.46135860847812965), 0: np.float64(0.46135860847812965)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.0771250046320793), 2: np.float64(0.977565256328996), 5: np.float64(1.7926459665764432), 13: np.float64(0.465246707154806), 46: np.float64(0.46205568843589157), 71: np.float64(0.46205568843589157), 0: np.float64(0.46205568843589157)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.1787513267586516), 2: np.float64(1.0255701317796728), 5: np.float64(1.8047485006946753), 13: np.float64(0.4652507742309357), 46: np.float64(0.4620597555120213), 71: np.float64(0.4620597555120213), 0: np.float64(0.4620597555120213)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.1787566021914357), 2: np.float64(1.118059223326669), 5: np.float64(1.830983031983758), 13: np.float64(0.4652560496637199), 46: np.float64(0.4620650309448055), 71: np.float64(0.4620650309448055), 0: np.float64(0.4620650309448055)}
learned probs (dictionary) for beta: 0.75 

probs= {1: np.float64(1.1927035993987958), 2: np.float64(1.1180595475237083), 5: np.float64(1.8375711269756871), 13: np.float64(0.46546966067627416), 46: np.float64(0.46206535514184466), 71: np.float64(0.46206535514184466), 0: np.float64(0.46206535514184466)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.3681636805784323), 2: np.float64(1.1826077041359688), 5: np.float64(1.8415623398752876), 13: np.float64(0.4654697980033998), 46: np.float64(0.46206549246897033), 71: np.float64(0.46206549246897033), 0: np.float64(0.46206549246897033)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.3682312661438583), 2: np.float64(1.1826752897013948), 5: np.float64(2.295906826482731), 13: np.float64(0.46553738356882585), 46: np.float64(0.46213307803439635), 71: np.float64(0.46213307803439635), 0: np.float64(0.46213307803439635)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.4817607799849868), 2: np.float64(1.2244404638097346), 5: np.float64(2.3023612974393646), 13: np.float64(0.46553759384230037), 46: np.float64(0.46213328830787087), 71: np.float64(0.46213328830787087), 0: np.float64(0.46213328830787087)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.4817610471287481), 2: np.float64(1.3246824384344862), 5: np.float64(2.3208679870958058), 13: np.float64(0.4655378609860618), 46: np.float64(0.4621335554516323), 71: np.float64(0.4621335554516323), 0: np.float64(0.4621335554516323)}
learned probs (dictionary) for beta: 1 

probs= {1: np.float64(1.4968938178227231), 2: np.float64(1.3246824514214197), 5: np.float64(2.326435022322081), 13: np.float64(0.4655880031180776), 46: np.float64(0.4621335684385658), 71: np.float64(0.4621335684385658), 0: np.float64(0.4621335684385658)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.685348891567011), 2: np.float64(1.378675734041799), 5: np.float64(2.3279866482557776), 13: np.float64(0.46558800754348667), 46: np.float64(0.4621335728639749), 71: np.float64(0.4621335728639749), 0: np.float64(0.4621335728639749)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.6853537754233874), 2: np.float64(1.3786806178981754), 5: np.float64(2.7827073451175184), 13: np.float64(0.4655928913998632), 46: np.float64(0.4621384567203514), 71: np.float64(0.4621384567203514), 0: np.float64(0.4621384567203514)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.8085133499295019), 2: np.float64(1.413966426773437), 5: np.float64(2.7860119275843247), 13: np.float64(0.4655928999378176), 46: np.float64(0.4621384652583058), 71: np.float64(0.4621384652583058), 0: np.float64(0.4621384652583058)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.808513360832008), 2: np.float64(1.5200578061195584), 5: np.float64(2.7986704937256723), 13: np.float64(0.4655929108403238), 46: np.float64(0.462138476160812), 71: np.float64(0.462138476160812), 0: np.float64(0.462138476160812)}
learned probs (dictionary) for beta: 1.25 

probs= {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
empirical probabilities from test set: {1: 0.22, 2: 0.237, 5: 0.209, 13: 0.179, 46: 0.06, 71: 0.067, 0: 0.028}
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.025 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.05 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.1 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.25 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.5 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  0.75 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  1 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

