p= 0.1 num clusters= 4
linkage completed in  10.842540979385376
silhouette_score of the clusters -0.01000867958890752
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 27: 1, 100: 1} [8, 1, 2, 3, 7, 27, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0, 16: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 11, 12, 15, 16, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 16: 6, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 16]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 11: 1, 12: 1, 100: 1} [8, 1, 2, 3, 4, 7, 11, 12, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 21: 1} [2, 4, 6, 7, 10, 21]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 4, 8: 4, 10: 1, 13: 2, 20: 4, 100: 0} [6, 100, 10, 1, 3, 13, 7, 8, 20, 5, 4]
empirical probabilities from test set: {2: 0.266, 3: 0.242, 4: 0.243, 59: 0.068, 40: 0.077, 84: 0.052, 0: 0.052}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.1315565973392029), 3: np.float64(0.11785418353445301), 4: np.float64(0.09799653876038592), 59: np.float64(0.1631481700914896), 40: np.float64(0.1631481700914896), 84: np.float64(0.1631481700914896), 0: np.float64(0.1631481700914896)}
err dic= {2: np.float64(0.1344434026607971), 3: np.float64(0.12414581646554698), 4: np.float64(0.14500346123961408), 59: np.float64(0.0951481700914896), 40: np.float64(0.0861481700914896), 84: np.float64(0.11114817009148961), 0: np.float64(0.11114817009148961)} 

err list= [np.float64(0.1344434026607971), np.float64(0.12414581646554698), np.float64(0.14500346123961408), np.float64(0.0951481700914896), np.float64(0.0861481700914896), np.float64(0.11114817009148961), np.float64(0.11114817009148961)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.1346997687852814), 3: np.float64(0.15281067268608067), 4: np.float64(0.13527379198329034), 59: np.float64(0.14430394163633706), 40: np.float64(0.14430394163633706), 84: np.float64(0.14430394163633706), 0: np.float64(0.14430394163633706)}
err dic= {2: np.float64(0.13130023121471862), 3: np.float64(0.08918932731391932), 4: np.float64(0.10772620801670965), 59: np.float64(0.07630394163633705), 40: np.float64(0.06730394163633706), 84: np.float64(0.09230394163633707), 0: np.float64(0.09230394163633707)} 

err list= [np.float64(0.13130023121471862), np.float64(0.08918932731391932), np.float64(0.10772620801670965), np.float64(0.07630394163633705), np.float64(0.06730394163633706), np.float64(0.09230394163633707), np.float64(0.09230394163633707)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.14354749984016776), 3: np.float64(0.23580348507318577), 4: np.float64(0.2204626818020805), 59: np.float64(0.10004658332114158), 40: np.float64(0.10004658332114158), 84: np.float64(0.10004658332114158), 0: np.float64(0.10004658332114158)}
err dic= {2: np.float64(0.12245250015983225), 3: np.float64(0.006196514926814223), 4: np.float64(0.022537318197919487), 59: np.float64(0.032046583321141575), 40: np.float64(0.02304658332114158), 84: np.float64(0.04804658332114158), 0: np.float64(0.04804658332114158)} 

err list= [np.float64(0.12245250015983225), np.float64(0.006196514926814223), np.float64(0.022537318197919487), np.float64(0.032046583321141575), np.float64(0.02304658332114158), np.float64(0.04804658332114158), np.float64(0.04804658332114158)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.18010798139593273), 3: np.float64(0.3994907728034157), 4: np.float64(0.3581402273805107), 59: np.float64(0.01556525460503478), 40: np.float64(0.01556525460503478), 84: np.float64(0.01556525460503478), 0: np.float64(0.01556525460503478)}
err dic= {2: np.float64(0.08589201860406728), 3: np.float64(0.15749077280341572), 4: np.float64(0.11514022738051072), 59: np.float64(0.052434745394965225), 40: np.float64(0.06143474539496522), 84: np.float64(0.03643474539496522), 0: np.float64(0.03643474539496522)} 

err list= [np.float64(0.08589201860406728), np.float64(0.15749077280341572), np.float64(0.11514022738051072), np.float64(0.052434745394965225), np.float64(0.06143474539496522), np.float64(0.03643474539496522), np.float64(0.03643474539496522)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.2157143477451051), 3: np.float64(0.46113253996484194), 4: np.float64(0.3214906106047389), 59: np.float64(0.00041562542132868633), 40: np.float64(0.00041562542132868633), 84: np.float64(0.00041562542132868633), 0: np.float64(0.00041562542132868633)}
err dic= {2: np.float64(0.050285652254894925), 3: np.float64(0.21913253996484194), 4: np.float64(0.07849061060473889), 59: np.float64(0.06758437457867132), 40: np.float64(0.07658437457867132), 84: np.float64(0.051584374578671315), 0: np.float64(0.051584374578671315)} 

err list= [np.float64(0.050285652254894925), np.float64(0.21913253996484194), np.float64(0.07849061060473889), np.float64(0.06758437457867132), np.float64(0.07658437457867132), np.float64(0.051584374578671315), np.float64(0.051584374578671315)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.243428439497115), 3: np.float64(0.49119005525577714), 4: np.float64(0.26534461848669655), 59: np.float64(9.221690102828973e-06), 40: np.float64(9.221690102828973e-06), 84: np.float64(9.221690102828973e-06), 0: np.float64(9.221690102828973e-06)}
err dic= {2: np.float64(0.022571560502885002), 3: np.float64(0.24919005525577714), 4: np.float64(0.022344618486696555), 59: np.float64(0.06799077830989718), 40: np.float64(0.07699077830989717), 84: np.float64(0.05199077830989717), 0: np.float64(0.05199077830989717)} 

err list= [np.float64(0.022571560502885002), np.float64(0.24919005525577714), np.float64(0.022344618486696555), np.float64(0.06799077830989718), np.float64(0.07699077830989717), np.float64(0.05199077830989717), np.float64(0.05199077830989717)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.2683996010090201), 3: np.float64(0.5143332475083322), 4: np.float64(0.21726650150194143), 59: np.float64(1.624951765778141e-07), 40: np.float64(1.624951765778141e-07), 84: np.float64(1.624951765778141e-07), 0: np.float64(1.624951765778141e-07)}
err dic= {2: np.float64(0.0023996010090200914), 3: np.float64(0.2723332475083322), 4: np.float64(0.02573349849805856), 59: np.float64(0.06799983750482343), 40: np.float64(0.07699983750482342), 84: np.float64(0.05199983750482342), 0: np.float64(0.05199983750482342)} 

err list= [np.float64(0.0023996010090200914), np.float64(0.2723332475083322), np.float64(0.02573349849805856), np.float64(0.06799983750482343), np.float64(0.07699983750482342), np.float64(0.05199983750482342), np.float64(0.05199983750482342)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.2902706982864875), 3: np.float64(0.5331361458665506), 4: np.float64(0.17659314421262814), 59: np.float64(2.908583473571698e-09), 40: np.float64(2.908583473571698e-09), 84: np.float64(2.908583473571698e-09), 0: np.float64(2.908583473571698e-09)}
err dic= {2: np.float64(0.02427069828648748), 3: np.float64(0.29113614586655057), 4: np.float64(0.06640685578737185), 59: np.float64(0.06799999709141653), 40: np.float64(0.07699999709141653), 84: np.float64(0.051999997091416526), 0: np.float64(0.051999997091416526)} 

err list= [np.float64(0.02427069828648748), np.float64(0.29113614586655057), np.float64(0.06640685578737185), np.float64(0.06799999709141653), np.float64(0.07699999709141653), np.float64(0.051999997091416526), np.float64(0.051999997091416526)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: np.float64(0.13148223350253807), 3: np.float64(0.10631895093062604), 4: np.float64(0.1084293570219966), 59: np.float64(0.04044966159052453), 40: np.float64(0.039063874788494074), 84: np.float64(0.05433460236886634), 0: np.float64(0.21238240270727582)} 

err MNL list= [np.float64(0.13148223350253807), np.float64(0.10631895093062604), np.float64(0.1084293570219966), np.float64(0.04044966159052453), np.float64(0.039063874788494074), np.float64(0.05433460236886634), np.float64(0.21238240270727582)]
sampled assortment [6, 1, 5, 30, 95, 91] number: 1
#  Learning probs for MM model, A = [6, 1, 5, 30, 95, 91]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 3, 4, 5, 7, 14, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 1, 3, 6, 10, 11, 17, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 12: 6, 13: 2, 15: 3, 20: 5, 31: 9, 34: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 20, 12, 31, 34]
#  Learning probs for MM model, A = [6, 1, 5, 30, 95, 91]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 100: 1} [8, 1, 3, 4, 7, 10, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 14: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 16: 1, 21: 1, 100: 1} [2, 1, 4, 6, 7, 10, 11, 16, 21, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 7, 11]
empirical probabilities from test set: {6: 0.252, 1: 0.264, 5: 0.229, 30: 0.106, 95: 0.052, 91: 0.063, 0: 0.034}
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.11291417389269896), 1: np.float64(0.10549334761374586), 5: np.float64(0.12074820293101546), 30: np.float64(0.16521106889063492), 95: np.float64(0.16521106889063492), 91: np.float64(0.16521106889063492), 0: np.float64(0.16521106889063492)}
err dic= {6: np.float64(0.13908582610730102), 1: np.float64(0.15850665238625417), 5: np.float64(0.10825179706898455), 30: np.float64(0.05921106889063492), 95: np.float64(0.11321106889063492), 91: np.float64(0.10221106889063492), 0: np.float64(0.1312110688906349)} 

err list= [np.float64(0.13908582610730102), np.float64(0.15850665238625417), np.float64(0.10825179706898455), np.float64(0.05921106889063492), np.float64(0.11321106889063492), np.float64(0.10221106889063492), np.float64(0.1312110688906349)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.13944224535654995), 1: np.float64(0.15239846602671986), 5: np.float64(0.13682503418540198), 30: np.float64(0.14283356360783264), 95: np.float64(0.14283356360783264), 91: np.float64(0.14283356360783264), 0: np.float64(0.14283356360783264)}
err dic= {6: np.float64(0.11255775464345005), 1: np.float64(0.11160153397328015), 5: np.float64(0.09217496581459803), 30: np.float64(0.036833563607832645), 95: np.float64(0.09083356360783265), 91: np.float64(0.07983356360783264), 0: np.float64(0.10883356360783264)} 

