p= 0.1 num clusters= 1
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 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 100]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
empirical probabilities from test set: {2: 0.275, 3: 0.247, 4: 0.252, 59: 0.059, 40: 0.072, 84: 0.06, 0: 0.035}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.12409301185912805), 3: np.float64(0.12102914447965715), 4: np.float64(0.11804092425531884), 59: np.float64(0.15920922985147534), 40: np.float64(0.15920922985147534), 84: np.float64(0.15920922985147534), 0: np.float64(0.15920922985147534)}
err dic= {2: np.float64(0.15090698814087197), 3: np.float64(0.12597085552034284), 4: np.float64(0.13395907574468116), 59: np.float64(0.10020922985147535), 40: np.float64(0.08720922985147535), 84: np.float64(0.09920922985147534), 0: np.float64(0.12420922985147534)} 

err list= [np.float64(0.15090698814087197), np.float64(0.12597085552034284), np.float64(0.13395907574468116), np.float64(0.10020922985147535), np.float64(0.08720922985147535), np.float64(0.09920922985147534), np.float64(0.12420922985147534)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.17526212373108796), 3: np.float64(0.16671448909349587), 4: np.float64(0.1585837275163367), 59: np.float64(0.12485991491477247), 40: np.float64(0.12485991491477247), 84: np.float64(0.12485991491477247), 0: np.float64(0.12485991491477247)}
err dic= {2: np.float64(0.09973787626891206), 3: np.float64(0.08028551090650413), 4: np.float64(0.0934162724836633), 59: np.float64(0.06585991491477247), 40: np.float64(0.052859914914772474), 84: np.float64(0.06485991491477247), 0: np.float64(0.08985991491477247)} 

err list= [np.float64(0.09973787626891206), np.float64(0.08028551090650413), np.float64(0.0934162724836633), np.float64(0.06585991491477247), np.float64(0.052859914914772474), np.float64(0.06485991491477247), np.float64(0.08985991491477247)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.2770188325827486), 3: np.float64(0.25065700522150985), 4: np.float64(0.22680383741725685), 59: np.float64(0.061380081194621634), 40: np.float64(0.061380081194621634), 84: np.float64(0.061380081194621634), 0: np.float64(0.061380081194621634)}
err dic= {2: np.float64(0.0020188325827485976), 3: np.float64(0.003657005221509857), 4: np.float64(0.025196162582743153), 59: np.float64(0.0023800811946216374), 40: np.float64(0.01061991880537836), 84: np.float64(0.0013800811946216365), 0: np.float64(0.02638008119462163)} 

err list= [np.float64(0.0020188325827485976), np.float64(0.003657005221509857), np.float64(0.025196162582743153), np.float64(0.0023800811946216374), np.float64(0.01061991880537836), np.float64(0.0013800811946216365), np.float64(0.02638008119462163)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.4131465088043342), 3: np.float64(0.32175882458003174), 4: np.float64(0.25058602454306333), 59: np.float64(0.0036271605181429018), 40: np.float64(0.0036271605181429018), 84: np.float64(0.0036271605181429018), 0: np.float64(0.0036271605181429018)}
err dic= {2: np.float64(0.13814650880433416), 3: np.float64(0.07475882458003175), 4: np.float64(0.001413975456936667), 59: np.float64(0.055372839481857096), 40: np.float64(0.06837283948185709), 84: np.float64(0.0563728394818571), 0: np.float64(0.0313728394818571)} 

err list= [np.float64(0.13814650880433416), np.float64(0.07475882458003175), np.float64(0.001413975456936667), np.float64(0.055372839481857096), np.float64(0.06837283948185709), np.float64(0.0563728394818571), np.float64(0.0313728394818571)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5063386539118819), 3: np.float64(0.30710991779518093), 4: np.float64(0.18627158104460348), 59: np.float64(6.996181208344174e-05), 40: np.float64(6.996181208344174e-05), 84: np.float64(6.996181208344174e-05), 0: np.float64(6.996181208344174e-05)}
err dic= {2: np.float64(0.2313386539118819), 3: np.float64(0.060109917795180934), 4: np.float64(0.06572841895539652), 59: np.float64(0.058930038187916554), 40: np.float64(0.07193003818791656), 84: np.float64(0.059930038187916555), 0: np.float64(0.03493003818791656)} 

err list= [np.float64(0.2313386539118819), np.float64(0.060109917795180934), np.float64(0.06572841895539652), np.float64(0.058930038187916554), np.float64(0.07193003818791656), np.float64(0.059930038187916555), np.float64(0.03493003818791656)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5897955607131157), 3: np.float64(0.2785996958360083), 4: np.float64(0.1316011779167505), 59: np.float64(8.913835314722744e-07), 40: np.float64(8.913835314722744e-07), 84: np.float64(8.913835314722744e-07), 0: np.float64(8.913835314722744e-07)}
err dic= {2: np.float64(0.31479556071311565), 3: np.float64(0.0315996958360083), 4: np.float64(0.12039882208324951), 59: np.float64(0.058999108616468524), 40: np.float64(0.07199910861646852), 84: np.float64(0.059999108616468524), 0: np.float64(0.03499910861646853)} 

err list= [np.float64(0.31479556071311565), np.float64(0.0315996958360083), np.float64(0.12039882208324951), np.float64(0.058999108616468524), np.float64(0.07199910861646852), np.float64(0.059999108616468524), np.float64(0.03499910861646853)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652409350711036), 3: np.float64(0.24472846343832536), 4: np.float64(0.09003057036843688), 59: np.float64(7.780533580382233e-09), 40: np.float64(7.780533580382233e-09), 84: np.float64(7.780533580382233e-09), 0: np.float64(7.780533580382233e-09)}
err dic= {2: np.float64(0.3902409350711036), 3: np.float64(0.002271536561674642), 4: np.float64(0.16196942963156313), 59: np.float64(0.05899999221946642), 40: np.float64(0.07199999221946642), 84: np.float64(0.05999999221946642), 0: np.float64(0.034999992219466425)} 

err list= [np.float64(0.3902409350711036), np.float64(0.002271536561674642), np.float64(0.16196942963156313), np.float64(0.05899999221946642), np.float64(0.07199999221946642), np.float64(0.05999999221946642), np.float64(0.034999992219466425)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.7306791290068032), 3: np.float64(0.20934307542607475), 4: np.float64(0.059977795299034985), 59: np.float64(6.702166793012352e-11), 40: np.float64(6.702166793012352e-11), 84: np.float64(6.702166793012352e-11), 0: np.float64(6.702166793012352e-11)}
err dic= {2: np.float64(0.4556791290068032), 3: np.float64(0.03765692457392525), 4: np.float64(0.192022204700965), 59: np.float64(0.05899999993297833), 40: np.float64(0.07199999993297833), 84: np.float64(0.05999999993297833), 0: np.float64(0.03499999993297834)} 

err list= [np.float64(0.4556791290068032), np.float64(0.03765692457392525), np.float64(0.192022204700965), np.float64(0.05899999993297833), np.float64(0.07199999993297833), np.float64(0.05999999993297833), np.float64(0.03499999993297834)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855970345874242), 3: np.float64(0.17529039213962347), 4: np.float64(0.039112573270595245), 59: np.float64(5.891211272274141e-13), 40: np.float64(5.891211272274141e-13), 84: np.float64(5.891211272274141e-13), 0: np.float64(5.891211272274141e-13)}
err dic= {2: np.float64(0.5105970345874242), 3: np.float64(0.07170960786037653), 4: np.float64(0.21288742672940475), 59: np.float64(0.05899999999941088), 40: np.float64(0.07199999999941087), 84: np.float64(0.05999999999941088), 0: np.float64(0.034999999999410884)} 

err list= [np.float64(0.5105970345874242), np.float64(0.07170960786037653), np.float64(0.21288742672940475), np.float64(0.05899999999941088), np.float64(0.07199999999941087), np.float64(0.05999999999941088), np.float64(0.034999999999410884)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845643329505), 3: np.float64(0.14433395511320668), 4: np.float64(0.025081480553821468), 59: np.float64(5.250180010662512e-15), 40: np.float64(5.250180010662512e-15), 84: np.float64(5.250180010662512e-15), 0: np.float64(5.250180010662512e-15)}
err dic= {2: np.float64(0.5555845643329504), 3: np.float64(0.10266604488679332), 4: np.float64(0.22691851944617852), 59: np.float64(0.058999999999994744), 40: np.float64(0.07199999999999475), 84: np.float64(0.059999999999994745), 0: np.float64(0.03499999999999475)} 

err list= [np.float64(0.5555845643329504), np.float64(0.10266604488679332), np.float64(0.22691851944617852), np.float64(0.058999999999994744), np.float64(0.07199999999999475), np.float64(0.059999999999994745), np.float64(0.03499999999999475)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973343), 3: np.float64(0.11731042782619829), 4: np.float64(0.015876239976466762), 59: np.float64(4.7174029730763036e-17), 40: np.float64(4.7174029730763036e-17), 84: np.float64(4.7174029730763036e-17), 0: np.float64(4.7174029730763036e-17)}
err dic= {2: np.float64(0.5918133321973342), 3: np.float64(0.12968957217380173), 4: np.float64(0.23612376002353325), 59: np.float64(0.05899999999999995), 40: np.float64(0.07199999999999995), 84: np.float64(0.05999999999999995), 0: np.float64(0.034999999999999955)} 