beta is  1.25 

learned probs for this beta: {1: np.float64(1.8246334824621921), 2: np.float64(1.5200578065342436), 5: np.float64(2.80328898589869), 13: np.float64(0.46560429537838127), 46: np.float64(0.4621384765754972), 71: np.float64(0.4621384765754972), 0: np.float64(0.4621384765754972)}
err dic= {1: np.float64(1.6046334824621922), 2: np.float64(1.2830578065342437), 5: np.float64(2.59428898589869), 13: np.float64(0.2866042953783813), 46: np.float64(0.40213847657549723), 71: np.float64(0.3951384765754972), 0: np.float64(0.4341384765754972)} 

err list= [np.float64(1.6046334824621922), np.float64(1.2830578065342437), np.float64(2.59428898589869), np.float64(0.2866042953783813), np.float64(0.40213847657549723), np.float64(0.3951384765754972), np.float64(0.4341384765754972)]
results for assortment [1, 2, 5, 13, 46, 71] :

err MNL dic= {1: np.float64(0.08462837142268889), 2: np.float64(0.10605497220506482), 5: np.float64(0.07275334568663783), 13: np.float64(0.05433456866378422), 46: np.float64(0.05190035001029443), 71: np.float64(0.03651039736462838), 0: np.float64(0.22936051060325305)} 