err list= [np.float64(0.11255775464345005), np.float64(0.11160153397328015), np.float64(0.09217496581459803), np.float64(0.036833563607832645), np.float64(0.09083356360783265), np.float64(0.07983356360783264), np.float64(0.10883356360783264)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.19087290919421984), 1: np.float64(0.2670162499795963), 5: np.float64(0.16616210998429332), 30: np.float64(0.09398718271047271), 95: np.float64(0.09398718271047271), 91: np.float64(0.09398718271047271), 0: np.float64(0.09398718271047271)}
err dic= {6: np.float64(0.06112709080578016), 1: np.float64(0.003016249979596264), 5: np.float64(0.0628378900157067), 30: np.float64(0.012012817289527286), 95: np.float64(0.04198718271047271), 91: np.float64(0.03098718271047271), 0: np.float64(0.05998718271047271)} 

err list= [np.float64(0.06112709080578016), np.float64(0.003016249979596264), np.float64(0.0628378900157067), np.float64(0.012012817289527286), np.float64(0.04198718271047271), np.float64(0.03098718271047271), np.float64(0.05998718271047271)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.22165106867248088), 1: np.float64(0.5365520385146855), 5: np.float64(0.17077812279106339), 30: np.float64(0.017754692505442315), 95: np.float64(0.017754692505442315), 91: np.float64(0.017754692505442315), 0: np.float64(0.017754692505442315)}
err dic= {6: np.float64(0.03034893132751912), 1: np.float64(0.27255203851468546), 5: np.float64(0.05822187720893662), 30: np.float64(0.08824530749455768), 95: np.float64(0.03424530749455768), 91: np.float64(0.045245307494557685), 0: np.float64(0.016245307494557687)} 

err list= [np.float64(0.03034893132751912), np.float64(0.27255203851468546), np.float64(0.05822187720893662), np.float64(0.08824530749455768), np.float64(0.03424530749455768), np.float64(0.045245307494557685), np.float64(0.016245307494557687)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.15884556186046933), 1: np.float64(0.7197739978861578), 5: np.float64(0.11618335862082338), 30: np.float64(0.0012992704081376978), 95: np.float64(0.0012992704081376978), 91: np.float64(0.0012992704081376978), 0: np.float64(0.0012992704081376978)}
err dic= {6: np.float64(0.09315443813953067), 1: np.float64(0.4557739978861578), 5: np.float64(0.11281664137917663), 30: np.float64(0.1047007295918623), 95: np.float64(0.0507007295918623), 91: np.float64(0.061700729591862305), 0: np.float64(0.03270072959186231)} 

err list= [np.float64(0.09315443813953067), np.float64(0.4557739978861578), np.float64(0.11281664137917663), np.float64(0.1047007295918623), np.float64(0.0507007295918623), np.float64(0.061700729591862305), np.float64(0.03270072959186231)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.11557322814771567), 1: np.float64(0.8101762904878429), 5: np.float64(0.07406612240306908), 30: np.float64(4.608974034313486e-05), 95: np.float64(4.608974034313486e-05), 91: np.float64(4.608974034313486e-05), 0: np.float64(4.608974034313486e-05)}
err dic= {6: np.float64(0.13642677185228433), 1: np.float64(0.5461762904878429), 5: np.float64(0.15493387759693095), 30: np.float64(0.10595391025965686), 95: np.float64(0.051953910259656864), 91: np.float64(0.06295391025965687), 0: np.float64(0.03395391025965687)} 

err list= [np.float64(0.13642677185228433), np.float64(0.5461762904878429), np.float64(0.15493387759693095), np.float64(0.10595391025965686), np.float64(0.051953910259656864), np.float64(0.06295391025965687), np.float64(0.03395391025965687)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  1 

learned probs for this beta: {6: np.float64(0.08945193688882029), 1: np.float64(0.866623334472597), 5: np.float64(0.04392045351857635), 30: np.float64(1.068780001626772e-06), 95: np.float64(1.068780001626772e-06), 91: np.float64(1.068780001626772e-06), 0: np.float64(1.068780001626772e-06)}
err dic= {6: np.float64(0.1625480631111797), 1: np.float64(0.602623334472597), 5: np.float64(0.18507954648142366), 30: np.float64(0.10599893121999837), 95: np.float64(0.05199893121999837), 91: np.float64(0.06299893121999837), 0: np.float64(0.03399893121999838)} 

err list= [np.float64(0.1625480631111797), np.float64(0.602623334472597), np.float64(0.18507954648142366), np.float64(0.10599893121999837), np.float64(0.05199893121999837), np.float64(0.06299893121999837), np.float64(0.03399893121999838)]
results for assortment [6, 1, 5, 30, 95, 91] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.07447180126097505), 1: np.float64(0.9010308448140992), 5: np.float64(0.02449725847605441), 30: np.float64(2.386221788254765e-08), 95: np.float64(2.386221788254765e-08), 91: np.float64(2.386221788254765e-08), 0: np.float64(2.386221788254765e-08)}
err dic= {6: np.float64(0.17752819873902495), 1: np.float64(0.6370308448140992), 5: np.float64(0.2045027415239456), 30: np.float64(0.10599997613778211), 95: np.float64(0.051999976137782115), 91: np.float64(0.06299997613778212), 0: np.float64(0.03399997613778212)} 

err list= [np.float64(0.17752819873902495), np.float64(0.6370308448140992), np.float64(0.2045027415239456), np.float64(0.10599997613778211), np.float64(0.051999976137782115), np.float64(0.06299997613778212), np.float64(0.03399997613778212)]
results for assortment [6, 1, 5, 30, 95, 91] :

err MNL dic= {6: np.float64(0.11679763693838419), 1: np.float64(0.12770938487847855), 5: np.float64(0.09182841892522156), 30: np.float64(0.017179768875991083), 95: np.float64(0.054389594237446236), 91: np.float64(0.0396584443177696), 0: np.float64(0.22510763331087733)} 

err MNL list= [np.float64(0.11679763693838419), np.float64(0.12770938487847855), np.float64(0.09182841892522156), np.float64(0.017179768875991083), np.float64(0.054389594237446236), np.float64(0.0396584443177696), np.float64(0.22510763331087733)]
sampled assortment [2, 7, 4, 87, 76, 91] number: 2
#  Learning probs for MM model, A = [2, 7, 4, 87, 76, 91]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 14: 1} [8, 1, 2, 3, 4, 7, 14]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 14: 0, 100: 0} [1, 4, 5, 6, 7, 9, 12, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 14: 5, 15: 3, 16: 8, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 7, 11, 14, 16]
#  Learning probs for MM model, A = [2, 7, 4, 87, 76, 91]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 8: 0, 13: 1, 17: 1, 100: 1} [8, 1, 3, 4, 6, 7, 13, 17, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 15: 1, 16: 1} [2, 1, 3, 6, 7, 10, 11, 14, 15, 16]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 5, 10: 2, 13: 2, 15: 4, 17: 7, 20: 4, 26: 10, 100: 0} [6, 100, 1, 3, 10, 13, 5, 15, 20, 7, 8, 17, 26]
empirical probabilities from test set: {2: 0.275, 7: 0.232, 4: 0.258, 87: 0.045, 76: 0.076, 91: 0.06, 0: 0.054}
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.1518694837019198), 7: np.float64(0.10149625352839067), 4: np.float64(0.11583667650504798), 87: np.float64(0.15769939656616067), 76: np.float64(0.15769939656616067), 91: np.float64(0.15769939656616067), 0: np.float64(0.15769939656616067)}
err dic= {2: np.float64(0.12313051629808022), 7: np.float64(0.13050374647160934), 4: np.float64(0.14216332349495203), 87: np.float64(0.11269939656616067), 76: np.float64(0.08169939656616067), 91: np.float64(0.09769939656616067), 0: np.float64(0.10369939656616067)} 

err list= [np.float64(0.12313051629808022), np.float64(0.13050374647160934), np.float64(0.14216332349495203), np.float64(0.11269939656616067), np.float64(0.08169939656616067), np.float64(0.09769939656616067), np.float64(0.10369939656616067)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.15015686630905356), 7: np.float64(0.13593593529837333), 4: np.float64(0.14602668273585612), 87: np.float64(0.14197012891417982), 76: np.float64(0.14197012891417982), 91: np.float64(0.14197012891417982), 0: np.float64(0.14197012891417982)}
err dic= {2: np.float64(0.12484313369094646), 7: np.float64(0.09606406470162668), 4: np.float64(0.11197331726414389), 87: np.float64(0.09697012891417982), 76: np.float64(0.06597012891417982), 91: np.float64(0.08197012891417982), 0: np.float64(0.08797012891417982)} 

err list= [np.float64(0.12484313369094646), np.float64(0.09606406470162668), np.float64(0.11197331726414389), np.float64(0.09697012891417982), np.float64(0.06597012891417982), np.float64(0.08197012891417982), np.float64(0.08797012891417982)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.14728122400670046), 7: np.float64(0.21039799769362744), 4: np.float64(0.22282210642560635), 87: np.float64(0.10487466796851667), 76: np.float64(0.10487466796851667), 91: np.float64(0.10487466796851667), 0: np.float64(0.10487466796851667)}
err dic= {2: np.float64(0.12771877599329956), 7: np.float64(0.021602002306372575), 4: np.float64(0.03517789357439366), 87: np.float64(0.059874667968516676), 76: np.float64(0.028874667968516676), 91: np.float64(0.04487466796851668), 0: np.float64(0.050874667968516675)} 

err list= [np.float64(0.12771877599329956), np.float64(0.021602002306372575), np.float64(0.03517789357439366), np.float64(0.059874667968516676), np.float64(0.028874667968516676), np.float64(0.04487466796851668), np.float64(0.050874667968516675)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.1372574736522587), 7: np.float64(0.32581085387093806), 4: np.float64(0.43673450408931885), 87: np.float64(0.025049292096870828), 76: np.float64(0.025049292096870828), 91: np.float64(0.025049292096870828), 0: np.float64(0.025049292096870828)}
err dic= {2: np.float64(0.1377425263477413), 7: np.float64(0.09381085387093804), 4: np.float64(0.17873450408931885), 87: np.float64(0.01995070790312917), 76: np.float64(0.05095070790312917), 91: np.float64(0.034950707903129166), 0: np.float64(0.02895070790312917)} 

err list= [np.float64(0.1377425263477413), np.float64(0.09381085387093804), np.float64(0.17873450408931885), np.float64(0.01995070790312917), np.float64(0.05095070790312917), np.float64(0.034950707903129166), np.float64(0.02895070790312917)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.14667138344756378), 7: np.float64(0.27256397910933644), 4: np.float64(0.5731080394885835), 87: np.float64(0.0019141494886293882), 76: np.float64(0.0019141494886293882), 91: np.float64(0.0019141494886293882), 0: np.float64(0.0019141494886293882)}
err dic= {2: np.float64(0.12832861655243624), 7: np.float64(0.04056397910933643), 4: np.float64(0.31510803948858346), 87: np.float64(0.04308585051137061), 76: np.float64(0.07408585051137061), 91: np.float64(0.05808585051137061), 0: np.float64(0.05208585051137061)} 