err list= [np.float64(0.5918133321973342), np.float64(0.12968957217380173), np.float64(0.23612376002353325), np.float64(0.05899999999999995), np.float64(0.07199999999999995), np.float64(0.05999999999999995), np.float64(0.034999999999999955)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: 0.275, 3: 0.247, 4: 0.252, 59: 0.059, 40: 0.072, 84: 0.06, 0: np.float64(0.2293824027072758)} 

err MNL list= [0.275, 0.247, 0.252, 0.059, 0.072, 0.06, np.float64(0.2293824027072758)]
sampled assortment [3, 4, 8, 74, 40, 87] number: 1
#  Learning probs for MM model, A = [3, 4, 8, 74, 40, 87]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
#  Learning probs for MM model, A = [3, 4, 8, 74, 40, 87]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
empirical probabilities from test set: {3: 0.259, 4: 0.246, 8: 0.256, 74: 0.066, 40: 0.077, 87: 0.047, 0: 0.049}
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.1224786185412812), 4: np.float64(0.11945461067484864), 8: np.float64(0.10862840253100912), 74: np.float64(0.16235959206321546), 40: np.float64(0.16235959206321546), 87: np.float64(0.16235959206321546), 0: np.float64(0.16235959206321546)}
err dic= {3: np.float64(0.1365213814587188), 4: np.float64(0.12654538932515136), 8: np.float64(0.14737159746899087), 74: np.float64(0.09635959206321545), 40: np.float64(0.08535959206321546), 87: np.float64(0.11535959206321546), 0: np.float64(0.11335959206321546)} 

err list= [np.float64(0.1365213814587188), np.float64(0.12654538932515136), np.float64(0.14737159746899087), np.float64(0.09635959206321545), np.float64(0.08535959206321546), np.float64(0.11535959206321546), np.float64(0.11335959206321546)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.1722791885793415), 4: np.float64(0.16387703340577692), 8: np.float64(0.1359997435995198), 74: np.float64(0.13196100860384227), 40: np.float64(0.13196100860384227), 87: np.float64(0.13196100860384227), 0: np.float64(0.13196100860384227)}
err dic= {3: np.float64(0.08672081142065852), 4: np.float64(0.08212296659422308), 8: np.float64(0.1200002564004802), 74: np.float64(0.06596100860384227), 40: np.float64(0.054961008603842273), 87: np.float64(0.08496100860384227), 0: np.float64(0.08296100860384227)} 

err list= [np.float64(0.08672081142065852), np.float64(0.08212296659422308), np.float64(0.1200002564004802), np.float64(0.06596100860384227), np.float64(0.054961008603842273), np.float64(0.08496100860384227), np.float64(0.08296100860384227)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.27805895574182693), 4: np.float64(0.2515981475752097), 8: np.float64(0.17588946608702966), 74: np.float64(0.07361335764898327), 40: np.float64(0.07361335764898327), 87: np.float64(0.07361335764898327), 0: np.float64(0.07361335764898327)}
err dic= {3: np.float64(0.019058955741826922), 4: np.float64(0.005598147575209711), 8: np.float64(0.08011053391297035), 74: np.float64(0.007613357648983271), 40: np.float64(0.003386642351016725), 87: np.float64(0.026613357648983274), 0: np.float64(0.024613357648983272)} 

err list= [np.float64(0.019058955741826922), np.float64(0.005598147575209711), np.float64(0.08011053391297035), np.float64(0.007613357648983271), np.float64(0.003386642351016725), np.float64(0.026613357648983274), np.float64(0.024613357648983272)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.4616710653889188), 4: np.float64(0.35954978724629955), 8: np.float64(0.15396971319916875), 74: np.float64(0.00620235854140308), 40: np.float64(0.00620235854140308), 87: np.float64(0.00620235854140308), 0: np.float64(0.00620235854140308)}
err dic= {3: np.float64(0.20267106538891877), 4: np.float64(0.11354978724629955), 8: np.float64(0.10203028680083126), 74: np.float64(0.05979764145859692), 40: np.float64(0.07079764145859692), 87: np.float64(0.04079764145859692), 0: np.float64(0.04279764145859692)} 

err list= [np.float64(0.20267106538891877), np.float64(0.11354978724629955), np.float64(0.10203028680083126), np.float64(0.05979764145859692), np.float64(0.07079764145859692), np.float64(0.04079764145859692), np.float64(0.04279764145859692)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5838056276370026), 4: np.float64(0.3540960124746191), 8: np.float64(0.06150071287955243), 74: np.float64(0.0001494117522067137), 40: np.float64(0.0001494117522067137), 87: np.float64(0.0001494117522067137), 0: np.float64(0.0001494117522067137)}
err dic= {3: np.float64(0.3248056276370026), 4: np.float64(0.10809601247461909), 8: np.float64(0.19449928712044756), 74: np.float64(0.06585058824779329), 40: np.float64(0.07685058824779328), 87: np.float64(0.046850588247793284), 0: np.float64(0.048850588247793286)} 

err list= [np.float64(0.3248056276370026), np.float64(0.10809601247461909), np.float64(0.19449928712044756), np.float64(0.06585058824779329), np.float64(0.07685058824779328), np.float64(0.046850588247793284), np.float64(0.048850588247793286)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.665140358512257), 4: np.float64(0.3141900582393575), 8: np.float64(0.020659510054652944), 74: np.float64(2.518298433243092e-06), 40: np.float64(2.518298433243092e-06), 87: np.float64(2.518298433243092e-06), 0: np.float64(2.518298433243092e-06)}
err dic= {3: np.float64(0.40614035851225694), 4: np.float64(0.06819005823935748), 8: np.float64(0.23534048994534706), 74: np.float64(0.06599748170156676), 40: np.float64(0.07699748170156676), 87: np.float64(0.04699748170156676), 0: np.float64(0.04899748170156676)} 

err list= [np.float64(0.40614035851225694), np.float64(0.06819005823935748), np.float64(0.23534048994534706), np.float64(0.06599748170156676), np.float64(0.07699748170156676), np.float64(0.04699748170156676), np.float64(0.04899748170156676)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.7263954157131992), 4: np.float64(0.26722593960206925), 8: np.float64(0.006378533771457059), 74: np.float64(2.7728318657609067e-08), 40: np.float64(2.7728318657609067e-08), 87: np.float64(2.7728318657609067e-08), 0: np.float64(2.7728318657609067e-08)}
err dic= {3: np.float64(0.4673954157131992), 4: np.float64(0.021225939602069255), 8: np.float64(0.24962146622854295), 74: np.float64(0.06599997227168135), 40: np.float64(0.07699997227168134), 87: np.float64(0.046999972271681345), 0: np.float64(0.04899997227168135)} 

err list= [np.float64(0.4673954157131992), np.float64(0.021225939602069255), np.float64(0.24962146622854295), np.float64(0.06599997227168135), np.float64(0.07699997227168134), np.float64(0.046999972271681345), np.float64(0.04899997227168135)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.775832219631019), 4: np.float64(0.2222796524829755), 8: np.float64(0.0018881267033875448), 74: np.float64(2.9565432930331417e-10), 40: np.float64(2.9565432930331417e-10), 87: np.float64(2.9565432930331417e-10), 0: np.float64(2.9565432930331417e-10)}
err dic= {3: np.float64(0.516832219631019), 4: np.float64(0.02372034751702451), 8: np.float64(0.25411187329661244), 74: np.float64(0.06599999970434567), 40: np.float64(0.07699999970434566), 87: np.float64(0.04699999970434567), 0: np.float64(0.048999999704345674)} 

err list= [np.float64(0.516832219631019), np.float64(0.02372034751702451), np.float64(0.25411187329661244), np.float64(0.06599999970434567), np.float64(0.07699999970434566), np.float64(0.04699999970434567), np.float64(0.048999999704345674)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.8171262003024956), 4: np.float64(0.18232549993497377), 8: np.float64(0.0005482997497056778), 74: np.float64(3.206150840561245e-12), 40: np.float64(3.206150840561245e-12), 87: np.float64(3.206150840561245e-12), 0: np.float64(3.206150840561245e-12)}
err dic= {3: np.float64(0.5581262003024956), 4: np.float64(0.06367450006502623), 8: np.float64(0.25545170025029434), 74: np.float64(0.06599999999679385), 40: np.float64(0.07699999999679384), 87: np.float64(0.04699999999679385), 0: np.float64(0.04899999999679385)} 

err list= [np.float64(0.5581262003024956), np.float64(0.06367450006502623), np.float64(0.25545170025029434), np.float64(0.06599999999679385), np.float64(0.07699999999679384), np.float64(0.04699999999679385), np.float64(0.04899999999679385)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.8518182496429446), 4: np.float64(0.14802381634351017), 8: np.float64(0.00015793401340312224), 74: np.float64(3.536140957945578e-14), 40: np.float64(3.536140957945578e-14), 87: np.float64(3.536140957945578e-14), 0: np.float64(3.536140957945578e-14)}
err dic= {3: np.float64(0.5928182496429446), 4: np.float64(0.09797618365648983), 8: np.float64(0.25584206598659687), 74: np.float64(0.06599999999996464), 40: np.float64(0.07699999999996464), 87: np.float64(0.04699999999996464), 0: np.float64(0.04899999999996464)} 