err MNL list= [np.float64(0.08462837142268889), np.float64(0.10605497220506482), np.float64(0.07275334568663783), np.float64(0.05433456866378422), np.float64(0.05190035001029443), np.float64(0.03651039736462838), np.float64(0.22936051060325305)]
sampled assortment [2, 9, 6, 78, 95, 94] number: 3
#  Learning probs for MM model, A = [2, 9, 6, 78, 95, 94]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 10: 1, 22: 1, 100: 1} [8, 1, 2, 3, 4, 5, 6, 7, 10, 22, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 13: 0, 14: 0, 100: 0} [3, 5, 6, 7, 9, 11, 12, 13, 14, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 6: 1, 7: 2, 10: 1, 12: 2, 14: 1} [1, 2, 6, 10, 14, 7, 12]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 5: 1, 6: 1, 10: 1, 16: 2, 18: 3, 21: 1, 100: 1} [2, 3, 5, 6, 10, 21, 100, 16, 18]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 5: 2, 7: 2, 10: 2, 11: 5, 13: 3, 14: 4, 15: 4, 18: 6, 23: 6, 24: 7, 29: 9, 38: 7, 72: 12, 100: 0} [3, 100, 1, 5, 7, 10, 13, 14, 15, 11, 18, 23, 24, 38, 29, 72]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.028495719737940035), 9: np.float64(0.037919484588319695), 6: np.float64(0.025906857320461073), 78: np.float64(0.037919484588319695), 95: np.float64(0.037919484588319695), 94: np.float64(0.037919484588319695), 0: np.float64(0.037919484588319695)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10047493279419112), 9: np.float64(0.0841953348417514), 6: np.float64(0.07448494178577689), 78: np.float64(0.10989869764457078), 95: np.float64(0.10989869764457078), 94: np.float64(0.10989869764457078), 0: np.float64(0.10989869764457078)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.11309733279389231), 9: np.float64(0.11155870447515218), 6: np.float64(0.08679569361907187), 78: np.float64(0.13726206727797155), 95: np.float64(0.13726206727797155), 94: np.float64(0.13726206727797155), 0: np.float64(0.13726206727797155)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12511922382565696), 9: np.float64(0.13066778233731347), 6: np.float64(0.09797841327650045), 78: np.float64(0.15637114514013284), 95: np.float64(0.15637114514013284), 94: np.float64(0.15637114514013284), 0: np.float64(0.15637114514013284)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12808350953994263), 9: np.float64(0.13363206805159913), 6: np.float64(0.1009426989907861), 78: np.float64(0.1593354308544185), 95: np.float64(0.1593354308544185), 94: np.float64(0.1593354308544185), 0: np.float64(0.1593354308544185)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.16741555383149676), 9: np.float64(0.16804404017768973), 6: np.float64(0.1335507940687796), 78: np.float64(0.1937474029805091), 95: np.float64(0.1937474029805091), 94: np.float64(0.1937474029805091), 0: np.float64(0.1937474029805091)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.23321432211214038), 9: np.float64(0.22790116314977926), 6: np.float64(0.19944982969347055), 78: np.float64(0.25954617126115276), 95: np.float64(0.25954617126115276), 94: np.float64(0.25954617126115276), 0: np.float64(0.25954617126115276)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2498232196628993), 9: np.float64(0.2537696092278675), 6: np.float64(0.2152487017522703), 78: np.float64(0.285414617339241), 95: np.float64(0.285414617339241), 94: np.float64(0.285414617339241), 0: np.float64(0.285414617339241)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.266533786678649), 9: np.float64(0.2712803831595315), 6: np.float64(0.22973426507820016), 78: np.float64(0.302925391270905), 95: np.float64(0.302925391270905), 94: np.float64(0.302925391270905), 0: np.float64(0.302925391270905)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2694980723929348), 9: np.float64(0.27424466887381727), 6: np.float64(0.2326985507924859), 78: np.float64(0.30588967698519076), 95: np.float64(0.30588967698519076), 94: np.float64(0.30588967698519076), 0: np.float64(0.30588967698519076)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.33566335023915334), 9: np.float64(0.3005848581602647), 6: np.float64(0.2788323265140296), 78: np.float64(0.3322298662716382), 95: np.float64(0.3322298662716382), 94: np.float64(0.3322298662716382), 0: np.float64(0.3322298662716382)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.3868226209603085), 9: np.float64(0.3907551325677018), 6: np.float64(0.38761569850081856), 78: np.float64(0.3833891369927933), 95: np.float64(0.3833891369927933), 94: np.float64(0.3833891369927933), 0: np.float64(0.3833891369927933)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.413913839285015), 9: np.float64(0.41278425929468526), 6: np.float64(0.41212884654119447), 78: np.float64(0.4054182637197768), 95: np.float64(0.4054182637197768), 94: np.float64(0.4054182637197768), 0: np.float64(0.4054182637197768)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.4429131312566293), 9: np.float64(0.4263343931763944), 6: np.float64(0.43412888516103476), 78: np.float64(0.4189683976014859), 95: np.float64(0.4189683976014859), 94: np.float64(0.4189683976014859), 0: np.float64(0.4189683976014859)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.445877416970915), 9: np.float64(0.4292986788906801), 6: np.float64(0.43709317087532046), 78: np.float64(0.4219326833157716), 95: np.float64(0.4219326833157716), 94: np.float64(0.4219326833157716), 0: np.float64(0.4219326833157716)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5892794821577629), 9: np.float64(0.4365838218520818), 6: np.float64(0.5012653908814654), 78: np.float64(0.4292178262771733), 95: np.float64(0.4292178262771733), 94: np.float64(0.4292178262771733), 0: np.float64(0.4292178262771733)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6036994219812641), 9: np.float64(0.5869909883995696), 6: np.float64(0.7335085252164717), 78: np.float64(0.4436377661006745), 95: np.float64(0.4436377661006745), 94: np.float64(0.4436377661006745), 0: np.float64(0.4436377661006745)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.6702317128965838), 9: np.float64(0.5956714501636287), 6: np.float64(0.7853239254808572), 78: np.float64(0.45231822786473347), 95: np.float64(0.45231822786473347), 94: np.float64(0.45231822786473347), 0: np.float64(0.45231822786473347)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.7365123623522016), 9: np.float64(0.5990073760082117), 6: np.float64(0.8211136468023237), 78: np.float64(0.4556541537093166), 95: np.float64(0.4556541537093166), 94: np.float64(0.4556541537093166), 0: np.float64(0.4556541537093166)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.7394766480664874), 9: np.float64(0.6019716617224975), 6: np.float64(0.8240779325166094), 78: np.float64(0.4586184394236023), 95: np.float64(0.4586184394236023), 94: np.float64(0.4586184394236023), 0: np.float64(0.4586184394236023)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.9384948665829066), 9: np.float64(0.6023465042850961), 6: np.float64(0.8671855011871982), 78: np.float64(0.4589932819862009), 95: np.float64(0.4589932819862009), 94: np.float64(0.4589932819862009), 0: np.float64(0.4589932819862009)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.939254161210451), 9: np.float64(0.7384991739224229), 6: np.float64(1.1819863584121488), 78: np.float64(0.45975257661374525), 95: np.float64(0.45975257661374525), 94: np.float64(0.45975257661374525), 0: np.float64(0.45975257661374525)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.0377895578321368), 9: np.float64(0.7391891467744863), 6: np.float64(1.2417510975301458), 78: np.float64(0.4604425494658087), 95: np.float64(0.4604425494658087), 94: np.float64(0.4604425494658087), 0: np.float64(0.4604425494658087)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.128089415753851), 9: np.float64(0.7393284317256464), 6: np.float64(1.2695048148526313), 78: np.float64(0.46058183441696876), 95: np.float64(0.46058183441696876), 94: np.float64(0.46058183441696876), 0: np.float64(0.46058183441696876)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(1.1310537014681368), 9: np.float64(0.7422927174399321), 6: np.float64(1.272469100566917), 78: np.float64(0.46354612013125446), 95: np.float64(0.46354612013125446), 94: np.float64(0.46354612013125446), 0: np.float64(0.46354612013125446)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.3532213655410108), 9: np.float64(0.7423118906221234), 6: np.float64(1.2942055705830866), 78: np.float64(0.46356529331344587), 95: np.float64(0.46356529331344587), 94: np.float64(0.46356529331344587), 0: np.float64(0.46356529331344587)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.3532659572621084), 9: np.float64(0.8427430323775672), 6: np.float64(1.648301470222155), 78: np.float64(0.4636098850345436), 95: np.float64(0.4636098850345436), 94: np.float64(0.4636098850345436), 0: np.float64(0.4636098850345436)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.4629494018133755), 9: np.float64(0.8427941853482254), 6: np.float64(1.7001122608175974), 78: np.float64(0.46366103800520175), 95: np.float64(0.46366103800520175), 94: np.float64(0.46366103800520175), 0: np.float64(0.46366103800520175)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.5645883685850146), 9: np.float64(0.84280111670888), 6: np.float64(1.717188637242685), 78: np.float64(0.4636679693658564), 95: np.float64(0.4636679693658564), 94: np.float64(0.4636679693658564), 0: np.float64(0.4636679693658564)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.5675526542993004), 9: np.float64(0.8457654024231658), 6: np.float64(1.7201529229569708), 78: np.float64(0.4666322550801421), 95: np.float64(0.4666322550801421), 94: np.float64(0.4666322550801421), 0: np.float64(0.4666322550801421)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.801614615936173), 9: np.float64(0.8457664483294298), 6: np.float64(1.730085731788778), 78: np.float64(0.4666333009864062), 95: np.float64(0.4666333009864062), 94: np.float64(0.4666333009864062), 0: np.float64(0.4666333009864062)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.80161750645666), 9: np.float64(0.9166353470197323), 6: np.float64(2.113952380496041), 78: np.float64(0.4666361915068931), 95: np.float64(0.4666361915068931), 94: np.float64(0.4666361915068931), 0: np.float64(0.4666361915068931)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.9198494360835128), 9: np.float64(0.9166399418544121), 6: np.float64(2.157447476695789), 78: np.float64(0.46664078634157297), 95: np.float64(0.46664078634157297), 94: np.float64(0.46664078634157297), 0: np.float64(0.46664078634157297)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(2.028794201260815), 9: np.float64(0.9166403062546143), 6: np.float64(2.167250889517475), 78: np.float64(0.46664115074177526), 95: np.float64(0.46664115074177526), 94: np.float64(0.46664115074177526), 0: np.float64(0.46664115074177526)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(2.0317584869751006), 9: np.float64(0.9196045919689001), 6: np.float64(2.1702151752317604), 78: np.float64(0.46960543645606095), 95: np.float64(0.46960543645606095), 94: np.float64(0.46960543645606095), 0: np.float64(0.46960543645606095)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.2714971399250787), 9: np.float64(0.9196046383446302), 6: np.float64(2.174476290403131), 78: np.float64(0.46960548283179115), 95: np.float64(0.46960548283179115), 94: np.float64(0.46960548283179115), 0: np.float64(0.46960548283179115)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.2714972941523883), 9: np.float64(0.9680801917186895), 6: np.float64(2.5807499658925246), 78: np.float64(0.46960563705910063), 95: np.float64(0.46960563705910063), 94: np.float64(0.46960563705910063), 0: np.float64(0.46960563705910063)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.3972241488678447), 9: np.float64(0.9680805513815738), 6: np.float64(2.616771312862647), 78: np.float64(0.4696059967219849), 95: np.float64(0.4696059967219849), 94: np.float64(0.4696059967219849), 0: np.float64(0.4696059967219849)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.510616338987527), 9: np.float64(0.9680805667458001), 6: np.float64(2.6221290459218327), 78: np.float64(0.46960601208621117), 95: np.float64(0.46960601208621117), 94: np.float64(0.46960601208621117), 0: np.float64(0.46960601208621117)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(2.5135806247018126), 9: np.float64(0.9710448524600859), 6: np.float64(2.6250933316361182), 78: np.float64(0.47257029780049686), 95: np.float64(0.47257029780049686), 94: np.float64(0.47257029780049686), 0: np.float64(0.47257029780049686)}
#  Learning probs for MM model, A = [2, 9, 6, 78, 95, 94]
#cluster  1 with weight 0.244
Learned cluster center of cluster 1:  {1: 1, 3: 1, 7: 1, 8: 0, 22: 1, 100: 1} [8, 1, 3, 7, 22, 100]
#cluster  3 with weight 0.45475
Learned cluster center of cluster 3:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 15: 0, 100: 0} [3, 4, 5, 6, 7, 9, 12, 15, 100]
#cluster  5 with weight 0.16175
Learned cluster center of cluster 5:  {1: 0, 2: 1, 4: 1, 6: 1, 10: 1, 14: 1, 19: 1} [1, 2, 4, 6, 10, 14, 19]
#cluster  4 with weight 0.11875
Learned cluster center of cluster 4:  {2: 0, 3: 1, 5: 1, 6: 1, 10: 1, 100: 1} [2, 3, 5, 6, 10, 100]
#cluster  2 with weight 0.02075
Learned cluster center of cluster 2:  {1: 2, 3: 0, 4: 5, 5: 2, 6: 3, 7: 2, 9: 8, 11: 6, 12: 5, 13: 3, 14: 4, 18: 9, 23: 6, 24: 8, 33: 10, 55: 12, 100: 0} [3, 100, 1, 5, 7, 6, 13, 14, 4, 12, 11, 23, 9, 24, 18, 33, 55]
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.03485714285714288), 9: np.float64(0.03485714285714288), 6: np.float64(0.03485714285714288), 78: np.float64(0.03485714285714288), 95: np.float64(0.03485714285714288), 94: np.float64(0.03485714285714288), 0: np.float64(0.03485714285714288)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.10895494720514774), 9: np.float64(0.07596086432344414), 6: np.float64(0.07801439965081597), 78: np.float64(0.10895494720514774), 95: np.float64(0.10895494720514774), 94: np.float64(0.10895494720514774), 0: np.float64(0.10895494720514774)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12158917018825294), 9: np.float64(0.10337810458079583), 6: np.float64(0.09004397538095249), 78: np.float64(0.13637218746249943), 95: np.float64(0.13637218746249943), 94: np.float64(0.13637218746249943), 0: np.float64(0.13637218746249943)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.12977111892246115), 9: np.float64(0.12397113943125243), 6: np.float64(0.09764685239446134), 78: np.float64(0.15696522231295604), 95: np.float64(0.15696522231295604), 94: np.float64(0.15696522231295604), 0: np.float64(0.15696522231295604)}
learned probs (dictionary) for beta: 0.025 