err list= [np.float64(0.12832861655243624), np.float64(0.04056397910933643), np.float64(0.31510803948858346), np.float64(0.04308585051137061), np.float64(0.07408585051137061), np.float64(0.05808585051137061), np.float64(0.05208585051137061)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.16090319189269586), 7: np.float64(0.1962501451314233), 4: np.float64(0.6422760102256635), 87: np.float64(0.00014266318755433042), 76: np.float64(0.00014266318755433042), 91: np.float64(0.00014266318755433042), 0: np.float64(0.00014266318755433042)}
err dic= {2: np.float64(0.11409680810730416), 7: np.float64(0.03574985486857671), 4: np.float64(0.3842760102256635), 87: np.float64(0.04485733681244567), 76: np.float64(0.07585733681244566), 91: np.float64(0.05985733681244567), 0: np.float64(0.05385733681244567)} 

err list= [np.float64(0.11409680810730416), np.float64(0.03574985486857671), np.float64(0.3842760102256635), np.float64(0.04485733681244567), np.float64(0.07585733681244566), np.float64(0.05985733681244567), np.float64(0.05385733681244567)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  1 

learned probs for this beta: {2: np.float64(0.1693220976015317), 7: np.float64(0.1404825697102599), 4: np.float64(0.6901647656874693), 87: np.float64(7.641750184840616e-06), 76: np.float64(7.641750184840616e-06), 91: np.float64(7.641750184840616e-06), 0: np.float64(7.641750184840616e-06)}
err dic= {2: np.float64(0.10567790239846833), 7: np.float64(0.0915174302897401), 4: np.float64(0.4321647656874693), 87: np.float64(0.04499235824981516), 76: np.float64(0.07599235824981515), 91: np.float64(0.05999235824981516), 0: np.float64(0.05399235824981516)} 

err list= [np.float64(0.10567790239846833), np.float64(0.0915174302897401), np.float64(0.4321647656874693), np.float64(0.04499235824981516), np.float64(0.07599235824981515), np.float64(0.05999235824981516), np.float64(0.05399235824981516)]
results for assortment [2, 7, 4, 87, 76, 91] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.1734180630979637), 7: np.float64(0.10515577717544422), 4: np.float64(0.7214245486604147), 87: np.float64(4.0276654431810334e-07), 76: np.float64(4.0276654431810334e-07), 91: np.float64(4.0276654431810334e-07), 0: np.float64(4.0276654431810334e-07)}
err dic= {2: np.float64(0.10158193690203632), 7: np.float64(0.1268442228245558), 4: np.float64(0.4634245486604147), 87: np.float64(0.04499959723345568), 76: np.float64(0.07599959723345567), 91: np.float64(0.05999959723345568), 0: np.float64(0.05399959723345568)} 

err list= [np.float64(0.10158193690203632), np.float64(0.1268442228245558), np.float64(0.4634245486604147), np.float64(0.04499959723345568), np.float64(0.07599959723345567), np.float64(0.05999959723345568), np.float64(0.05399959723345568)]
results for assortment [2, 7, 4, 87, 76, 91] :

err MNL dic= {2: np.float64(0.13950788240306777), 7: np.float64(0.09528291435875588), 4: np.float64(0.12245462292288026), 87: np.float64(0.06450149126544524), 76: np.float64(0.03493949723050703), 91: np.float64(0.04550703025138475), 0: np.float64(0.21229740093736688)} 

err MNL list= [np.float64(0.13950788240306777), np.float64(0.09528291435875588), np.float64(0.12245462292288026), np.float64(0.06450149126544524), np.float64(0.03493949723050703), np.float64(0.04550703025138475), np.float64(0.21229740093736688)]
sampled assortment [4, 6, 3, 86, 46, 37] number: 3
#  Learning probs for MM model, A = [4, 6, 3, 86, 46, 37]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 11, 13, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 5: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 5, 6, 10, 11, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 9: 8, 10: 2, 11: 6, 13: 2, 15: 3, 16: 6, 17: 5, 19: 5, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 7, 17, 19, 20, 11, 16, 9]
#  Learning probs for MM model, A = [4, 6, 3, 86, 46, 37]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 15: 1, 100: 1} [8, 1, 3, 5, 7, 15, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 100: 0} [1, 3, 4, 5, 7, 9, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 11: 1, 14: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 10, 11, 14, 17, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 4, 13: 3, 15: 3, 17: 5, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 7, 8, 11, 20, 5, 17]
empirical probabilities from test set: {4: 0.232, 6: 0.255, 3: 0.253, 86: 0.039, 46: 0.079, 37: 0.113, 0: 0.029}
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.11207291887153695), 6: np.float64(0.1490751264899132), 3: np.float64(0.0989362782378327), 86: np.float64(0.1599789191001796), 46: np.float64(0.1599789191001796), 37: np.float64(0.1599789191001796), 0: np.float64(0.1599789191001796)}
err dic= {4: np.float64(0.11992708112846306), 6: np.float64(0.10592487351008681), 3: np.float64(0.15406372176216732), 86: np.float64(0.1209789191001796), 46: np.float64(0.08097891910017961), 37: np.float64(0.04697891910017961), 0: np.float64(0.1309789191001796)} 

err list= [np.float64(0.11992708112846306), np.float64(0.10592487351008681), np.float64(0.15406372176216732), np.float64(0.1209789191001796), np.float64(0.08097891910017961), np.float64(0.04697891910017961), np.float64(0.1309789191001796)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.13755971430467465), 6: np.float64(0.1489042495767167), 3: np.float64(0.14063850066109218), 86: np.float64(0.1432243838643796), 46: np.float64(0.1432243838643796), 37: np.float64(0.1432243838643796), 0: np.float64(0.1432243838643796)}
err dic= {4: np.float64(0.09444028569532537), 6: np.float64(0.10609575042328331), 3: np.float64(0.11236149933890782), 86: np.float64(0.1042243838643796), 46: np.float64(0.0642243838643796), 37: np.float64(0.030224383864379603), 0: np.float64(0.11422438386437961)} 

err list= [np.float64(0.09444028569532537), np.float64(0.10609575042328331), np.float64(0.11236149933890782), np.float64(0.1042243838643796), np.float64(0.0642243838643796), np.float64(0.030224383864379603), np.float64(0.11422438386437961)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.1963874830663897), 6: np.float64(0.1429805603025376), 3: np.float64(0.24435996033750254), 86: np.float64(0.10406799907339268), 46: np.float64(0.10406799907339268), 37: np.float64(0.10406799907339268), 0: np.float64(0.10406799907339268)}
err dic= {4: np.float64(0.03561251693361031), 6: np.float64(0.11201943969746239), 3: np.float64(0.008640039662497462), 86: np.float64(0.06506799907339267), 46: np.float64(0.025067999073392674), 37: np.float64(0.008932000926607328), 0: np.float64(0.07506799907339268)} 

err list= [np.float64(0.03561251693361031), np.float64(0.11201943969746239), np.float64(0.008640039662497462), np.float64(0.06506799907339267), np.float64(0.025067999073392674), np.float64(0.008932000926607328), np.float64(0.07506799907339268)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.29290064277913946), 6: np.float64(0.1013995003866131), 3: np.float64(0.5055896702058077), 86: np.float64(0.025027546657109993), 46: np.float64(0.025027546657109993), 37: np.float64(0.025027546657109993), 0: np.float64(0.025027546657109993)}
err dic= {4: np.float64(0.06090064277913945), 6: np.float64(0.1536004996133869), 3: np.float64(0.2525896702058077), 86: np.float64(0.013972453342890007), 46: np.float64(0.05397245334289001), 37: np.float64(0.08797245334289001), 0: np.float64(0.003972453342890009)} 

err list= [np.float64(0.06090064277913945), np.float64(0.1536004996133869), np.float64(0.2525896702058077), np.float64(0.013972453342890007), np.float64(0.05397245334289001), np.float64(0.08797245334289001), np.float64(0.003972453342890009)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.2667613745888579), 6: np.float64(0.07656988984454563), 3: np.float64(0.6482923588707113), 86: np.float64(0.002094094173971396), 46: np.float64(0.002094094173971396), 37: np.float64(0.002094094173971396), 0: np.float64(0.002094094173971396)}
err dic= {4: np.float64(0.03476137458885789), 6: np.float64(0.17843011015545437), 3: np.float64(0.39529235887071135), 86: np.float64(0.0369059058260286), 46: np.float64(0.0769059058260286), 37: np.float64(0.1109059058260286), 0: np.float64(0.026905905826028607)} 

err list= [np.float64(0.03476137458885789), np.float64(0.17843011015545437), np.float64(0.39529235887071135), np.float64(0.0369059058260286), np.float64(0.0769059058260286), np.float64(0.1109059058260286), np.float64(0.026905905826028607)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.22875105922161368), 6: np.float64(0.06997972656714135), 3: np.float64(0.7008931914021853), 86: np.float64(9.400570226493593e-05), 46: np.float64(9.400570226493593e-05), 37: np.float64(9.400570226493593e-05), 0: np.float64(9.400570226493593e-05)}
err dic= {4: np.float64(0.0032489407783863333), 6: np.float64(0.18502027343285865), 3: np.float64(0.4478931914021853), 86: np.float64(0.038905994297735065), 46: np.float64(0.07890599429773507), 37: np.float64(0.11290599429773507), 0: np.float64(0.028905994297735067)} 

err list= [np.float64(0.0032489407783863333), np.float64(0.18502027343285865), np.float64(0.4478931914021853), np.float64(0.038905994297735065), np.float64(0.07890599429773507), np.float64(0.11290599429773507), np.float64(0.028905994297735067)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  1 

learned probs for this beta: {4: np.float64(0.19366986178183787), 6: np.float64(0.06589377629438378), 3: np.float64(0.7404252206413563), 86: np.float64(2.785320605539019e-06), 46: np.float64(2.785320605539019e-06), 37: np.float64(2.785320605539019e-06), 0: np.float64(2.785320605539019e-06)}
err dic= {4: np.float64(0.03833013821816214), 6: np.float64(0.18910622370561622), 3: np.float64(0.4874252206413563), 86: np.float64(0.03899721467939446), 46: np.float64(0.07899721467939447), 37: np.float64(0.11299721467939447), 0: np.float64(0.02899721467939446)} 