err list= [np.float64(0.5928182496429446), np.float64(0.09797618365648983), np.float64(0.25584206598659687), np.float64(0.06599999999996464), np.float64(0.07699999999996464), np.float64(0.04699999999996464), np.float64(0.04899999999996464)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402411458), 4: np.float64(0.11919751703720448), 8: np.float64(4.5342721647808975e-05), 74: np.float64(3.95304049191327e-16), 40: np.float64(3.95304049191327e-16), 87: np.float64(3.95304049191327e-16), 0: np.float64(3.95304049191327e-16)}
err dic= {3: np.float64(0.6217571402411458), 4: np.float64(0.1268024829627955), 8: np.float64(0.2559546572783522), 74: np.float64(0.06599999999999961), 40: np.float64(0.07699999999999961), 87: np.float64(0.046999999999999605), 0: np.float64(0.048999999999999606)} 

err list= [np.float64(0.6217571402411458), np.float64(0.1268024829627955), np.float64(0.2559546572783522), np.float64(0.06599999999999961), np.float64(0.07699999999999961), np.float64(0.046999999999999605), np.float64(0.048999999999999606)]
results for assortment [3, 4, 8, 74, 40, 87] :

err MNL dic= {3: 0.259, 4: 0.246, 8: 0.256, 74: 0.066, 40: 0.077, 87: 0.047, 0: np.float64(0.21578843404120113)} 

err MNL list= [0.259, 0.246, 0.256, 0.066, 0.077, 0.047, np.float64(0.21578843404120113)]
sampled assortment [1, 3, 9, 83, 79, 70] number: 2
#  Learning probs for MM model, A = [1, 3, 9, 83, 79, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 5, 6, 7, 8, 10, 11, 100]
#  Learning probs for MM model, A = [1, 3, 9, 83, 79, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 5, 6, 7, 8, 9, 10, 100]
empirical probabilities from test set: {1: 0.265, 3: 0.251, 9: 0.235, 83: 0.052, 79: 0.068, 70: 0.081, 0: 0.048}
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.1181026668120053), 3: np.float64(0.11252675248539093), 9: np.float64(0.09990706081864444), 83: np.float64(0.16736587997098987), 79: np.float64(0.16736587997098987), 70: np.float64(0.16736587997098987), 0: np.float64(0.16736587997098987)}
err dic= {1: np.float64(0.1468973331879947), 3: np.float64(0.13847324751460907), 9: np.float64(0.13509293918135556), 83: np.float64(0.11536587997098988), 79: np.float64(0.09936587997098986), 70: np.float64(0.08636587997098986), 0: np.float64(0.11936587997098987)} 

err list= [np.float64(0.1468973331879947), np.float64(0.13847324751460907), np.float64(0.13509293918135556), np.float64(0.11536587997098988), np.float64(0.09936587997098986), np.float64(0.08636587997098986), np.float64(0.11936587997098987)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.17155551661977786), 3: np.float64(0.15597254917282258), 9: np.float64(0.12348355356380303), 83: np.float64(0.1372470951609019), 79: np.float64(0.1372470951609019), 70: np.float64(0.1372470951609019), 0: np.float64(0.1372470951609019)}
err dic= {1: np.float64(0.09344448338022215), 3: np.float64(0.09502745082717742), 9: np.float64(0.11151644643619696), 83: np.float64(0.0852470951609019), 79: np.float64(0.06924709516090188), 70: np.float64(0.056247095160901886), 0: np.float64(0.08924709516090189)} 

err list= [np.float64(0.09344448338022215), np.float64(0.09502745082717742), np.float64(0.11151644643619696), np.float64(0.0852470951609019), np.float64(0.06924709516090188), np.float64(0.056247095160901886), np.float64(0.08924709516090189)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.2933324942189724), 3: np.float64(0.24422949939866792), 9: np.float64(0.156000564599709), 83: np.float64(0.07660936044566327), 79: np.float64(0.07660936044566327), 70: np.float64(0.07660936044566327), 0: np.float64(0.07660936044566327)}
err dic= {1: np.float64(0.02833249421897238), 3: np.float64(0.00677050060133208), 9: np.float64(0.07899943540029097), 83: np.float64(0.024609360445663274), 79: np.float64(0.008609360445663267), 70: np.float64(0.004390639554336731), 0: np.float64(0.02860936044566327)} 

err list= [np.float64(0.02833249421897238), np.float64(0.00677050060133208), np.float64(0.07899943540029097), np.float64(0.024609360445663274), np.float64(0.008609360445663267), np.float64(0.004390639554336731), np.float64(0.02860936044566327)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5203056646963848), 3: np.float64(0.33933038290902345), 9: np.float64(0.11703894219685197), 83: np.float64(0.005831252549435032), 79: np.float64(0.005831252549435032), 70: np.float64(0.005831252549435032), 0: np.float64(0.005831252549435032)}
err dic= {1: np.float64(0.2553056646963848), 3: np.float64(0.08833038290902345), 9: np.float64(0.11796105780314801), 83: np.float64(0.04616874745056496), 79: np.float64(0.06216874745056497), 70: np.float64(0.07516874745056497), 0: np.float64(0.04216874745056497)} 

err list= [np.float64(0.2553056646963848), np.float64(0.08833038290902345), np.float64(0.11796105780314801), np.float64(0.04616874745056496), np.float64(0.06216874745056497), np.float64(0.07516874745056497), np.float64(0.04216874745056497)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6765121043076572), 3: np.float64(0.29161362275187974), 9: np.float64(0.0314043478582959), 83: np.float64(0.00011748127054238516), 79: np.float64(0.00011748127054238516), 70: np.float64(0.00011748127054238516), 0: np.float64(0.00011748127054238516)}
err dic= {1: np.float64(0.41151210430765717), 3: np.float64(0.04061362275187974), 9: np.float64(0.20359565214170408), 83: np.float64(0.051882518729457615), 79: np.float64(0.06788251872945762), 70: np.float64(0.08088251872945762), 0: np.float64(0.04788251872945762)} 

err list= [np.float64(0.41151210430765717), np.float64(0.04061362275187974), np.float64(0.20359565214170408), np.float64(0.051882518729457615), np.float64(0.06788251872945762), np.float64(0.08088251872945762), np.float64(0.04788251872945762)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7741011424326985), 3: np.float64(0.21917696559977407), 9: np.float64(0.006715554278790676), 83: np.float64(1.5844221841460975e-06), 79: np.float64(1.5844221841460975e-06), 70: np.float64(1.5844221841460975e-06), 0: np.float64(1.5844221841460975e-06)}
err dic= {1: np.float64(0.5091011424326984), 3: np.float64(0.031823034400225936), 9: np.float64(0.22828444572120932), 83: np.float64(0.05199841557781585), 79: np.float64(0.06799841557781586), 70: np.float64(0.08099841557781585), 0: np.float64(0.04799841557781585)} 

err list= [np.float64(0.5091011424326984), np.float64(0.031823034400225936), np.float64(0.22828444572120932), np.float64(0.05199841557781585), np.float64(0.06799841557781586), np.float64(0.08099841557781585), np.float64(0.04799841557781585)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8431196693587691), 3: np.float64(0.15557128680477764), 9: np.float64(0.0013089882991092516), 83: np.float64(1.3884336071456628e-08), 79: np.float64(1.3884336071456628e-08), 70: np.float64(1.3884336071456628e-08), 0: np.float64(1.3884336071456628e-08)}
err dic= {1: np.float64(0.5781196693587691), 3: np.float64(0.09542871319522236), 9: np.float64(0.23369101170089074), 83: np.float64(0.05199998611566393), 79: np.float64(0.06799998611566394), 70: np.float64(0.08099998611566393), 0: np.float64(0.04799998611566393)} 

err list= [np.float64(0.5781196693587691), np.float64(0.09542871319522236), np.float64(0.23369101170089074), np.float64(0.05199998611566393), np.float64(0.06799998611566394), np.float64(0.08099998611566393), np.float64(0.04799998611566393)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931967339976635), 3: np.float64(0.10655825333388864), 9: np.float64(0.0002450121972727352), 83: np.float64(1.177936864157326e-10), 79: np.float64(1.177936864157326e-10), 70: np.float64(1.177936864157326e-10), 0: np.float64(1.177936864157326e-10)}
err dic= {1: np.float64(0.6281967339976635), 3: np.float64(0.14444174666611137), 9: np.float64(0.23475498780272724), 83: np.float64(0.05199999988220631), 79: np.float64(0.06799999988220631), 70: np.float64(0.08099999988220631), 0: np.float64(0.047999999882206316)} 