probs= {2: np.float64(0.13281085002735782), 9: np.float64(0.1270108705361491), 6: np.float64(0.1001584657650814), 78: np.float64(0.1600049534178527), 95: np.float64(0.1600049534178527), 94: np.float64(0.1600049534178527), 0: np.float64(0.1600049534178527)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.16766799288450066), 9: np.float64(0.16186801339329193), 6: np.float64(0.13501560862222423), 78: np.float64(0.19486209627499554), 95: np.float64(0.19486209627499554), 94: np.float64(0.19486209627499554), 0: np.float64(0.19486209627499554)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2370144051030622), 9: np.float64(0.21326473201897492), 6: np.float64(0.19163682890373146), 78: np.float64(0.2642085084935571), 95: np.float64(0.2642085084935571), 94: np.float64(0.2642085084935571), 0: np.float64(0.2642085084935571)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.25366242348430196), 9: np.float64(0.23926493577221486), 6: np.float64(0.20673779175629187), 78: np.float64(0.29020871224679706), 95: np.float64(0.29020871224679706), 94: np.float64(0.29020871224679706), 0: np.float64(0.29020871224679706)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.2644696871313221), 9: np.float64(0.2589855213539657), 6: np.float64(0.2160776002005176), 78: np.float64(0.3099292978285479), 95: np.float64(0.3099292978285479), 94: np.float64(0.3099292978285479), 0: np.float64(0.3099292978285479)}
learned probs (dictionary) for beta: 0.05 