err list= [np.float64(0.03833013821816214), np.float64(0.18910622370561622), np.float64(0.4874252206413563), np.float64(0.03899721467939446), np.float64(0.07899721467939447), np.float64(0.11299721467939447), np.float64(0.02899721467939446)]
results for assortment [4, 6, 3, 86, 46, 37] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.16154985693682325), 6: np.float64(0.06262723847309577), 3: np.float64(0.7758225859981535), 86: np.float64(7.964798186543423e-08), 46: np.float64(7.964798186543423e-08), 37: np.float64(7.964798186543423e-08), 0: np.float64(7.964798186543423e-08)}
err dic= {4: np.float64(0.07045014306317676), 6: np.float64(0.19237276152690425), 3: np.float64(0.5228225859981535), 86: np.float64(0.03899992035201814), 46: np.float64(0.07899992035201814), 37: np.float64(0.11299992035201814), 0: np.float64(0.028999920352018135)} 

err list= [np.float64(0.07045014306317676), np.float64(0.19237276152690425), np.float64(0.5228225859981535), np.float64(0.03899992035201814), np.float64(0.07899992035201814), np.float64(0.11299992035201814), np.float64(0.028999920352018135)]
results for assortment [4, 6, 3, 86, 46, 37] :

err MNL dic= {4: np.float64(0.09867714390486668), 6: np.float64(0.11832442768086332), 3: np.float64(0.11857703389386559), 86: np.float64(0.06472465818010373), 46: np.float64(0.03488757923411387), 37: np.float64(0.0030354130651160244), 0: np.float64(0.23293095500026192)} 

err MNL list= [np.float64(0.09867714390486668), np.float64(0.11832442768086332), np.float64(0.11857703389386559), np.float64(0.06472465818010373), np.float64(0.03488757923411387), np.float64(0.0030354130651160244), np.float64(0.23293095500026192)]
sampled assortment [5, 7, 1, 41, 13, 35] number: 4
#  Learning probs for MM model, A = [5, 7, 1, 41, 13, 35]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 100: 1} [2, 3, 6, 10, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 17: 6, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 5, 7, 20, 17]
#  Learning probs for MM model, A = [5, 7, 1, 41, 13, 35]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1} [8, 1, 3, 4, 5, 7, 13]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 15: 0, 100: 0} [1, 4, 5, 6, 7, 9, 11, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 9: 1, 10: 1, 15: 1, 100: 1} [2, 1, 4, 6, 9, 10, 15, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 19: 6, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 5, 11, 19]
empirical probabilities from test set: {5: 0.21, 7: 0.174, 1: 0.233, 41: 0.092, 13: 0.18, 35: 0.086, 0: 0.025}
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.10589262018853415), 7: np.float64(0.10304693248609327), 1: np.float64(0.10174032152147133), 41: np.float64(0.18146425898683216), 13: np.float64(0.14492734884340516), 35: np.float64(0.18146425898683216), 0: np.float64(0.18146425898683216)}
err dic= {5: np.float64(0.10410737981146584), 7: np.float64(0.07095306751390672), 1: np.float64(0.13125967847852868), 41: np.float64(0.08946425898683216), 13: np.float64(0.03507265115659483), 35: np.float64(0.09546425898683217), 0: np.float64(0.15646425898683217)} 

err list= [np.float64(0.10410737981146584), np.float64(0.07095306751390672), np.float64(0.13125967847852868), np.float64(0.08946425898683216), np.float64(0.03507265115659483), np.float64(0.09546425898683217), np.float64(0.15646425898683217)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.13188363716987014), 7: np.float64(0.12430774748106296), 1: np.float64(0.14575450357352387), 41: np.float64(0.15513858565815428), 13: np.float64(0.13263835480108058), 35: np.float64(0.15513858565815428), 0: np.float64(0.15513858565815428)}
err dic= {5: np.float64(0.07811636283012985), 7: np.float64(0.049692252518937025), 1: np.float64(0.08724549642647614), 41: np.float64(0.06313858565815428), 13: np.float64(0.047361645198919416), 35: np.float64(0.06913858565815428), 0: np.float64(0.13013858565815428)} 

err list= [np.float64(0.07811636283012985), np.float64(0.049692252518937025), np.float64(0.08724549642647614), np.float64(0.06313858565815428), np.float64(0.047361645198919416), np.float64(0.06913858565815428), np.float64(0.13013858565815428)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.18418786077472893), 7: np.float64(0.1618099899505621), 1: np.float64(0.2528077108214576), 41: np.float64(0.09903512261012393), 13: np.float64(0.10408907062287925), 35: np.float64(0.09903512261012393), 0: np.float64(0.09903512261012393)}
err dic= {5: np.float64(0.025812139225271064), 7: np.float64(0.0121900100494379), 1: np.float64(0.019807710821457575), 41: np.float64(0.007035122610123928), 13: np.float64(0.07591092937712074), 35: np.float64(0.013035122610123934), 0: np.float64(0.07403512261012393)} 

err list= [np.float64(0.025812139225271064), np.float64(0.0121900100494379), np.float64(0.019807710821457575), np.float64(0.007035122610123928), np.float64(0.07591092937712074), np.float64(0.013035122610123934), np.float64(0.07403512261012393)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.23251599438719103), 7: np.float64(0.1639366023704341), 1: np.float64(0.5051060750052464), 41: np.float64(0.015205729003474503), 13: np.float64(0.05282414122670388), 35: np.float64(0.015205729003474503), 0: np.float64(0.015205729003474503)}
err dic= {5: np.float64(0.02251599438719104), 7: np.float64(0.010063397629565901), 1: np.float64(0.2721060750052464), 41: np.float64(0.0767942709965255), 13: np.float64(0.12717585877329612), 35: np.float64(0.0707942709965255), 0: np.float64(0.009794270996525498)} 

err list= [np.float64(0.02251599438719104), np.float64(0.010063397629565901), np.float64(0.2721060750052464), np.float64(0.0767942709965255), np.float64(0.12717585877329612), np.float64(0.0707942709965255), np.float64(0.009794270996525498)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.19098882065957398), 7: np.float64(0.09028904409560205), 1: np.float64(0.6908429549220808), 41: np.float64(0.0008529699858052034), 13: np.float64(0.025320270365328256), 35: np.float64(0.0008529699858052034), 0: np.float64(0.0008529699858052034)}
err dic= {5: np.float64(0.01901117934042601), 7: np.float64(0.08371095590439794), 1: np.float64(0.4578429549220808), 41: np.float64(0.0911470300141948), 13: np.float64(0.15467972963467175), 35: np.float64(0.0851470300141948), 0: np.float64(0.024147030014194798)} 

err list= [np.float64(0.01901117934042601), np.float64(0.08371095590439794), np.float64(0.4578429549220808), np.float64(0.0911470300141948), np.float64(0.15467972963467175), np.float64(0.0851470300141948), np.float64(0.024147030014194798)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.14326328964361593), 7: np.float64(0.04447624221495785), 1: np.float64(0.799285685024798), 41: np.float64(2.5928131092984426e-05), 13: np.float64(0.012896998723349214), 35: np.float64(2.5928131092984426e-05), 0: np.float64(2.5928131092984426e-05)}
err dic= {5: np.float64(0.06673671035638407), 7: np.float64(0.12952375778504213), 1: np.float64(0.566285685024798), 41: np.float64(0.09197407186890702), 13: np.float64(0.1671030012766508), 35: np.float64(0.08597407186890701), 0: np.float64(0.024974071868907016)} 

err list= [np.float64(0.06673671035638407), np.float64(0.12952375778504213), np.float64(0.566285685024798), np.float64(0.09197407186890702), np.float64(0.1671030012766508), np.float64(0.08597407186890701), np.float64(0.024974071868907016)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  1 

learned probs for this beta: {5: np.float64(0.10087060200560197), 7: np.float64(0.02016242311772782), 1: np.float64(0.8725617972380617), 41: np.float64(5.151364641656295e-07), 13: np.float64(0.006403632229216133), 35: np.float64(5.151364641656295e-07), 0: np.float64(5.151364641656295e-07)}
err dic= {5: np.float64(0.10912939799439803), 7: np.float64(0.15383757688227218), 1: np.float64(0.6395617972380617), 41: np.float64(0.09199948486353583), 13: np.float64(0.17359636777078385), 35: np.float64(0.08599948486353583), 0: np.float64(0.024999484863535835)} 

err list= [np.float64(0.10912939799439803), np.float64(0.15383757688227218), np.float64(0.6395617972380617), np.float64(0.09199948486353583), np.float64(0.17359636777078385), np.float64(0.08599948486353583), np.float64(0.024999484863535835)]
results for assortment [5, 7, 1, 41, 13, 35] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.06792333169262083), 7: np.float64(0.008592080221500214), 1: np.float64(0.9203640193734868), 41: np.float64(9.908275800286544e-09), 13: np.float64(0.0031205389875646984), 35: np.float64(9.908275800286544e-09), 0: np.float64(9.908275800286544e-09)}
err dic= {5: np.float64(0.14207666830737917), 7: np.float64(0.16540791977849978), 1: np.float64(0.6873640193734868), 41: np.float64(0.0919999900917242), 13: np.float64(0.1768794610124353), 35: np.float64(0.0859999900917242), 0: np.float64(0.0249999900917242)} 

err list= [np.float64(0.14207666830737917), np.float64(0.16540791977849978), np.float64(0.6873640193734868), np.float64(0.0919999900917242), np.float64(0.1768794610124353), np.float64(0.0859999900917242), np.float64(0.0249999900917242)]
results for assortment [5, 7, 1, 41, 13, 35] :

err MNL dic= {5: np.float64(0.07577079107505069), 7: np.float64(0.04382758620689653), 1: np.float64(0.09963286004056796), 41: np.float64(0.01869979716024342), 13: np.float64(0.057180527383367125), 35: np.float64(0.02916227180527385), 0: np.float64(0.22854969574036513)} 

err MNL list= [np.float64(0.07577079107505069), np.float64(0.04382758620689653), np.float64(0.09963286004056796), np.float64(0.01869979716024342), np.float64(0.057180527383367125), np.float64(0.02916227180527385), np.float64(0.22854969574036513)]
sampled assortment [8, 4, 3, 17, 54, 22] number: 5
#  Learning probs for MM model, A = [8, 4, 3, 17, 54, 22]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 1, 2, 3, 4, 7, 12, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 9: 0, 15: 0, 100: 0} [1, 3, 4, 5, 6, 9, 15, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 6, 10, 11, 14, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 3, 10: 2, 11: 4, 13: 2, 14: 5, 15: 3, 19: 5, 100: 0} [6, 100, 1, 3, 10, 13, 8, 15, 5, 11, 7, 14, 19]
#  Learning probs for MM model, A = [8, 4, 3, 17, 54, 22]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 3, 4, 7, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 1, 7, 10, 11, 14, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 4: 6, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 13: 2, 15: 4, 17: 6, 20: 4, 25: 7, 100: 0} [6, 100, 1, 3, 10, 13, 5, 7, 8, 15, 20, 4, 17, 25]
empirical probabilities from test set: {8: 0.232, 4: 0.201, 3: 0.217, 17: 0.128, 54: 0.057, 22: 0.128, 0: 0.037}
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.025 