err list= [np.float64(0.6281967339976635), np.float64(0.14444174666611137), np.float64(0.23475498780272724), np.float64(0.05199999988220631), np.float64(0.06799999988220631), np.float64(0.08099999988220631), np.float64(0.047999999882206316)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707240571096), 3: np.float64(0.07108431986998921), 9: np.float64(4.495606884942909e-05), 83: np.float64(1.0129314133297565e-12), 79: np.float64(1.0129314133297565e-12), 70: np.float64(1.0129314133297565e-12), 0: np.float64(1.0129314133297565e-12)}
err dic= {1: np.float64(0.6638707240571096), 3: np.float64(0.1799156801300108), 9: np.float64(0.23495504393115055), 83: np.float64(0.051999999998987065), 79: np.float64(0.06799999999898708), 70: np.float64(0.08099999999898708), 0: np.float64(0.04799999999898707)} 

err list= [np.float64(0.6638707240571096), np.float64(0.1799156801300108), np.float64(0.23495504393115055), np.float64(0.051999999998987065), np.float64(0.06799999999898708), np.float64(0.08099999999898708), np.float64(0.04799999999898707)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535429244147408), 3: np.float64(0.04644892580559984), 9: np.float64(8.149779623625685e-06), 83: np.float64(8.81232931345464e-15), 79: np.float64(8.81232931345464e-15), 70: np.float64(8.81232931345464e-15), 0: np.float64(8.81232931345464e-15)}
err dic= {1: np.float64(0.6885429244147407), 3: np.float64(0.20455107419440016), 9: np.float64(0.23499185022037636), 83: np.float64(0.051999999999991185), 79: np.float64(0.06799999999999119), 70: np.float64(0.08099999999999119), 0: np.float64(0.04799999999999119)} 

err list= [np.float64(0.6885429244147407), np.float64(0.20455107419440016), np.float64(0.23499185022037636), np.float64(0.051999999999991185), np.float64(0.06799999999999119), np.float64(0.08099999999999119), np.float64(0.04799999999999119)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386587635772), 3: np.float64(0.02985987660352396), 9: np.float64(1.4646328981753244e-06), 83: np.float64(7.724663246383616e-17), 79: np.float64(7.724663246383616e-17), 70: np.float64(7.724663246383616e-17), 0: np.float64(7.724663246383616e-17)}
err dic= {1: np.float64(0.7051386587635772), 3: np.float64(0.22114012339647604), 9: np.float64(0.2349985353671018), 83: np.float64(0.05199999999999992), 79: np.float64(0.06799999999999992), 70: np.float64(0.08099999999999992), 0: np.float64(0.047999999999999925)} 

err list= [np.float64(0.7051386587635772), np.float64(0.22114012339647604), np.float64(0.2349985353671018), np.float64(0.05199999999999992), np.float64(0.06799999999999992), np.float64(0.08099999999999992), np.float64(0.047999999999999925)]
results for assortment [1, 3, 9, 83, 79, 70] :

err MNL dic= {1: 0.265, 3: 0.251, 9: 0.235, 83: 0.052, 79: 0.068, 70: 0.081, 0: np.float64(0.21829740093736688)} 

err MNL list= [0.265, 0.251, 0.235, 0.052, 0.068, 0.081, np.float64(0.21829740093736688)]
sampled assortment [1, 4, 8, 32, 27, 82] number: 3
#  Learning probs for MM model, A = [1, 4, 8, 32, 27, 82]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [1, 4, 8, 32, 27, 82]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 100]
empirical probabilities from test set: {1: 0.222, 4: 0.23, 8: 0.232, 32: 0.102, 27: 0.12, 82: 0.05, 0: 0.044}
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.1182874377430962), 4: np.float64(0.11009636834764545), 8: np.float64(0.10006735106044846), 32: np.float64(0.16788721071220244), 27: np.float64(0.16788721071220244), 82: np.float64(0.16788721071220244), 0: np.float64(0.16788721071220244)}
err dic= {1: np.float64(0.1037125622569038), 4: np.float64(0.11990363165235456), 8: np.float64(0.13193264893955153), 32: np.float64(0.06588721071220245), 27: np.float64(0.04788721071220245), 82: np.float64(0.11788721071220244), 0: np.float64(0.12388721071220245)} 

err list= [np.float64(0.1037125622569038), np.float64(0.11990363165235456), np.float64(0.13193264893955153), np.float64(0.06588721071220245), np.float64(0.04788721071220245), np.float64(0.11788721071220244), np.float64(0.12388721071220245)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.17230697244049142), 4: np.float64(0.14970073780564166), 8: np.float64(0.12405264052728499), 32: np.float64(0.13848491230664814), 27: np.float64(0.13848491230664814), 82: np.float64(0.13848491230664814), 0: np.float64(0.13848491230664814)}
err dic= {1: np.float64(0.04969302755950858), 4: np.float64(0.08029926219435835), 8: np.float64(0.10794735947271503), 32: np.float64(0.036484912306648146), 27: np.float64(0.018484912306648144), 82: np.float64(0.08848491230664814), 0: np.float64(0.09448491230664814)} 

err list= [np.float64(0.04969302755950858), np.float64(0.08029926219435835), np.float64(0.10794735947271503), np.float64(0.036484912306648146), np.float64(0.018484912306648144), np.float64(0.08848491230664814), np.float64(0.09448491230664814)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.29757493136180546), 4: np.float64(0.22776106079827538), 8: np.float64(0.15851049188131805), 32: np.float64(0.07903837898965085), 27: np.float64(0.07903837898965085), 82: np.float64(0.07903837898965085), 0: np.float64(0.07903837898965085)}
err dic= {1: np.float64(0.07557493136180546), 4: np.float64(0.0022389392017246323), 8: np.float64(0.07348950811868196), 32: np.float64(0.02296162101034914), 27: np.float64(0.04096162101034914), 82: np.float64(0.02903837898965085), 0: np.float64(0.035038378989650856)} 

err list= [np.float64(0.07557493136180546), np.float64(0.0022389392017246323), np.float64(0.07348950811868196), np.float64(0.02296162101034914), np.float64(0.04096162101034914), np.float64(0.02903837898965085), np.float64(0.035038378989650856)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5489599009493322), 4: np.float64(0.29900591045465463), 8: np.float64(0.1259441186450955), 32: np.float64(0.006522517487729529), 27: np.float64(0.006522517487729529), 82: np.float64(0.006522517487729529), 0: np.float64(0.006522517487729529)}
err dic= {1: np.float64(0.32695990094933225), 4: np.float64(0.06900591045465462), 8: np.float64(0.10605588135490451), 32: np.float64(0.09547748251227046), 27: np.float64(0.11347748251227047), 82: np.float64(0.043477482512270474), 0: np.float64(0.03747748251227047)} 

err list= [np.float64(0.32695990094933225), np.float64(0.06900591045465462), np.float64(0.10605588135490451), np.float64(0.09547748251227046), np.float64(0.11347748251227047), np.float64(0.043477482512270474), np.float64(0.03747748251227047)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7379327799013197), 4: np.float64(0.22450398605974614), 8: np.float64(0.037006704408466026), 32: np.float64(0.0001391324076175437), 27: np.float64(0.0001391324076175437), 82: np.float64(0.0001391324076175437), 0: np.float64(0.0001391324076175437)}
err dic= {1: np.float64(0.5159327799013197), 4: np.float64(0.005496013940253869), 8: np.float64(0.194993295591534), 32: np.float64(0.10186086759238246), 27: np.float64(0.11986086759238246), 82: np.float64(0.04986086759238246), 0: np.float64(0.04386086759238245)} 

err list= [np.float64(0.5159327799013197), np.float64(0.005496013940253869), np.float64(0.194993295591534), np.float64(0.10186086759238246), np.float64(0.11986086759238246), np.float64(0.04986086759238246), np.float64(0.04386086759238245)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8494805892473118), 4: np.float64(0.14196075286601056), 8: np.float64(0.008550557556916295), 32: np.float64(2.0250824402619015e-06), 27: np.float64(2.0250824402619015e-06), 82: np.float64(2.0250824402619015e-06), 0: np.float64(2.0250824402619015e-06)}
err dic= {1: np.float64(0.6274805892473119), 4: np.float64(0.08803924713398945), 8: np.float64(0.2234494424430837), 32: np.float64(0.10199797491755973), 27: np.float64(0.11999797491755973), 82: np.float64(0.049997974917559744), 0: np.float64(0.04399797491755974)} 

err list= [np.float64(0.6274805892473119), np.float64(0.08803924713398945), np.float64(0.2234494424430837), np.float64(0.10199797491755973), np.float64(0.11999797491755973), np.float64(0.049997974917559744), np.float64(0.04399797491755974)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159710963711151), 4: np.float64(0.08226342636476729), 8: np.float64(0.0017654021937096036), 32: np.float64(1.8767602034974545e-08), 27: np.float64(1.8767602034974545e-08), 82: np.float64(1.8767602034974545e-08), 0: np.float64(1.8767602034974545e-08)}
err dic= {1: np.float64(0.6939710963711151), 4: np.float64(0.14773657363523274), 8: np.float64(0.2302345978062904), 32: np.float64(0.10199998123239795), 27: np.float64(0.11999998123239795), 82: np.float64(0.04999998123239797), 0: np.float64(0.04399998123239796)} 