probs= {2: np.float64(0.26736168124420423), 9: np.float64(0.26187751546684784), 6: np.float64(0.21947563552322472), 78: np.float64(0.31282129194143005), 95: np.float64(0.31282129194143005), 94: np.float64(0.31282129194143005), 0: np.float64(0.31282129194143005)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.30221882410134704), 9: np.float64(0.29673465832399065), 6: np.float64(0.2543327783803675), 78: np.float64(0.34767843479857286), 95: np.float64(0.34767843479857286), 94: np.float64(0.34767843479857286), 0: np.float64(0.34767843479857286)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.36025993339229656), 9: np.float64(0.3712059870538219), 6: np.float64(0.34440590319578895), 78: np.float64(0.4057195440895224), 95: np.float64(0.4057195440895224), 94: np.float64(0.4057195440895224), 0: np.float64(0.4057195440895224)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.38754537790892973), 9: np.float64(0.39359586301785754), 6: np.float64(0.36692107885897735), 78: np.float64(0.428109420053558), 95: np.float64(0.428109420053558), 94: np.float64(0.428109420053558), 0: np.float64(0.428109420053558)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.40556680382101157), 9: np.float64(0.4110369804392073), 6: np.float64(0.3804440658401466), 78: np.float64(0.44555053747490775), 95: np.float64(0.44555053747490775), 94: np.float64(0.44555053747490775), 0: np.float64(0.44555053747490775)}
learned probs (dictionary) for beta: 0.1 