learned probs for this beta: {8: np.float64(0.13292021411051683), 4: np.float64(0.10234414205601773), 3: np.float64(0.10537482868548559), 17: np.float64(0.16484020378699446), 54: np.float64(0.16484020378699446), 22: np.float64(0.16484020378699446), 0: np.float64(0.16484020378699446)}
err dic= {8: np.float64(0.09907978588948319), 4: np.float64(0.09865585794398228), 3: np.float64(0.11162517131451441), 17: np.float64(0.03684020378699446), 54: np.float64(0.10784020378699447), 22: np.float64(0.03684020378699446), 0: np.float64(0.12784020378699446)} 

err list= [np.float64(0.09907978588948319), np.float64(0.09865585794398228), np.float64(0.11162517131451441), np.float64(0.03684020378699446), np.float64(0.10784020378699447), np.float64(0.03684020378699446), np.float64(0.12784020378699446)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.12966445310448693), 4: np.float64(0.1317143970182809), 3: np.float64(0.13994996009809074), 17: np.float64(0.1496677974447852), 54: np.float64(0.1496677974447852), 22: np.float64(0.1496677974447852), 0: np.float64(0.1496677974447852)}
err dic= {8: np.float64(0.10233554689551308), 4: np.float64(0.06928560298171912), 3: np.float64(0.07705003990190926), 17: np.float64(0.021667797444785197), 54: np.float64(0.0926677974447852), 22: np.float64(0.021667797444785197), 0: np.float64(0.1126677974447852)} 

err list= [np.float64(0.10233554689551308), np.float64(0.06928560298171912), np.float64(0.07705003990190926), np.float64(0.021667797444785197), np.float64(0.0926677974447852), np.float64(0.021667797444785197), np.float64(0.1126677974447852)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.12264171319739502), 4: np.float64(0.19952948601752746), 3: np.float64(0.2255898860049958), 17: np.float64(0.11305972869502076), 54: np.float64(0.11305972869502076), 22: np.float64(0.11305972869502076), 0: np.float64(0.11305972869502076)}
err dic= {8: np.float64(0.109358286802605), 4: np.float64(0.0014705139824725544), 3: np.float64(0.0085898860049958), 17: np.float64(0.014940271304979241), 54: np.float64(0.05605972869502076), 22: np.float64(0.014940271304979241), 0: np.float64(0.07605972869502076)} 

err list= [np.float64(0.109358286802605), np.float64(0.0014705139824725544), np.float64(0.0085898860049958), np.float64(0.014940271304979241), np.float64(0.05605972869502076), np.float64(0.014940271304979241), np.float64(0.07605972869502076)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.12502731466346123), 4: np.float64(0.308955295372488), 3: np.float64(0.41447694556037723), 17: np.float64(0.03788511110091812), 54: np.float64(0.03788511110091812), 22: np.float64(0.03788511110091812), 0: np.float64(0.03788511110091812)}
err dic= {8: np.float64(0.10697268533653878), 4: np.float64(0.10795529537248799), 3: np.float64(0.19747694556037723), 17: np.float64(0.09011488889908188), 54: np.float64(0.019114888899081882), 22: np.float64(0.09011488889908188), 0: np.float64(0.000885111100918122)} 

err list= [np.float64(0.10697268533653878), np.float64(0.10795529537248799), np.float64(0.19747694556037723), np.float64(0.09011488889908188), np.float64(0.019114888899081882), np.float64(0.09011488889908188), np.float64(0.000885111100918122)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.1380519190881854), 4: np.float64(0.27679918909965484), 3: np.float64(0.4830824075834286), 17: np.float64(0.025516621057182946), 54: np.float64(0.025516621057182946), 22: np.float64(0.025516621057182946), 0: np.float64(0.025516621057182946)}
err dic= {8: np.float64(0.09394808091181461), 4: np.float64(0.07579918909965483), 3: np.float64(0.2660824075834286), 17: np.float64(0.10248337894281706), 54: np.float64(0.03148337894281705), 22: np.float64(0.10248337894281706), 0: np.float64(0.011483378942817053)} 

err list= [np.float64(0.09394808091181461), np.float64(0.07579918909965483), np.float64(0.2660824075834286), np.float64(0.10248337894281706), np.float64(0.03148337894281705), np.float64(0.10248337894281706), np.float64(0.011483378942817053)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.15160620688076315), 4: np.float64(0.2326091118420478), 3: np.float64(0.5148953976340698), 17: np.float64(0.02522232091077977), 54: np.float64(0.02522232091077977), 22: np.float64(0.02522232091077977), 0: np.float64(0.02522232091077977)}
err dic= {8: np.float64(0.08039379311923686), 4: np.float64(0.03160911184204779), 3: np.float64(0.2978953976340698), 17: np.float64(0.10277767908922023), 54: np.float64(0.03177767908922023), 22: np.float64(0.10277767908922023), 0: np.float64(0.011777679089220228)} 

err list= [np.float64(0.08039379311923686), np.float64(0.03160911184204779), np.float64(0.2978953976340698), np.float64(0.10277767908922023), np.float64(0.03177767908922023), np.float64(0.10277767908922023), np.float64(0.011777679089220228)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.16561189025532375), 4: np.float64(0.19460415112141646), 3: np.float64(0.538926131274728), 17: np.float64(0.025214456837132925), 54: np.float64(0.025214456837132925), 22: np.float64(0.025214456837132925), 0: np.float64(0.025214456837132925)}
err dic= {8: np.float64(0.06638810974467627), 4: np.float64(0.006395848878583549), 3: np.float64(0.321926131274728), 17: np.float64(0.10278554316286707), 54: np.float64(0.03178554316286708), 22: np.float64(0.10278554316286707), 0: np.float64(0.011785543162867073)} 

err list= [np.float64(0.06638810974467627), np.float64(0.006395848878583549), np.float64(0.321926131274728), np.float64(0.10278554316286707), np.float64(0.03178554316286708), np.float64(0.10278554316286707), np.float64(0.011785543162867073)]
results for assortment [8, 4, 3, 17, 54, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.17863698889021598), 4: np.float64(0.1623890452131367), 3: np.float64(0.5581168073128395), 17: np.float64(0.02521428964595193), 54: np.float64(0.02521428964595193), 22: np.float64(0.02521428964595193), 0: np.float64(0.02521428964595193)}
err dic= {8: np.float64(0.05336301110978403), 4: np.float64(0.0386109547868633), 3: np.float64(0.34111680731283955), 17: np.float64(0.10278571035404807), 54: np.float64(0.03178571035404807), 22: np.float64(0.10278571035404807), 0: np.float64(0.011785710354048066)} 

err list= [np.float64(0.05336301110978403), np.float64(0.0386109547868633), np.float64(0.34111680731283955), np.float64(0.10278571035404807), np.float64(0.03178571035404807), np.float64(0.10278571035404807), np.float64(0.011785710354048066)]
results for assortment [8, 4, 3, 17, 54, 22] :

err MNL dic= {8: np.float64(0.10399135980250979), 4: np.float64(0.07011129397243368), 3: np.float64(0.08503126928615512), 17: np.float64(0.004260028800658303), 54: np.float64(0.04915099773709113), 22: np.float64(0.005905780703558947), 0: np.float64(0.22014873482822464)} 

err MNL list= [np.float64(0.10399135980250979), np.float64(0.07011129397243368), np.float64(0.08503126928615512), np.float64(0.004260028800658303), np.float64(0.04915099773709113), np.float64(0.005905780703558947), np.float64(0.22014873482822464)]
sampled assortment [7, 4, 9, 90, 59, 62] number: 6
#  Learning probs for MM model, A = [7, 4, 9, 90, 59, 62]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 9, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 13: 0, 100: 0} [1, 3, 4, 5, 7, 9, 12, 13, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 21: 1} [2, 1, 3, 6, 10, 11, 12, 21]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 2: 9, 3: 2, 5: 4, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 8, 11, 2]
#  Learning probs for MM model, A = [7, 4, 9, 90, 59, 62]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 9: 1, 10: 1, 13: 1, 16: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 9, 10, 13, 16, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 14: 1, 16: 1, 21: 1} [2, 1, 6, 10, 14, 16, 21]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 4, 10: 2, 13: 2, 14: 7, 15: 3, 20: 5, 35: 9, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 20, 14, 35]
empirical probabilities from test set: {7: 0.231, 4: 0.246, 9: 0.252, 90: 0.067, 59: 0.073, 62: 0.08, 0: 0.051}
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.10584958167455884), 4: np.float64(0.11202650760673603), 9: np.float64(0.10528907762920416), 90: np.float64(0.1692087082723743), 59: np.float64(0.1692087082723743), 62: np.float64(0.1692087082723743), 0: np.float64(0.1692087082723743)}
err dic= {7: np.float64(0.12515041832544116), 4: np.float64(0.13397349239326395), 9: np.float64(0.14671092237079586), 90: np.float64(0.1022087082723743), 59: np.float64(0.09620870827237431), 62: np.float64(0.0892087082723743), 0: np.float64(0.11820870827237431)} 

err list= [np.float64(0.12515041832544116), np.float64(0.13397349239326395), np.float64(0.14671092237079586), np.float64(0.1022087082723743), np.float64(0.09620870827237431), np.float64(0.0892087082723743), np.float64(0.11820870827237431)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.1305109454772363), 4: np.float64(0.14200562572696943), 9: np.float64(0.12428224585707913), 90: np.float64(0.15080029573467882), 59: np.float64(0.15080029573467882), 62: np.float64(0.15080029573467882), 0: np.float64(0.15080029573467882)}
err dic= {7: np.float64(0.10048905452276372), 4: np.float64(0.10399437427303057), 9: np.float64(0.12771775414292086), 90: np.float64(0.08380029573467881), 59: np.float64(0.07780029573467882), 62: np.float64(0.07080029573467882), 0: np.float64(0.09980029573467883)} 

err list= [np.float64(0.10048905452276372), np.float64(0.10399437427303057), np.float64(0.12771775414292086), np.float64(0.08380029573467881), np.float64(0.07780029573467882), np.float64(0.07080029573467882), np.float64(0.09980029573467883)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.18078310902260883), 4: np.float64(0.21239406513251058), 9: np.float64(0.15939490395054356), 90: np.float64(0.11185698047358451), 59: np.float64(0.11185698047358451), 62: np.float64(0.11185698047358451), 0: np.float64(0.11185698047358451)}
err dic= {7: np.float64(0.05021689097739118), 4: np.float64(0.03360593486748942), 9: np.float64(0.09260509604945644), 90: np.float64(0.04485698047358451), 59: np.float64(0.03885698047358452), 62: np.float64(0.03185698047358451), 0: np.float64(0.06085698047358452)} 