err list= [np.float64(0.6939710963711151), np.float64(0.14773657363523274), np.float64(0.2302345978062904), np.float64(0.10199998123239795), np.float64(0.11999998123239795), np.float64(0.04999998123239797), np.float64(0.04399998123239796)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545811647486212), 4: np.float64(0.04507527200789388), 8: np.float64(0.00034356258213180386), 32: np.float64(1.6533824763419278e-10), 27: np.float64(1.6533824763419278e-10), 82: np.float64(1.6533824763419278e-10), 0: np.float64(1.6533824763419278e-10)}
err dic= {1: np.float64(0.7325811647486212), 4: np.float64(0.18492472799210613), 8: np.float64(0.2316564374178682), 32: np.float64(0.10199999983466175), 27: np.float64(0.11999999983466175), 82: np.float64(0.04999999983466175), 0: np.float64(0.04399999983466175)} 

err list= [np.float64(0.7325811647486212), np.float64(0.18492472799210613), np.float64(0.2316564374178682), np.float64(0.10199999983466175), np.float64(0.11999999983466175), np.float64(0.04999999983466175), np.float64(0.04399999983466175)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9761795795604401), 4: np.float64(0.023755777298286526), 8: np.float64(6.46431354451248e-05), 32: np.float64(1.45706299676164e-12), 27: np.float64(1.45706299676164e-12), 82: np.float64(1.45706299676164e-12), 0: np.float64(1.45706299676164e-12)}
err dic= {1: np.float64(0.7541795795604401), 4: np.float64(0.2062442227017135), 8: np.float64(0.23193535686455488), 32: np.float64(0.10199999999854294), 27: np.float64(0.11999999999854294), 82: np.float64(0.04999999999854294), 0: np.float64(0.043999999998542934)} 

err list= [np.float64(0.7541795795604401), np.float64(0.2062442227017135), np.float64(0.23193535686455488), np.float64(0.10199999999854294), np.float64(0.11999999999854294), np.float64(0.04999999999854294), np.float64(0.043999999998542934)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141691253223), 4: np.float64(0.012173924284655625), 8: np.float64(1.190658997042886e-05), 32: np.float64(1.2876236444336182e-14), 27: np.float64(1.2876236444336182e-14), 82: np.float64(1.2876236444336182e-14), 0: np.float64(1.2876236444336182e-14)}
err dic= {1: np.float64(0.7658141691253223), 4: np.float64(0.21782607571534437), 8: np.float64(0.23198809341002957), 32: np.float64(0.10199999999998711), 27: np.float64(0.11999999999998712), 82: np.float64(0.049999999999987124), 0: np.float64(0.04399999999998712)} 

err list= [np.float64(0.7658141691253223), np.float64(0.21782607571534437), np.float64(0.23198809341002957), np.float64(0.10199999999998711), np.float64(0.11999999999998712), np.float64(0.049999999999987124), np.float64(0.04399999999998712)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855163026794), 4: np.float64(0.0061123224453547564), 8: np.float64(2.161251964873196e-06), 32: np.float64(1.139920694549718e-16), 27: np.float64(1.139920694549718e-16), 82: np.float64(1.139920694549718e-16), 0: np.float64(1.139920694549718e-16)}
err dic= {1: np.float64(0.7718855163026794), 4: np.float64(0.22388767755464525), 8: np.float64(0.23199783874803515), 32: np.float64(0.10199999999999988), 27: np.float64(0.11999999999999988), 82: np.float64(0.04999999999999989), 0: np.float64(0.043999999999999886)} 

err list= [np.float64(0.7718855163026794), np.float64(0.22388767755464525), np.float64(0.23199783874803515), np.float64(0.10199999999999988), np.float64(0.11999999999999988), np.float64(0.04999999999999989), np.float64(0.043999999999999886)]
results for assortment [1, 4, 8, 32, 27, 82] :

err MNL dic= {1: 0.222, 4: 0.23, 8: 0.232, 32: 0.102, 27: 0.12, 82: 0.05, 0: np.float64(0.21605096999011808)} 

err MNL list= [0.222, 0.23, 0.232, 0.102, 0.12, 0.05, np.float64(0.21605096999011808)]
sampled assortment [9, 4, 6, 51, 82, 41] number: 4
#  Learning probs for MM model, A = [9, 4, 6, 51, 82, 41]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
#  Learning probs for MM model, A = [9, 4, 6, 51, 82, 41]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 10, 100]
empirical probabilities from test set: {9: 0.221, 4: 0.245, 6: 0.256, 51: 0.086, 82: 0.04, 41: 0.093, 0: 0.059}
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.15968267884427334), 4: np.float64(0.10324391431205762), 6: np.float64(0.09834269146657701), 51: np.float64(0.15968267884427334), 82: np.float64(0.15968267884427334), 41: np.float64(0.15968267884427334), 0: np.float64(0.15968267884427334)}
err dic= {9: np.float64(0.06131732115572666), 4: np.float64(0.14175608568794237), 6: np.float64(0.157657308533423), 51: np.float64(0.07368267884427335), 82: np.float64(0.11968267884427333), 41: np.float64(0.06668267884427334), 0: np.float64(0.10068267884427334)} 

err list= [np.float64(0.06131732115572666), np.float64(0.14175608568794237), np.float64(0.157657308533423), np.float64(0.07368267884427335), np.float64(0.11968267884427333), np.float64(0.06668267884427334), np.float64(0.10068267884427334)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.14477221086488545), 4: np.float64(0.14470880419291093), 6: np.float64(0.1314301414826631), 51: np.float64(0.14477221086488545), 82: np.float64(0.14477221086488545), 41: np.float64(0.14477221086488545), 0: np.float64(0.14477221086488545)}
err dic= {9: np.float64(0.07622778913511455), 4: np.float64(0.10029119580708906), 6: np.float64(0.1245698585173369), 51: np.float64(0.05877221086488546), 82: np.float64(0.10477221086488545), 41: np.float64(0.051772210864885454), 0: np.float64(0.08577221086488546)} 

err list= [np.float64(0.07622778913511455), np.float64(0.10029119580708906), np.float64(0.1245698585173369), np.float64(0.05877221086488546), np.float64(0.10477221086488545), np.float64(0.051772210864885454), np.float64(0.08577221086488546)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.10952331172693312), 4: np.float64(0.24732135983824913), 6: np.float64(0.2050620815270864), 51: np.float64(0.10952331172693312), 82: np.float64(0.10952331172693312), 41: np.float64(0.10952331172693312), 0: np.float64(0.10952331172693312)}
err dic= {9: np.float64(0.11147668827306688), 4: np.float64(0.002321359838249132), 6: np.float64(0.050937918472913596), 51: np.float64(0.02352331172693313), 82: np.float64(0.06952331172693313), 41: np.float64(0.016523311726933124), 0: np.float64(0.050523311726933126)} 

err list= [np.float64(0.11147668827306688), np.float64(0.002321359838249132), np.float64(0.050937918472913596), np.float64(0.02352331172693313), np.float64(0.06952331172693313), np.float64(0.016523311726933124), np.float64(0.050523311726933126)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.02718651887406421), 4: np.float64(0.5239986893561825), 6: np.float64(0.3400687162734943), 51: np.float64(0.02718651887406421), 82: np.float64(0.02718651887406421), 41: np.float64(0.02718651887406421), 0: np.float64(0.02718651887406421)}
err dic= {9: np.float64(0.1938134811259358), 4: np.float64(0.27899868935618255), 6: np.float64(0.08406871627349427), 51: np.float64(0.05881348112593578), 82: np.float64(0.012813481125935791), 41: np.float64(0.0658134811259358), 0: np.float64(0.03181348112593579)} 

err list= [np.float64(0.1938134811259358), np.float64(0.27899868935618255), np.float64(0.08406871627349427), np.float64(0.05881348112593578), np.float64(0.012813481125935791), np.float64(0.0658134811259358), np.float64(0.03181348112593579)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.0009800080070977988), 4: np.float64(0.6944778629495796), 6: np.float64(0.30062209701493253), 51: np.float64(0.0009800080070977988), 82: np.float64(0.0009800080070977988), 41: np.float64(0.0009800080070977988), 0: np.float64(0.0009800080070977988)}
err dic= {9: np.float64(0.2200199919929022), 4: np.float64(0.4494778629495796), 6: np.float64(0.04462209701493253), 51: np.float64(0.0850199919929022), 82: np.float64(0.0390199919929022), 41: np.float64(0.0920199919929022), 0: np.float64(0.0580199919929022)} 

err list= [np.float64(0.2200199919929022), np.float64(0.4494778629495796), np.float64(0.04462209701493253), np.float64(0.0850199919929022), np.float64(0.0390199919929022), np.float64(0.0920199919929022), np.float64(0.0580199919929022)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(2.8462592965198254e-05), 4: np.float64(0.7789131230016254), 6: np.float64(0.22094456403354873), 51: np.float64(2.8462592965198254e-05), 82: np.float64(2.8462592965198254e-05), 41: np.float64(2.8462592965198254e-05), 0: np.float64(2.8462592965198254e-05)}
err dic= {9: np.float64(0.2209715374070348), 4: np.float64(0.5339131230016254), 6: np.float64(0.035055435966451276), 51: np.float64(0.0859715374070348), 82: np.float64(0.0399715374070348), 41: np.float64(0.0929715374070348), 0: np.float64(0.0589715374070348)} 