probs= {2: np.float64(0.40809790505693644), 9: np.float64(0.41356808167513215), 6: np.float64(0.38600745842459744), 78: np.float64(0.4480816387108326), 95: np.float64(0.4480816387108326), 94: np.float64(0.4480816387108326), 0: np.float64(0.4480816387108326)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.4429550479140793), 9: np.float64(0.448425224532275), 6: np.float64(0.4208646012817403), 78: np.float64(0.4829387815679755), 95: np.float64(0.4829387815679755), 94: np.float64(0.4829387815679755), 0: np.float64(0.4829387815679755)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.4676520326488804), 9: np.float64(0.5776776606498077), 6: np.float64(0.6228772414902021), 78: np.float64(0.5076357663027765), 95: np.float64(0.5076357663027765), 94: np.float64(0.5076357663027765), 0: np.float64(0.5076357663027765)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5369652194398273), 9: np.float64(0.587323755932283), 6: np.float64(0.6670835782868787), 78: np.float64(0.5172818615852518), 95: np.float64(0.5172818615852518), 94: np.float64(0.5172818615852518), 0: np.float64(0.5172818615852518)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5878888821181919), 9: np.float64(0.5956356256879812), 6: np.float64(0.693350566830023), 78: np.float64(0.52559373134095), 95: np.float64(0.52559373134095), 94: np.float64(0.52559373134095), 0: np.float64(0.52559373134095)}
learned probs (dictionary) for beta: 0.25 

probs= {2: np.float64(0.5892502716170591), 9: np.float64(0.5969970151868484), 6: np.float64(0.7059322298368195), 78: np.float64(0.5269551208398172), 95: np.float64(0.5269551208398172), 94: np.float64(0.5269551208398172), 0: np.float64(0.5269551208398172)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.624107414474202), 9: np.float64(0.6318541580439914), 6: np.float64(0.7407893726939623), 78: np.float64(0.56181226369696), 95: np.float64(0.56181226369696), 94: np.float64(0.56181226369696), 0: np.float64(0.56181226369696)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.6267817471933852), 9: np.float64(0.7646088160179411), 6: np.float64(1.0494130511240967), 78: np.float64(0.5644865964161432), 95: np.float64(0.5644865964161432), 94: np.float64(0.5644865964161432), 0: np.float64(0.5644865964161432)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.7365944109958831), 9: np.float64(0.7655487173182127), 6: np.float64(1.0966508808202406), 78: np.float64(0.5654264977164148), 95: np.float64(0.5654264977164148), 94: np.float64(0.5654264977164148), 0: np.float64(0.5654264977164148)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.8242506483540277), 9: np.float64(0.7664828725771644), 6: np.float64(1.1230738671673375), 78: np.float64(0.5663606529753665), 95: np.float64(0.5663606529753665), 94: np.float64(0.5663606529753665), 0: np.float64(0.5663606529753665)}
learned probs (dictionary) for beta: 0.5 