err list= [np.float64(0.05021689097739118), np.float64(0.03360593486748942), np.float64(0.09260509604945644), np.float64(0.04485698047358451), np.float64(0.03885698047358452), np.float64(0.03185698047358451), np.float64(0.06085698047358452)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.25767694209788644), 4: np.float64(0.38700988423559296), 9: np.float64(0.1858784823761234), 90: np.float64(0.04235867282259951), 59: np.float64(0.04235867282259951), 62: np.float64(0.04235867282259951), 0: np.float64(0.04235867282259951)}
err dic= {7: np.float64(0.02667694209788643), 4: np.float64(0.14100988423559296), 9: np.float64(0.06612151762387661), 90: np.float64(0.024641327177400495), 59: np.float64(0.030641327177400486), 62: np.float64(0.03764132717740049), 0: np.float64(0.008641327177400487)} 

err list= [np.float64(0.02667694209788643), np.float64(0.14100988423559296), np.float64(0.06612151762387661), np.float64(0.024641327177400495), np.float64(0.030641327177400486), np.float64(0.03764132717740049), np.float64(0.008641327177400487)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.23960519011936313), 4: np.float64(0.5284077209801223), 9: np.float64(0.12602341051908653), 90: np.float64(0.02649091959535689), 59: np.float64(0.02649091959535689), 62: np.float64(0.02649091959535689), 0: np.float64(0.02649091959535689)}
err dic= {7: np.float64(0.008605190119363115), 4: np.float64(0.28240772098012235), 9: np.float64(0.12597658948091348), 90: np.float64(0.040509080404643114), 59: np.float64(0.046509080404643105), 62: np.float64(0.05350908040464311), 0: np.float64(0.024509080404643106)} 

err list= [np.float64(0.008605190119363115), np.float64(0.28240772098012235), np.float64(0.12597658948091348), np.float64(0.040509080404643114), np.float64(0.046509080404643105), np.float64(0.05350908040464311), np.float64(0.024509080404643106)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.1938728621751436), 4: np.float64(0.6255739516171783), 9: np.float64(0.07937941051261539), 90: np.float64(0.02529344392376565), 59: np.float64(0.02529344392376565), 62: np.float64(0.02529344392376565), 0: np.float64(0.02529344392376565)}
err dic= {7: np.float64(0.03712713782485641), 4: np.float64(0.37957395161717833), 9: np.float64(0.17262058948738462), 90: np.float64(0.04170655607623436), 59: np.float64(0.04770655607623435), 62: np.float64(0.054706556076234356), 0: np.float64(0.025706556076234347)} 

err list= [np.float64(0.03712713782485641), np.float64(0.37957395161717833), np.float64(0.17262058948738462), np.float64(0.04170655607623436), np.float64(0.04770655607623435), np.float64(0.054706556076234356), np.float64(0.025706556076234347)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  1 

learned probs for this beta: {7: np.float64(0.15382855246560767), 4: np.float64(0.6928128409970796), 9: np.float64(0.052488491467361835), 90: np.float64(0.025217528767487746), 59: np.float64(0.025217528767487746), 62: np.float64(0.025217528767487746), 0: np.float64(0.025217528767487746)}
err dic= {7: np.float64(0.07717144753439234), 4: np.float64(0.44681284099707963), 9: np.float64(0.19951150853263816), 90: np.float64(0.04178247123251226), 59: np.float64(0.04778247123251225), 62: np.float64(0.05478247123251226), 0: np.float64(0.02578247123251225)} 

err list= [np.float64(0.07717144753439234), np.float64(0.44681284099707963), np.float64(0.19951150853263816), np.float64(0.04178247123251226), np.float64(0.04778247123251225), np.float64(0.05478247123251226), np.float64(0.02578247123251225)]
results for assortment [7, 4, 9, 90, 59, 62] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.12554384476460506), 4: np.float64(0.7352534935907109), 9: np.float64(0.03834500038676359), 90: np.float64(0.02521441531448004), 59: np.float64(0.02521441531448004), 62: np.float64(0.02521441531448004), 0: np.float64(0.02521441531448004)}
err dic= {7: np.float64(0.10545615523539495), 4: np.float64(0.4892534935907109), 9: np.float64(0.21365499961323642), 90: np.float64(0.04178558468551996), 59: np.float64(0.04778558468551995), 62: np.float64(0.05478558468551996), 0: np.float64(0.025785584685519957)} 

err list= [np.float64(0.10545615523539495), np.float64(0.4892534935907109), np.float64(0.21365499961323642), np.float64(0.04178558468551996), np.float64(0.04778558468551995), np.float64(0.05478558468551996), np.float64(0.025785584685519957)]
results for assortment [7, 4, 9, 90, 59, 62] :

err MNL dic= {7: np.float64(0.0948051782682513), 4: np.float64(0.11097241086587437), 9: np.float64(0.11994354838709675), 90: np.float64(0.04314431239388794), 59: np.float64(0.03581791171477079), 62: np.float64(0.03247877758913412), 0: np.float64(0.21428013582342953)} 

err MNL list= [np.float64(0.0948051782682513), np.float64(0.11097241086587437), np.float64(0.11994354838709675), np.float64(0.04314431239388794), np.float64(0.03581791171477079), np.float64(0.03247877758913412), np.float64(0.21428013582342953)]
sampled assortment [5, 9, 1, 51, 62, 82] number: 7
#  Learning probs for MM model, A = [5, 9, 1, 51, 62, 82]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 19: 1, 100: 1} [8, 1, 2, 3, 4, 7, 12, 19, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 12: 0, 100: 0} [1, 3, 4, 5, 7, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 6, 10, 11, 13, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 6: 0, 7: 4, 10: 2, 11: 5, 13: 2, 15: 4, 100: 0} [6, 100, 1, 3, 10, 13, 7, 15, 11]
#  Learning probs for MM model, A = [5, 9, 1, 51, 62, 82]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 14, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 10, 11, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 17: 1, 21: 1, 100: 1} [2, 1, 6, 7, 10, 11, 17, 21, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 4, 8: 4, 10: 2, 11: 5, 13: 2, 15: 4, 17: 6, 19: 5, 20: 5, 21: 9, 100: 0} [6, 100, 1, 3, 10, 13, 7, 8, 15, 5, 11, 19, 20, 17, 21]
empirical probabilities from test set: {5: 0.248, 9: 0.236, 1: 0.271, 51: 0.089, 62: 0.066, 82: 0.05, 0: 0.04}
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.11454270749231105), 9: np.float64(0.12484298960796181), 1: np.float64(0.11553776043258696), 51: np.float64(0.16126913561678513), 62: np.float64(0.16126913561678513), 82: np.float64(0.16126913561678513), 0: np.float64(0.16126913561678513)}
err dic= {5: np.float64(0.13345729250768895), 9: np.float64(0.11115701039203818), 1: np.float64(0.15546223956741306), 51: np.float64(0.07226913561678514), 62: np.float64(0.09526913561678513), 82: np.float64(0.11126913561678513), 0: np.float64(0.12126913561678512)} 

err list= [np.float64(0.13345729250768895), np.float64(0.11115701039203818), np.float64(0.15546223956741306), np.float64(0.07226913561678514), np.float64(0.09526913561678513), np.float64(0.11126913561678513), np.float64(0.12126913561678512)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.14332075469485253), 9: np.float64(0.13397037892431002), 1: np.float64(0.16892823896108383), 51: np.float64(0.1384451568549399), 62: np.float64(0.1384451568549399), 82: np.float64(0.1384451568549399), 0: np.float64(0.1384451568549399)}
err dic= {5: np.float64(0.10467924530514747), 9: np.float64(0.10202962107568997), 1: np.float64(0.10207176103891619), 51: np.float64(0.049445156854939915), 62: np.float64(0.07244515685493991), 82: np.float64(0.08844515685493991), 0: np.float64(0.0984451568549399)} 

err list= [np.float64(0.10467924530514747), np.float64(0.10202962107568997), np.float64(0.10207176103891619), np.float64(0.049445156854939915), np.float64(0.07244515685493991), np.float64(0.08844515685493991), np.float64(0.0984451568549399)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.1986473686019416), 9: np.float64(0.14257560205738468), 1: np.float64(0.2992198806080079), 51: np.float64(0.08988928718316685), 62: np.float64(0.08988928718316685), 82: np.float64(0.08988928718316685), 0: np.float64(0.08988928718316685)}
err dic= {5: np.float64(0.0493526313980584), 9: np.float64(0.09342439794261531), 1: np.float64(0.028219880608007897), 51: np.float64(0.0008892871831668592), 62: np.float64(0.023889287183166852), 82: np.float64(0.03988928718316685), 0: np.float64(0.049889287183166854)} 

err list= [np.float64(0.0493526313980584), np.float64(0.09342439794261531), np.float64(0.028219880608007897), np.float64(0.0008892871831668592), np.float64(0.023889287183166852), np.float64(0.03988928718316685), np.float64(0.049889287183166854)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.23877569304823265), 9: np.float64(0.09595664387103747), 1: np.float64(0.6052283506294418), 51: np.float64(0.015009828112821809), 62: np.float64(0.015009828112821809), 82: np.float64(0.015009828112821809), 0: np.float64(0.015009828112821809)}
err dic= {5: np.float64(0.009224306951767347), 9: np.float64(0.14004335612896252), 1: np.float64(0.3342283506294418), 51: np.float64(0.07399017188717819), 62: np.float64(0.05099017188717819), 82: np.float64(0.03499017188717819), 0: np.float64(0.02499017188717819)} 

err list= [np.float64(0.009224306951767347), np.float64(0.14004335612896252), np.float64(0.3342283506294418), np.float64(0.07399017188717819), np.float64(0.05099017188717819), np.float64(0.03499017188717819), np.float64(0.02499017188717819)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.1639924637148932), 9: np.float64(0.03209293441411969), 1: np.float64(0.8014549418374693), 51: np.float64(0.0006149150083797454), 62: np.float64(0.0006149150083797454), 82: np.float64(0.0006149150083797454), 0: np.float64(0.0006149150083797454)}
err dic= {5: np.float64(0.08400753628510679), 9: np.float64(0.2039070655858803), 1: np.float64(0.5304549418374693), 51: np.float64(0.08838508499162025), 62: np.float64(0.06538508499162025), 82: np.float64(0.049385084991620254), 0: np.float64(0.03938508499162026)} 