err list= [np.float64(0.2209715374070348), np.float64(0.5339131230016254), np.float64(0.035055435966451276), np.float64(0.0859715374070348), np.float64(0.0399715374070348), np.float64(0.0929715374070348), np.float64(0.0589715374070348)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(6.694988652065483e-07), 4: np.float64(0.8441491615422926), 6: np.float64(0.15584749096338146), 51: np.float64(6.694988652065483e-07), 82: np.float64(6.694988652065483e-07), 41: np.float64(6.694988652065483e-07), 0: np.float64(6.694988652065483e-07)}
err dic= {9: np.float64(0.2209993305011348), 4: np.float64(0.5991491615422926), 6: np.float64(0.10015250903661854), 51: np.float64(0.08599933050113479), 82: np.float64(0.03999933050113479), 41: np.float64(0.09299933050113479), 0: np.float64(0.05899933050113479)} 

err list= [np.float64(0.2209993305011348), np.float64(0.5991491615422926), np.float64(0.10015250903661854), np.float64(0.08599933050113479), np.float64(0.03999933050113479), np.float64(0.09299933050113479), np.float64(0.05899933050113479)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(1.5266998614534814e-08), 4: np.float64(0.8934014088900368), 6: np.float64(0.10659851477496991), 51: np.float64(1.5266998614534814e-08), 82: np.float64(1.5266998614534814e-08), 41: np.float64(1.5266998614534814e-08), 0: np.float64(1.5266998614534814e-08)}
err dic= {9: np.float64(0.2209999847330014), 4: np.float64(0.6484014088900368), 6: np.float64(0.1494014852250301), 51: np.float64(0.08599998473300138), 82: np.float64(0.039999984733001384), 41: np.float64(0.09299998473300139), 0: np.float64(0.05899998473300138)} 

err list= [np.float64(0.2209999847330014), np.float64(0.6484014088900368), np.float64(0.1494014852250301), np.float64(0.08599998473300138), np.float64(0.039999984733001384), np.float64(0.09299998473300139), np.float64(0.05899998473300138)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(3.5027300262155916e-10), 4: np.float64(0.9289099835951008), 6: np.float64(0.07109001465353457), 51: np.float64(3.5027300262155916e-10), 82: np.float64(3.5027300262155916e-10), 41: np.float64(3.5027300262155916e-10), 0: np.float64(3.5027300262155916e-10)}
err dic= {9: np.float64(0.220999999649727), 4: np.float64(0.6839099835951008), 6: np.float64(0.18490998534646544), 51: np.float64(0.08599999964972699), 82: np.float64(0.039999999649726996), 41: np.float64(0.092999999649727), 0: np.float64(0.05899999964972699)} 

err list= [np.float64(0.220999999649727), np.float64(0.6839099835951008), np.float64(0.18490998534646544), np.float64(0.08599999964972699), np.float64(0.039999999649726996), np.float64(0.092999999649727), np.float64(0.05899999964972699)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(8.100031505892972e-12), 4: np.float64(0.95355028177427), 6: np.float64(0.04644971818522959), 51: np.float64(8.100031505892972e-12), 82: np.float64(8.100031505892972e-12), 41: np.float64(8.100031505892972e-12), 0: np.float64(8.100031505892972e-12)}
err dic= {9: np.float64(0.22099999999189998), 4: np.float64(0.70855028177427), 6: np.float64(0.20955028181477042), 51: np.float64(0.08599999999189996), 82: np.float64(0.039999999991899966), 41: np.float64(0.09299999999189996), 0: np.float64(0.05899999999189996)} 

err list= [np.float64(0.22099999999189998), np.float64(0.70855028177427), np.float64(0.20955028181477042), np.float64(0.08599999999189996), np.float64(0.039999999991899966), np.float64(0.09299999999189996), np.float64(0.05899999999189996)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(1.8843288905954536e-13), 4: np.float64(0.9701400142421136), 6: np.float64(0.029859985756944145), 51: np.float64(1.8843288905954536e-13), 82: np.float64(1.8843288905954536e-13), 41: np.float64(1.8843288905954536e-13), 0: np.float64(1.8843288905954536e-13)}
err dic= {9: np.float64(0.22099999999981157), 4: np.float64(0.7251400142421136), 6: np.float64(0.22614001424305585), 51: np.float64(0.08599999999981156), 82: np.float64(0.03999999999981157), 41: np.float64(0.09299999999981157), 0: np.float64(0.058999999999811564)} 

err list= [np.float64(0.22099999999981157), np.float64(0.7251400142421136), np.float64(0.22614001424305585), np.float64(0.08599999999981156), np.float64(0.03999999999981157), np.float64(0.09299999999981157), np.float64(0.058999999999811564)]
results for assortment [9, 4, 6, 51, 82, 41] :

err MNL dic= {9: 0.221, 4: 0.245, 6: 0.256, 51: 0.086, 82: 0.04, 41: 0.093, 0: np.float64(0.20371542664985287)} 

err MNL list= [0.221, 0.245, 0.256, 0.086, 0.04, 0.093, np.float64(0.20371542664985287)]
sampled assortment [5, 9, 6, 39, 80, 68] number: 5
#  Learning probs for MM model, A = [5, 9, 6, 39, 80, 68]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 100]
#  Learning probs for MM model, A = [5, 9, 6, 39, 80, 68]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100]
empirical probabilities from test set: {5: 0.245, 9: 0.228, 6: 0.258, 39: 0.1, 80: 0.063, 68: 0.056, 0: 0.05}
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.12647748545563012), 9: np.float64(0.11484898112571608), 6: np.float64(0.12335474521329486), 39: np.float64(0.15882969705133354), 80: np.float64(0.15882969705133354), 68: np.float64(0.15882969705133354), 0: np.float64(0.15882969705133354)}
err dic= {5: np.float64(0.11852251454436988), 9: np.float64(0.11315101887428393), 6: np.float64(0.13464525478670514), 39: np.float64(0.058829697051333535), 80: np.float64(0.09582969705133354), 68: np.float64(0.10282969705133355), 0: np.float64(0.10882969705133354)} 

err list= [np.float64(0.11852251454436988), np.float64(0.11315101887428393), np.float64(0.13464525478670514), np.float64(0.058829697051333535), np.float64(0.09582969705133354), np.float64(0.10282969705133355), np.float64(0.10882969705133354)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.1733857111577953), 9: np.float64(0.14330201012440097), 6: np.float64(0.16492959024127682), 39: np.float64(0.1295956721191312), 80: np.float64(0.1295956721191312), 68: np.float64(0.1295956721191312), 0: np.float64(0.1295956721191312)}
err dic= {5: np.float64(0.07161428884220469), 9: np.float64(0.08469798987559904), 6: np.float64(0.09307040975872319), 39: np.float64(0.029595672119131194), 80: np.float64(0.0665956721191312), 68: np.float64(0.0735956721191312), 0: np.float64(0.0795956721191312)} 

err list= [np.float64(0.07161428884220469), np.float64(0.08469798987559904), np.float64(0.09307040975872319), np.float64(0.029595672119131194), np.float64(0.0665956721191312), np.float64(0.0735956721191312), np.float64(0.0795956721191312)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.26937841916239896), 9: np.float64(0.1857477769847532), 6: np.float64(0.2437436732695132), 39: np.float64(0.0752825326458353), 80: np.float64(0.0752825326458353), 68: np.float64(0.0752825326458353), 0: np.float64(0.0752825326458353)}
err dic= {5: np.float64(0.024378419162398968), 9: np.float64(0.04225222301524681), 6: np.float64(0.014256326730486796), 39: np.float64(0.024717467354164704), 80: np.float64(0.0122825326458353), 68: np.float64(0.0192825326458353), 0: np.float64(0.0252825326458353)} 

err list= [np.float64(0.024378419162398968), np.float64(0.04225222301524681), np.float64(0.014256326730486796), np.float64(0.024717467354164704), np.float64(0.0122825326458353), np.float64(0.0192825326458353), np.float64(0.0252825326458353)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.44280146494300976), 9: np.float64(0.18060921041011252), 6: np.float64(0.34485412764278106), 39: np.float64(0.007933799251024592), 80: np.float64(0.007933799251024592), 68: np.float64(0.007933799251024592), 0: np.float64(0.007933799251024592)}
err dic= {5: np.float64(0.19780146494300976), 9: np.float64(0.04739078958988749), 6: np.float64(0.08685412764278105), 39: np.float64(0.09206620074897541), 80: np.float64(0.055066200748975405), 68: np.float64(0.04806620074897541), 0: np.float64(0.04206620074897541)} 

err list= [np.float64(0.19780146494300976), np.float64(0.04739078958988749), np.float64(0.08685412764278105), np.float64(0.09206620074897541), np.float64(0.055066200748975405), np.float64(0.04806620074897541), np.float64(0.04206620074897541)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5648994772173784), 9: np.float64(0.09153101115357967), 6: np.float64(0.3426288525879779), 39: np.float64(0.00023516476026563127), 80: np.float64(0.00023516476026563127), 68: np.float64(0.00023516476026563127), 0: np.float64(0.00023516476026563127)}
err dic= {5: np.float64(0.31989947721737844), 9: np.float64(0.13646898884642034), 6: np.float64(0.08462885258797787), 39: np.float64(0.09976483523973437), 80: np.float64(0.06276483523973436), 68: np.float64(0.05576483523973437), 0: np.float64(0.04976483523973437)} 