probs= {2: np.float64(0.8245134227155366), 9: np.float64(0.7667456469386733), 6: np.float64(1.1422472209982837), 78: np.float64(0.5666234273368754), 95: np.float64(0.5666234273368754), 94: np.float64(0.5666234273368754), 0: np.float64(0.5666234273368754)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8593705655726795), 9: np.float64(0.8016027897958162), 6: np.float64(1.1771043638554266), 78: np.float64(0.6014805701940183), 95: np.float64(0.6014805701940183), 94: np.float64(0.6014805701940183), 0: np.float64(0.6014805701940183)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.8595875452281215), 9: np.float64(0.9017932593459475), 6: np.float64(1.530578996028086), 78: np.float64(0.6016975498494603), 95: np.float64(0.6016975498494603), 94: np.float64(0.6016975498494603), 0: np.float64(0.6016975498494603)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(0.9853297407853671), 9: np.float64(0.9018663216172736), 6: np.float64(1.5662214891142097), 78: np.float64(0.6017706121207865), 95: np.float64(0.6017706121207865), 94: np.float64(0.6017706121207865), 0: np.float64(0.6017706121207865)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.0867171169336212), 9: np.float64(0.9019403051092263), 6: np.float64(1.5832141955061922), 78: np.float64(0.6018445956127392), 95: np.float64(0.6018445956127392), 94: np.float64(0.6018445956127392), 0: np.float64(0.6018445956127392)}
learned probs (dictionary) for beta: 0.75 

probs= {2: np.float64(1.086750609030106), 9: np.float64(0.901973797205711), 6: np.float64(1.6037632429272837), 78: np.float64(0.6018780877092239), 95: np.float64(0.6018780877092239), 94: np.float64(0.6018780877092239), 0: np.float64(0.6018780877092239)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.121607751887249), 9: np.float64(0.9368309400628538), 6: np.float64(1.6386203857844266), 78: np.float64(0.6367352305663667), 95: np.float64(0.6367352305663667), 94: np.float64(0.6367352305663667), 0: np.float64(0.6367352305663667)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.1216282864130938), 9: np.float64(1.0076810700218608), 6: np.float64(2.0224175831961957), 78: np.float64(0.6367557650922115), 95: np.float64(0.6367557650922115), 94: np.float64(0.6367557650922115), 0: np.float64(0.6367557650922115)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.2581433484453974), 9: np.float64(1.0076877989917228), 6: np.float64(2.047618876314582), 78: np.float64(0.6367624940620735), 95: np.float64(0.6367624940620735), 94: np.float64(0.6367624940620735), 0: np.float64(0.6367624940620735)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.367062560751682), 9: np.float64(1.0076943278257646), 6: np.float64(2.057417019838089), 78: np.float64(0.6367690228961153), 95: np.float64(0.6367690228961153), 94: np.float64(0.6367690228961153), 0: np.float64(0.6367690228961153)}
learned probs (dictionary) for beta: 1 

probs= {2: np.float64(1.36706594708294), 9: np.float64(1.0076977141570227), 6: np.float64(2.07814670185054), 78: np.float64(0.6367724092273734), 95: np.float64(0.6367724092273734), 94: np.float64(0.6367724092273734), 0: np.float64(0.6367724092273734)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.401923089940083), 9: np.float64(1.0425548570141656), 6: np.float64(2.113003844707683), 78: np.float64(0.6716295520845162), 95: np.float64(0.6716295520845162), 94: np.float64(0.6716295520845162), 0: np.float64(0.6716295520845162)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.4019248471765076), 9: np.float64(1.0910290949785895), 6: np.float64(2.5192708205611356), 78: np.float64(0.671631309320941), 95: np.float64(0.671631309320941), 94: np.float64(0.671631309320941), 0: np.float64(0.671631309320941)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.546430209948263), 9: np.float64(1.091029651396184), 6: np.float64(2.5365126757014087), 78: np.float64(0.6716318657385353), 95: np.float64(0.6716318657385353), 94: np.float64(0.6716318657385353), 0: np.float64(0.6716318657385353)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.6598201064782272), 9: np.float64(1.0910301899958874), 6: np.float64(2.5418700861729264), 78: np.float64(0.6716324043382389), 95: np.float64(0.6716324043382389), 94: np.float64(0.6716324043382389), 0: np.float64(0.6716324043382389)}
learned probs (dictionary) for beta: 1.25 