err list= [np.float64(0.08400753628510679), np.float64(0.2039070655858803), np.float64(0.5304549418374693), np.float64(0.08838508499162025), np.float64(0.06538508499162025), np.float64(0.049385084991620254), np.float64(0.03938508499162026)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.09800766242159215), 9: np.float64(0.009589432968557758), 1: np.float64(0.8923476649201308), 51: np.float64(1.3809922429786569e-05), 62: np.float64(1.3809922429786569e-05), 82: np.float64(1.3809922429786569e-05), 0: np.float64(1.3809922429786569e-05)}
err dic= {5: np.float64(0.14999233757840785), 9: np.float64(0.22641056703144222), 1: np.float64(0.6213476649201308), 51: np.float64(0.0889861900775702), 62: np.float64(0.06598619007757021), 82: np.float64(0.049986190077570214), 0: np.float64(0.03998619007757021)} 

err list= [np.float64(0.14999233757840785), np.float64(0.22641056703144222), np.float64(0.6213476649201308), np.float64(0.0889861900775702), np.float64(0.06598619007757021), np.float64(0.049986190077570214), np.float64(0.03998619007757021)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  1 

learned probs for this beta: {5: np.float64(0.0544956639282603), 9: np.float64(0.002596966740992891), 1: np.float64(0.9429065555663082), 51: np.float64(2.034411096996718e-07), 62: np.float64(2.034411096996718e-07), 82: np.float64(2.034411096996718e-07), 0: np.float64(2.034411096996718e-07)}
err dic= {5: np.float64(0.1935043360717397), 9: np.float64(0.2334030332590071), 1: np.float64(0.6719065555663082), 51: np.float64(0.0889997965588903), 62: np.float64(0.06599979655889031), 82: np.float64(0.0499997965588903), 0: np.float64(0.0399997965588903)} 

err list= [np.float64(0.1935043360717397), np.float64(0.2334030332590071), np.float64(0.6719065555663082), np.float64(0.0889997965588903), np.float64(0.06599979655889031), np.float64(0.0499997965588903), np.float64(0.0399997965588903)]
results for assortment [5, 9, 1, 51, 62, 82] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.028862065909970456), 9: np.float64(0.0006588484004079916), 1: np.float64(0.9704790742249102), 51: np.float64(2.866177791007701e-09), 62: np.float64(2.866177791007701e-09), 82: np.float64(2.866177791007701e-09), 0: np.float64(2.866177791007701e-09)}
err dic= {5: np.float64(0.21913793409002955), 9: np.float64(0.23534115159959199), 1: np.float64(0.6994790742249102), 51: np.float64(0.0889999971338222), 62: np.float64(0.06599999713382221), 82: np.float64(0.049999997133822215), 0: np.float64(0.03999999713382221)} 

err list= [np.float64(0.21913793409002955), np.float64(0.23534115159959199), np.float64(0.6994790742249102), np.float64(0.0889999971338222), np.float64(0.06599999713382221), np.float64(0.049999997133822215), np.float64(0.03999999713382221)]
results for assortment [5, 9, 1, 51, 62, 82] :

err MNL dic= {5: np.float64(0.10935554158809974), 9: np.float64(0.10563125916614285), 1: np.float64(0.1332459668971297), 51: np.float64(0.023874502409386142), 62: np.float64(0.04504127383197151), 82: np.float64(0.05742719463649697), 0: np.float64(0.2218897967735177)} 

err MNL list= [np.float64(0.10935554158809974), np.float64(0.10563125916614285), np.float64(0.1332459668971297), np.float64(0.023874502409386142), np.float64(0.04504127383197151), np.float64(0.05742719463649697), np.float64(0.2218897967735177)]
sampled assortment [6, 7, 5, 90, 94, 72] number: 8
#  Learning probs for MM model, A = [6, 7, 5, 90, 94, 72]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 3, 4, 5, 7, 14, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 14: 0, 100: 0} [1, 3, 4, 5, 7, 9, 14, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 10: 1, 14: 1} [2, 1, 3, 4, 6, 10, 14]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 9: 7, 10: 1, 13: 2, 15: 3, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 9]
#  Learning probs for MM model, A = [6, 7, 5, 90, 94, 72]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 9: 1, 100: 1} [8, 1, 2, 3, 4, 7, 9, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 3, 4, 5, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 16: 2, 100: 1} [2, 1, 6, 7, 10, 11, 100, 16]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 2, 11: 4, 13: 2, 15: 3, 17: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 11, 7, 17]
empirical probabilities from test set: {6: 0.279, 7: 0.219, 5: 0.254, 90: 0.061, 94: 0.051, 72: 0.072, 0: 0.064}
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.14462558725062113), 7: np.float64(0.09710757380546181), 5: np.float64(0.12412591398220539), 90: np.float64(0.15853523124042826), 94: np.float64(0.15853523124042826), 72: np.float64(0.15853523124042826), 0: np.float64(0.15853523124042826)}
err dic= {6: np.float64(0.1343744127493789), 7: np.float64(0.12189242619453819), 5: np.float64(0.1298740860177946), 90: np.float64(0.09753523124042826), 94: np.float64(0.10753523124042827), 72: np.float64(0.08653523124042826), 0: np.float64(0.09453523124042826)} 

err list= [np.float64(0.1343744127493789), np.float64(0.12189242619453819), np.float64(0.1298740860177946), np.float64(0.09753523124042826), np.float64(0.10753523124042827), np.float64(0.08653523124042826), np.float64(0.09453523124042826)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.14504668724853345), 7: np.float64(0.1315513205539515), 5: np.float64(0.14500111017857675), 90: np.float64(0.14460022050473487), 94: np.float64(0.14460022050473487), 72: np.float64(0.14460022050473487), 0: np.float64(0.14460022050473487)}
err dic= {6: np.float64(0.13395331275146657), 7: np.float64(0.0874486794460485), 5: np.float64(0.10899888982142325), 90: np.float64(0.08360022050473487), 94: np.float64(0.09360022050473488), 72: np.float64(0.07260022050473487), 0: np.float64(0.08060022050473487)} 

err list= [np.float64(0.13395331275146657), np.float64(0.0874486794460485), np.float64(0.10899888982142325), np.float64(0.08360022050473487), np.float64(0.09360022050473488), np.float64(0.07260022050473487), np.float64(0.08060022050473487)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.14708332895110893), 7: np.float64(0.21186107488856024), 5: np.float64(0.19438401681017098), 90: np.float64(0.1116678948375402), 94: np.float64(0.1116678948375402), 72: np.float64(0.1116678948375402), 0: np.float64(0.1116678948375402)}
err dic= {6: np.float64(0.1319166710488911), 7: np.float64(0.0071389251114397645), 5: np.float64(0.059615983189829025), 90: np.float64(0.050667894837540195), 94: np.float64(0.0606678948375402), 72: np.float64(0.0396678948375402), 0: np.float64(0.04766789483754019)} 

err list= [np.float64(0.1319166710488911), np.float64(0.0071389251114397645), np.float64(0.059615983189829025), np.float64(0.050667894837540195), np.float64(0.0606678948375402), np.float64(0.0396678948375402), np.float64(0.04766789483754019)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.15505371705241588), 7: np.float64(0.39397533898101894), 5: np.float64(0.30869113333446546), 90: np.float64(0.03556995265802459), 94: np.float64(0.03556995265802459), 72: np.float64(0.03556995265802459), 0: np.float64(0.03556995265802459)}
err dic= {6: np.float64(0.12394628294758414), 7: np.float64(0.17497533898101894), 5: np.float64(0.05469113333446546), 90: np.float64(0.02543004734197541), 94: np.float64(0.015430047341975409), 72: np.float64(0.036430047341975406), 0: np.float64(0.028430047341975413)} 

err list= [np.float64(0.12394628294758414), np.float64(0.17497533898101894), np.float64(0.05469113333446546), np.float64(0.02543004734197541), np.float64(0.015430047341975409), np.float64(0.036430047341975406), np.float64(0.028430047341975413)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.16397200807808276), 7: np.float64(0.46079111949188195), 5: np.float64(0.35503829045122953), 90: np.float64(0.005049645494701598), 94: np.float64(0.005049645494701598), 72: np.float64(0.005049645494701598), 0: np.float64(0.005049645494701598)}
err dic= {6: np.float64(0.11502799192191726), 7: np.float64(0.24179111949188195), 5: np.float64(0.10103829045122953), 90: np.float64(0.0559503545052984), 94: np.float64(0.0459503545052984), 72: np.float64(0.0669503545052984), 0: np.float64(0.058950354505298404)} 

err list= [np.float64(0.11502799192191726), np.float64(0.24179111949188195), np.float64(0.10103829045122953), np.float64(0.0559503545052984), np.float64(0.0459503545052984), np.float64(0.0669503545052984), np.float64(0.058950354505298404)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.1736381587648067), 7: np.float64(0.4435257526476459), 5: np.float64(0.38125021361326816), 90: np.float64(0.00039646874356980325), 94: np.float64(0.00039646874356980325), 72: np.float64(0.00039646874356980325), 0: np.float64(0.00039646874356980325)}
err dic= {6: np.float64(0.10536184123519332), 7: np.float64(0.22452575264764588), 5: np.float64(0.12725021361326816), 90: np.float64(0.0606035312564302), 94: np.float64(0.0506035312564302), 72: np.float64(0.0716035312564302), 0: np.float64(0.0636035312564302)} 

err list= [np.float64(0.10536184123519332), np.float64(0.22452575264764588), np.float64(0.12725021361326816), np.float64(0.0606035312564302), np.float64(0.0506035312564302), np.float64(0.0716035312564302), np.float64(0.0636035312564302)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  1 

learned probs for this beta: {6: np.float64(0.18332357717382075), 7: np.float64(0.4073506788695017), 5: np.float64(0.4092458478016274), 90: np.float64(1.997403876256873e-05), 94: np.float64(1.997403876256873e-05), 72: np.float64(1.997403876256873e-05), 0: np.float64(1.997403876256873e-05)}
err dic= {6: np.float64(0.09567642282617927), 7: np.float64(0.18835067886950171), 5: np.float64(0.15524584780162742), 90: np.float64(0.06098002596123743), 94: np.float64(0.05098002596123743), 72: np.float64(0.07198002596123743), 0: np.float64(0.06398002596123743)} 

err list= [np.float64(0.09567642282617927), np.float64(0.18835067886950171), np.float64(0.15524584780162742), np.float64(0.06098002596123743), np.float64(0.05098002596123743), np.float64(0.07198002596123743), np.float64(0.06398002596123743)]
results for assortment [6, 7, 5, 90, 94, 72] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.19165047129067297), 7: np.float64(0.3734049552594888), 5: np.float64(0.4349406997202071), 90: np.float64(9.684324077801652e-07), 94: np.float64(9.684324077801652e-07), 72: np.float64(9.684324077801652e-07), 0: np.float64(9.684324077801652e-07)}
err dic= {6: np.float64(0.08734952870932705), 7: np.float64(0.1544049552594888), 5: np.float64(0.1809406997202071), 90: np.float64(0.06099903156759222), 94: np.float64(0.050999031567592217), 72: np.float64(0.07199903156759221), 0: np.float64(0.06399903156759222)} 