err list= [np.float64(0.31989947721737844), np.float64(0.13646898884642034), np.float64(0.08462885258797787), np.float64(0.09976483523973437), np.float64(0.06276483523973436), np.float64(0.05576483523973437), np.float64(0.04976483523973437)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6518715714233121), 9: np.float64(0.04018468873261342), 6: np.float64(0.3079223270230981), 39: np.float64(5.35320524419278e-06), 80: np.float64(5.35320524419278e-06), 68: np.float64(5.35320524419278e-06), 0: np.float64(5.35320524419278e-06)}
err dic= {5: np.float64(0.4068715714233121), 9: np.float64(0.1878153112673866), 6: np.float64(0.04992232702309807), 39: np.float64(0.09999464679475581), 80: np.float64(0.0629946467947558), 68: np.float64(0.055994646794755805), 0: np.float64(0.049994646794755807)} 

err list= [np.float64(0.4068715714233121), np.float64(0.1878153112673866), np.float64(0.04992232702309807), np.float64(0.09999464679475581), np.float64(0.0629946467947558), np.float64(0.055994646794755805), np.float64(0.049994646794755807)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7191000691019044), 9: np.float64(0.016357481235902766), 6: np.float64(0.2645421315675541), 39: np.float64(7.952365983655834e-08), 80: np.float64(7.952365983655834e-08), 68: np.float64(7.952365983655834e-08), 0: np.float64(7.952365983655834e-08)}
err dic= {5: np.float64(0.4741000691019044), 9: np.float64(0.21164251876409723), 6: np.float64(0.006542131567554066), 39: np.float64(0.09999992047634017), 80: np.float64(0.06299992047634016), 68: np.float64(0.05599992047634016), 0: np.float64(0.049999920476340165)} 

err list= [np.float64(0.4741000691019044), np.float64(0.21164251876409723), np.float64(0.006542131567554066), np.float64(0.09999992047634017), np.float64(0.06299992047634016), np.float64(0.05599992047634016), np.float64(0.049999920476340165)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723569118525044), 9: np.float64(0.006359123469909045), 6: np.float64(0.22128396013386556), 39: np.float64(1.1359301401166263e-09), 80: np.float64(1.1359301401166263e-09), 68: np.float64(1.1359301401166263e-09), 0: np.float64(1.1359301401166263e-09)}
err dic= {5: np.float64(0.5273569118525044), 9: np.float64(0.22164087653009096), 6: np.float64(0.03671603986613445), 39: np.float64(0.09999999886406986), 80: np.float64(0.06299999886406986), 68: np.float64(0.05599999886406986), 0: np.float64(0.04999999886406986)} 

err list= [np.float64(0.5273569118525044), np.float64(0.22164087653009096), np.float64(0.03671603986613445), np.float64(0.09999999886406986), np.float64(0.06299999886406986), np.float64(0.05599999886406986), np.float64(0.04999999886406986)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.8156057221843659), 9: np.float64(0.002408042341010769), 6: np.float64(0.18198623540897332), 39: np.float64(1.641240346449771e-11), 80: np.float64(1.641240346449771e-11), 68: np.float64(1.641240346449771e-11), 0: np.float64(1.641240346449771e-11)}
err dic= {5: np.float64(0.5706057221843659), 9: np.float64(0.22559195765898923), 6: np.float64(0.07601376459102668), 39: np.float64(0.0999999999835876), 80: np.float64(0.0629999999835876), 68: np.float64(0.055999999983587595), 0: np.float64(0.0499999999835876)} 

err list= [np.float64(0.5706057221843659), np.float64(0.22559195765898923), np.float64(0.07601376459102668), np.float64(0.0999999999835876), np.float64(0.0629999999835876), np.float64(0.055999999983587595), np.float64(0.0499999999835876)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511869021352355), 9: np.float64(0.0008989932663955852), 6: np.float64(0.14791410459740797), 39: np.float64(2.401100140134195e-13), 80: np.float64(2.401100140134195e-13), 68: np.float64(2.401100140134195e-13), 0: np.float64(2.401100140134195e-13)}
err dic= {5: np.float64(0.6061869021352355), 9: np.float64(0.22710100673360442), 6: np.float64(0.11008589540259203), 39: np.float64(0.09999999999975989), 80: np.float64(0.06299999999975989), 68: np.float64(0.055999999999759895), 0: np.float64(0.049999999999759896)} 

err list= [np.float64(0.6061869021352355), np.float64(0.22710100673360442), np.float64(0.11008589540259203), np.float64(0.09999999999975989), np.float64(0.06299999999975989), np.float64(0.055999999999759895), np.float64(0.049999999999759896)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036406466368), 9: np.float64(0.0003331497555675368), 6: np.float64(0.11916320959778123), 39: np.float64(3.5493213903654375e-15), 80: np.float64(3.5493213903654375e-15), 68: np.float64(3.5493213903654375e-15), 0: np.float64(3.5493213903654375e-15)}
err dic= {5: np.float64(0.6355036406466368), 9: np.float64(0.22766685024443248), 6: np.float64(0.13883679040221877), 39: np.float64(0.09999999999999645), 80: np.float64(0.06299999999999645), 68: np.float64(0.05599999999999645), 0: np.float64(0.04999999999999645)} 

err list= [np.float64(0.6355036406466368), np.float64(0.22766685024443248), np.float64(0.13883679040221877), np.float64(0.09999999999999645), np.float64(0.06299999999999645), np.float64(0.05599999999999645), np.float64(0.04999999999999645)]
results for assortment [5, 9, 6, 39, 80, 68] :

err MNL dic= {5: 0.245, 9: 0.228, 6: 0.258, 39: 0.1, 80: 0.063, 68: 0.056, 0: np.float64(0.2117252931323283)} 

err MNL list= [0.245, 0.228, 0.258, 0.1, 0.063, 0.056, np.float64(0.2117252931323283)]
sampled assortment [6, 3, 8, 15, 78, 97] number: 6
#  Learning probs for MM model, A = [6, 3, 8, 15, 78, 97]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [6, 3, 8, 15, 78, 97]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
empirical probabilities from test set: {6: 0.221, 3: 0.235, 8: 0.238, 15: 0.173, 78: 0.056, 97: 0.039, 0: 0.038}
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.10572087201395299), 3: np.float64(0.11360197143930176), 8: np.float64(0.10071220922709312), 15: np.float64(0.16999123682991327), 78: np.float64(0.16999123682991327), 97: np.float64(0.16999123682991327), 0: np.float64(0.16999123682991327)}
err dic= {6: np.float64(0.11527912798604702), 3: np.float64(0.12139802856069823), 8: np.float64(0.13728779077290687), 15: np.float64(0.00300876317008672), 78: np.float64(0.11399123682991327), 97: np.float64(0.13099123682991326), 0: np.float64(0.13199123682991326)} 

err list= [np.float64(0.11527912798604702), np.float64(0.12139802856069823), np.float64(0.13728779077290687), np.float64(0.00300876317008672), np.float64(0.11399123682991327), np.float64(0.13099123682991326), np.float64(0.13199123682991326)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.139119131157314), 3: np.float64(0.16024273764811536), 8: np.float64(0.12636832877735035), 15: np.float64(0.14356745060430795), 78: np.float64(0.14356745060430795), 97: np.float64(0.14356745060430795), 0: np.float64(0.14356745060430795)}
err dic= {6: np.float64(0.081880868842686), 3: np.float64(0.07475726235188462), 8: np.float64(0.11163167122264964), 15: np.float64(0.029432549395692037), 78: np.float64(0.08756745060430796), 97: np.float64(0.10456745060430794), 0: np.float64(0.10556745060430794)} 

err list= [np.float64(0.081880868842686), np.float64(0.07475726235188462), np.float64(0.11163167122264964), np.float64(0.029432549395692037), np.float64(0.08756745060430796), np.float64(0.10456745060430794), np.float64(0.10556745060430794)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.2042084331477853), 3: np.float64(0.2678161184896051), 8: np.float64(0.1691797788126069), 15: np.float64(0.08969891738750141), 78: np.float64(0.08969891738750141), 97: np.float64(0.08969891738750141), 0: np.float64(0.08969891738750141)}
err dic= {6: np.float64(0.016791566852214695), 3: np.float64(0.03281611848960514), 8: np.float64(0.06882022118739309), 15: np.float64(0.08330108261249858), 78: np.float64(0.03369891738750141), 97: np.float64(0.05069891738750141), 0: np.float64(0.05169891738750141)} 