probs= {2: np.float64(1.6598203648697776), 9: np.float64(1.0910304483874378), 6: np.float64(2.5626185358236238), 78: np.float64(0.6716326627297893), 95: np.float64(0.6716326627297893), 94: np.float64(0.6716326627297893), 0: np.float64(0.6716326627297893)}
empirical probabilities from test set: {2: 0.272, 9: 0.253, 6: 0.254, 78: 0.062, 95: 0.062, 94: 0.056, 0: 0.041}
results for assortment [2, 9, 6, 78, 95, 94] :

beta is  0.025 

learned probs for this beta: {2: np.float64(1.6598203648697776), 9: np.float64(1.0910304483874378), 6: np.float64(2.5626185358236238), 78: np.float64(0.6716326627297893), 95: np.float64(0.6716326627297893), 94: np.float64(0.6716326627297893), 0: np.float64(0.6716326627297893)}
err dic= {2: np.float64(1.3878203648697776), 9: np.float64(0.8380304483874378), 6: np.float64(2.3086185358236238), 78: np.float64(0.6096326627297892), 95: np.float64(0.6096326627297892), 94: np.float64(0.6156326627297892), 0: np.float64(0.6306326627297892)} 

err list= [np.float64(1.3878203648697776), np.float64(0.8380304483874378), np.float64(2.3086185358236238), np.float64(0.6096326627297892), np.float64(0.6096326627297892), np.float64(0.6156326627297892), np.float64(0.6306326627297892)]
results for assortment [2, 9, 6, 78, 95, 94] :

beta is  0.05 

learned probs for this beta: {2: np.float64(1.6598203648697776), 9: np.float64(1.0910304483874378), 6: np.float64(2.5626185358236238), 78: np.float64(0.6716326627297893), 95: np.float64(0.6716326627297893), 94: np.float64(0.6716326627297893), 0: np.float64(0.6716326627297893)}
err dic= {2: np.float64(1.3878203648697776), 9: np.float64(0.8380304483874378), 6: np.float64(2.3086185358236238), 78: np.float64(0.6096326627297892), 95: np.float64(0.6096326627297892), 94: np.float64(0.6156326627297892), 0: np.float64(0.6306326627297892)} 

err list= [np.float64(1.3878203648697776), np.float64(0.8380304483874378), np.float64(2.3086185358236238), np.float64(0.6096326627297892), np.float64(0.6096326627297892), np.float64(0.6156326627297892), np.float64(0.6306326627297892)]
results for assortment [2, 9, 6, 78, 95, 94] :

beta is  0.1 

learned probs for this beta: {2: np.float64(1.6598203648697776), 9: np.float64(1.0910304483874378), 6: np.float64(2.5626185358236238), 78: np.float64(0.6716326627297893), 95: np.float64(0.6716326627297893), 94: np.float64(0.6716326627297893), 0: np.float64(0.6716326627297893)}
err dic= {2: np.float64(1.3878203648697776), 9: np.float64(0.8380304483874378), 6: np.float64(2.3086185358236238), 78: np.float64(0.6096326627297892), 95: np.float64(0.6096326627297892), 94: np.float64(0.6156326627297892), 0: np.float64(0.6306326627297892)} 

err list= [np.float64(1.3878203648697776), np.float64(0.8380304483874378), np.float64(2.3086185358236238), np.float64(0.6096326627297892), np.float64(0.6096326627297892), np.float64(0.6156326627297892), np.float64(0.6306326627297892)]
results for assortment [2, 9, 6, 78, 95, 94] :

beta is  0.25 

learned probs for this beta: {2: np.float64(1.6598203648697776), 9: np.float64(1.0910304483874378), 6: np.float64(2.5626185358236238), 78: np.float64(0.6716326627297893), 95: np.float64(0.6716326627297893), 94: np.float64(0.6716326627297893), 0: np.float64(0.6716326627297893)}
err dic= {2: np.float64(1.3878203648697776), 9: np.float64(0.8380304483874378), 6: np.float64(2.3086185358236238), 78: np.float64(0.6096326627297892), 95: np.float64(0.6096326627297892), 94: np.float64(0.6156326627297892), 0: np.float64(0.6306326627297892)} 

err list= [np.float64(1.3878203648697776), np.float64(0.8380304483874378), np.float64(2.3086185358236238), np.float64(0.6096326627297892), np.float64(0.6096326627297892), np.float64(0.6156326627297892), np.float64(0.6306326627297892)]
results for assortment [2, 9, 6, 78, 95, 94] :

beta is  0.5 

learned probs for this beta: 