err list= [np.float64(0.08734952870932705), np.float64(0.1544049552594888), np.float64(0.1809406997202071), np.float64(0.06099903156759222), np.float64(0.050999031567592217), np.float64(0.07199903156759221), np.float64(0.06399903156759222)]
results for assortment [6, 7, 5, 90, 94, 72] :

err MNL dic= {6: np.float64(0.14143079356709728), 7: np.float64(0.08364539941998417), 5: np.float64(0.11442710255734248), 90: np.float64(0.04846480358555234), 94: np.float64(0.056408383865014504), 72: np.float64(0.03498655417875032), 0: np.float64(0.1996435539151068)} 

err MNL list= [np.float64(0.14143079356709728), np.float64(0.08364539941998417), np.float64(0.11442710255734248), np.float64(0.04846480358555234), np.float64(0.056408383865014504), np.float64(0.03498655417875032), np.float64(0.1996435539151068)]
sampled assortment [5, 8, 6, 55, 63, 25] number: 9
#  Learning probs for MM model, A = [5, 8, 6, 55, 63, 25]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 5, 7, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 100: 0} [1, 3, 4, 5, 6, 7, 9, 11, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 100: 1} [2, 3, 6, 7, 10, 11, 14, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 2, 14: 7, 15: 4, 100: 0} [6, 100, 1, 3, 10, 13, 5, 8, 15, 7, 14]
#  Learning probs for MM model, A = [5, 8, 6, 55, 63, 25]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 15: 1, 100: 1} [8, 1, 2, 3, 5, 7, 15, 100]
#cluster  2 with weight 0.5595
Learned cluster center of cluster 2:  {1: 0, 3: 0, 4: 0, 5: 0, 9: 0, 12: 0, 100: 0} [1, 3, 4, 5, 9, 12, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 6, 7, 10, 11, 100]
#cluster  4 with weight 0.0545
Learned cluster center of cluster 4:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 4, 10: 2, 11: 5, 13: 2, 15: 3, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 8, 5, 7, 11, 23]
empirical probabilities from test set: {5: 0.216, 8: 0.256, 6: 0.245, 55: 0.056, 63: 0.049, 25: 0.128, 0: 0.05}
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.09843924708288979), 8: np.float64(0.13959080631801635), 6: np.float64(0.1419967072366578), 55: np.float64(0.15499330984060886), 63: np.float64(0.15499330984060886), 25: np.float64(0.15499330984060886), 0: np.float64(0.15499330984060886)}
err dic= {5: np.float64(0.11756075291711021), 8: np.float64(0.11640919368198366), 6: np.float64(0.10300329276334219), 55: np.float64(0.09899330984060886), 63: np.float64(0.10599330984060885), 25: np.float64(0.026993309840608853), 0: np.float64(0.10499330984060885)} 

err list= [np.float64(0.11756075291711021), np.float64(0.11640919368198366), np.float64(0.10300329276334219), np.float64(0.09899330984060886), np.float64(0.10599330984060885), np.float64(0.026993309840608853), np.float64(0.10499330984060885)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.12330145941083255), 8: np.float64(0.1470255809744983), 6: np.float64(0.14562763422879216), 55: np.float64(0.14601133134646915), 63: np.float64(0.14601133134646915), 25: np.float64(0.14601133134646915), 0: np.float64(0.14601133134646915)}
err dic= {5: np.float64(0.09269854058916745), 8: np.float64(0.1089744190255017), 6: np.float64(0.09937236577120784), 55: np.float64(0.09001133134646916), 63: np.float64(0.09701133134646915), 25: np.float64(0.01801133134646915), 0: np.float64(0.09601133134646915)} 

err list= [np.float64(0.09269854058916745), np.float64(0.1089744190255017), np.float64(0.09937236577120784), np.float64(0.09001133134646916), np.float64(0.09701133134646915), np.float64(0.01801133134646915), np.float64(0.09601133134646915)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.18584155951622366), 8: np.float64(0.16473393673697856), 6: np.float64(0.15501366482241033), 55: np.float64(0.12360270973109697), 63: np.float64(0.12360270973109697), 25: np.float64(0.12360270973109697), 0: np.float64(0.12360270973109697)}
err dic= {5: np.float64(0.030158440483776333), 8: np.float64(0.09126606326302145), 6: np.float64(0.08998633517758967), 55: np.float64(0.06760270973109697), 63: np.float64(0.07460270973109696), 25: np.float64(0.004397290268903037), 0: np.float64(0.07360270973109696)} 

err list= [np.float64(0.030158440483776333), np.float64(0.09126606326302145), np.float64(0.08998633517758967), np.float64(0.06760270973109697), np.float64(0.07460270973109696), np.float64(0.004397290268903037), np.float64(0.07360270973109696)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.38636377757286083), 8: np.float64(0.1923257194194531), 6: np.float64(0.19051137604688212), 55: np.float64(0.057699781740201087), 63: np.float64(0.057699781740201087), 25: np.float64(0.057699781740201087), 0: np.float64(0.057699781740201087)}
err dic= {5: np.float64(0.17036377757286084), 8: np.float64(0.06367428058054692), 6: np.float64(0.054488623953117876), 55: np.float64(0.0016997817402010854), 63: np.float64(0.008699781740201085), 25: np.float64(0.07030021825979892), 0: np.float64(0.007699781740201084)} 

err list= [np.float64(0.17036377757286084), np.float64(0.06367428058054692), np.float64(0.054488623953117876), np.float64(0.0016997817402010854), np.float64(0.008699781740201085), np.float64(0.07030021825979892), np.float64(0.007699781740201084)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5551237122211207), 8: np.float64(0.18411451106343268), 6: np.float64(0.22401535739266368), 55: np.float64(0.009186604830695822), 63: np.float64(0.009186604830695822), 25: np.float64(0.009186604830695822), 0: np.float64(0.009186604830695822)}
err dic= {5: np.float64(0.3391237122211207), 8: np.float64(0.07188548893656732), 6: np.float64(0.020984642607336318), 55: np.float64(0.046813395169304176), 63: np.float64(0.03981339516930418), 25: np.float64(0.11881339516930418), 0: np.float64(0.040813395169304184)} 

err list= [np.float64(0.3391237122211207), np.float64(0.07188548893656732), np.float64(0.020984642607336318), np.float64(0.046813395169304176), np.float64(0.03981339516930418), np.float64(0.11881339516930418), np.float64(0.040813395169304184)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.5758286157292255), 8: np.float64(0.19224652695034175), 6: np.float64(0.22972552935900356), 55: np.float64(0.0005498319903572428), 63: np.float64(0.0005498319903572428), 25: np.float64(0.0005498319903572428), 0: np.float64(0.0005498319903572428)}
err dic= {5: np.float64(0.35982861572922553), 8: np.float64(0.06375347304965825), 6: np.float64(0.015274470640996435), 55: np.float64(0.05545016800964276), 63: np.float64(0.04845016800964276), 25: np.float64(0.12745016800964276), 0: np.float64(0.04945016800964276)} 

err list= [np.float64(0.35982861572922553), np.float64(0.06375347304965825), np.float64(0.015274470640996435), np.float64(0.05545016800964276), np.float64(0.04845016800964276), np.float64(0.12745016800964276), np.float64(0.04945016800964276)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  1 

learned probs for this beta: {5: np.float64(0.5679924095970819), 8: np.float64(0.201188688325454), 6: np.float64(0.2307355218586639), 55: np.float64(2.08450547000404e-05), 63: np.float64(2.08450547000404e-05), 25: np.float64(2.08450547000404e-05), 0: np.float64(2.08450547000404e-05)}
err dic= {5: np.float64(0.3519924095970819), 8: np.float64(0.054811311674546004), 6: np.float64(0.014264478141336107), 55: np.float64(0.05597915494529996), 63: np.float64(0.04897915494529996), 25: np.float64(0.12797915494529996), 0: np.float64(0.04997915494529996)} 

err list= [np.float64(0.3519924095970819), np.float64(0.054811311674546004), np.float64(0.014264478141336107), np.float64(0.05597915494529996), np.float64(0.04897915494529996), np.float64(0.12797915494529996), np.float64(0.04997915494529996)]
results for assortment [5, 8, 6, 55, 63, 25] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.5631660530170944), 8: np.float64(0.20588223096936045), 6: np.float64(0.23094868629565218), 55: np.float64(7.574294732218384e-07), 63: np.float64(7.574294732218384e-07), 25: np.float64(7.574294732218384e-07), 0: np.float64(7.574294732218384e-07)}
err dic= {5: np.float64(0.34716605301709447), 8: np.float64(0.05011776903063955), 6: np.float64(0.014051313704347812), 55: np.float64(0.055999242570526776), 63: np.float64(0.04899924257052678), 25: np.float64(0.12799924257052678), 0: np.float64(0.04999924257052678)} 

err list= [np.float64(0.34716605301709447), np.float64(0.05011776903063955), np.float64(0.014051313704347812), np.float64(0.055999242570526776), np.float64(0.04899924257052678), np.float64(0.12799924257052678), np.float64(0.04999924257052678)]
results for assortment [5, 8, 6, 55, 63, 25] :

err MNL dic= {5: np.float64(0.0784935064935065), 8: np.float64(0.1267012987012987), 6: np.float64(0.10946753246753246), 55: np.float64(0.051636363636363626), 63: np.float64(0.05946753246753246), 25: np.float64(0.006181818181818191), 0: np.float64(0.20974025974025973)} 

err MNL list= [np.float64(0.0784935064935065), np.float64(0.1267012987012987), np.float64(0.10946753246753246), np.float64(0.051636363636363626), np.float64(0.05946753246753246), np.float64(0.006181818181818191), np.float64(0.20974025974025973)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25]
 mean error for all betas:

mean_err= [0.09627807 0.09114551 0.08131683 0.07444927 0.07893792 0.08291629
 0.08543815 0.08715716]
mean_std= [0.         0.00513256 0.01451785 0.01730797 0.01789538 0.01860128
 0.01829581 0.01770818]
MNL: [0.09892301 0.09609584 0.10207012 0.0958796  0.07897479 0.07694278
 0.09306318 0.09949508 0.09700094 0.09166976]
 mean error for MNL:

mean_err_MNL= 0.09301151031982621
mean_std_MNL= 0.00806059579333366