err list= [np.float64(0.016791566852214695), np.float64(0.03281611848960514), np.float64(0.06882022118739309), np.float64(0.08330108261249858), np.float64(0.03369891738750141), np.float64(0.05069891738750141), np.float64(0.05169891738750141)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.27412879623423203), 3: np.float64(0.5084527575520718), 8: np.float64(0.17416756061534758), 15: np.float64(0.010812721399587085), 78: np.float64(0.010812721399587085), 97: np.float64(0.010812721399587085), 0: np.float64(0.010812721399587085)}
err dic= {6: np.float64(0.05312879623423203), 3: np.float64(0.27345275755207177), 8: np.float64(0.06383243938465241), 15: np.float64(0.1621872786004129), 78: np.float64(0.04518727860041292), 97: np.float64(0.028187278600412917), 0: np.float64(0.027187278600412916)} 

err list= [np.float64(0.05312879623423203), np.float64(0.27345275755207177), np.float64(0.06383243938465241), np.float64(0.1621872786004129), np.float64(0.04518727860041292), np.float64(0.028187278600412917), np.float64(0.027187278600412916)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.2110390939237753), 3: np.float64(0.7037556543032081), 8: np.float64(0.08390964535911455), 15: np.float64(0.0003239016034760089), 78: np.float64(0.0003239016034760089), 97: np.float64(0.0003239016034760089), 0: np.float64(0.0003239016034760089)}
err dic= {6: np.float64(0.009960906076224713), 3: np.float64(0.4687556543032081), 8: np.float64(0.15409035464088544), 15: np.float64(0.17267609839652398), 78: np.float64(0.055676098396523994), 97: np.float64(0.03867609839652399), 0: np.float64(0.03767609839652399)} 

err list= [np.float64(0.009960906076224713), np.float64(0.4687556543032081), np.float64(0.15409035464088544), np.float64(0.17267609839652398), np.float64(0.055676098396523994), np.float64(0.03867609839652399), np.float64(0.03767609839652399)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13672676587564925), 3: np.float64(0.8300140138449809), 8: np.float64(0.033227017181971845), 15: np.float64(8.050774349495225e-06), 78: np.float64(8.050774349495225e-06), 97: np.float64(8.050774349495225e-06), 0: np.float64(8.050774349495225e-06)}
err dic= {6: np.float64(0.08427323412435075), 3: np.float64(0.5950140138449809), 8: np.float64(0.20477298281802814), 15: np.float64(0.1729919492256505), 78: np.float64(0.055991949225650504), 97: np.float64(0.0389919492256505), 0: np.float64(0.0379919492256505)} 

err list= [np.float64(0.08427323412435075), np.float64(0.5950140138449809), np.float64(0.20477298281802814), np.float64(0.1729919492256505), np.float64(0.055991949225650504), np.float64(0.0389919492256505), np.float64(0.0379919492256505)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.08066507455791389), 3: np.float64(0.9074954187261305), 8: np.float64(0.011838994474286765), 15: np.float64(1.2806041725720404e-07), 78: np.float64(1.2806041725720404e-07), 97: np.float64(1.2806041725720404e-07), 0: np.float64(1.2806041725720404e-07)}
err dic= {6: np.float64(0.14033492544208612), 3: np.float64(0.6724954187261305), 8: np.float64(0.22616100552571322), 15: np.float64(0.17299987193958272), 78: np.float64(0.055999871939582745), 97: np.float64(0.03899987193958274), 0: np.float64(0.03799987193958274)} 

err list= [np.float64(0.14033492544208612), np.float64(0.6724954187261305), np.float64(0.22616100552571322), np.float64(0.17299987193958272), np.float64(0.055999871939582745), np.float64(0.03899987193958274), np.float64(0.03799987193958274)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.04464839979783241), 3: np.float64(0.9514153815779933), 8: np.float64(0.0039362109664764925), 15: np.float64(1.914424436343585e-09), 78: np.float64(1.914424436343585e-09), 97: np.float64(1.914424436343585e-09), 0: np.float64(1.914424436343585e-09)}
err dic= {6: np.float64(0.17635160020216759), 3: np.float64(0.7164153815779933), 8: np.float64(0.23406378903352348), 15: np.float64(0.17299999808557556), 78: np.float64(0.05599999808557556), 97: np.float64(0.03899999808557556), 0: np.float64(0.03799999808557556)} 

err list= [np.float64(0.17635160020216759), np.float64(0.7164153815779933), np.float64(0.23406378903352348), np.float64(0.17299999808557556), np.float64(0.05599999808557556), np.float64(0.03899999808557556), np.float64(0.03799999808557556)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023650013514278007), 3: np.float64(0.9750994306904143), 8: np.float64(0.0012505556819055168), 15: np.float64(2.835066151595426e-11), 78: np.float64(2.835066151595426e-11), 97: np.float64(2.835066151595426e-11), 0: np.float64(2.835066151595426e-11)}
err dic= {6: np.float64(0.197349986485722), 3: np.float64(0.7400994306904143), 8: np.float64(0.23674944431809447), 15: np.float64(0.17299999997164933), 78: np.float64(0.05599999997164934), 97: np.float64(0.03899999997164934), 0: np.float64(0.03799999997164934)} 

err list= [np.float64(0.197349986485722), np.float64(0.7400994306904143), np.float64(0.23674944431809447), np.float64(0.17299999997164933), np.float64(0.05599999997164934), np.float64(0.03899999997164934), np.float64(0.03799999997164934)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.012148820459777922), 3: np.float64(0.9874656934946061), 8: np.float64(0.0003854860439428213), 15: np.float64(4.1811741769013487e-13), 78: np.float64(4.1811741769013487e-13), 97: np.float64(4.1811741769013487e-13), 0: np.float64(4.1811741769013487e-13)}
err dic= {6: np.float64(0.2088511795402221), 3: np.float64(0.7524656934946061), 8: np.float64(0.23761451395605718), 15: np.float64(0.17299999999958188), 78: np.float64(0.055999999999581884), 97: np.float64(0.03899999999958188), 0: np.float64(0.03799999999958188)} 

err list= [np.float64(0.2088511795402221), np.float64(0.7524656934946061), np.float64(0.23761451395605718), np.float64(0.17299999999958188), np.float64(0.055999999999581884), np.float64(0.03899999999958188), np.float64(0.03799999999958188)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.006106510940607511), 3: np.float64(0.993777071539458), 8: np.float64(0.00011641751990941849), 15: np.float64(6.149345943359326e-15), 78: np.float64(6.149345943359326e-15), 97: np.float64(6.149345943359326e-15), 0: np.float64(6.149345943359326e-15)}
err dic= {6: np.float64(0.21489348905939248), 3: np.float64(0.7587770715394581), 8: np.float64(0.23788358248009056), 15: np.float64(0.17299999999999383), 78: np.float64(0.05599999999999385), 97: np.float64(0.03899999999999385), 0: np.float64(0.03799999999999385)} 

err list= [np.float64(0.21489348905939248), np.float64(0.7587770715394581), np.float64(0.23788358248009056), np.float64(0.17299999999999383), np.float64(0.05599999999999385), np.float64(0.03899999999999385), np.float64(0.03799999999999385)]
results for assortment [6, 3, 8, 15, 78, 97] :

err MNL dic= {6: 0.221, 3: 0.235, 8: 0.238, 15: 0.173, 78: 0.056, 97: 0.039, 0: np.float64(0.22226755504658788)} 

err MNL list= [0.221, 0.235, 0.238, 0.173, 0.056, 0.039, np.float64(0.22226755504658788)]
sampled assortment [8, 2, 4, 95, 11, 22] number: 7
#  Learning probs for MM model, A = [8, 2, 4, 95, 11, 22]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
#  Learning probs for MM model, A = [8, 2, 4, 95, 11, 22]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 11: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 100]
empirical probabilities from test set: {8: 0.235, 2: 0.202, 4: 0.197, 95: 0.042, 11: 0.166, 22: 0.137, 0: 0.021}
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.025 

learned probs for this beta: {8: np.float64(0.11346393306213137), 2: np.float64(0.1308555366574569), 4: np.float64(0.12471544604378902), 95: np.float64(0.17428376432304726), 11: np.float64(0.10811379126746194), 22: np.float64(0.17428376432304726), 0: np.float64(0.17428376432304726)}
err dic= {8: np.float64(0.12153606693786861), 2: np.float64(0.07114446334254312), 4: np.float64(0.07228455395621099), 95: np.float64(0.13228376432304725), 11: np.float64(0.057886208732538066), 22: np.float64(0.03728376432304725), 0: np.float64(0.15328376432304727)} 

err list= [np.float64(0.12153606693786861), np.float64(0.07114446334254312), np.float64(0.07228455395621099), np.float64(0.13228376432304725), np.float64(0.057886208732538066), np.float64(0.03728376432304725), np.float64(0.15328376432304727)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.13836982358231315), 2: np.float64(0.18304726871213806), 4: np.float64(0.16654657191399877), 95: np.float64(0.12876493955887536), 11: np.float64(0.1257415171149198), 22: np.float64(0.12876493955887536), 0: np.float64(0.12876493955887536)}
err dic= {8: np.float64(0.09663017641768684), 2: np.float64(0.018952731287861957), 4: np.float64(0.03045342808600124), 95: np.float64(0.08676493955887535), 11: np.float64(0.040258482885080216), 22: np.float64(0.008235060441124653), 0: np.float64(0.10776493955887535)} 

err list= [np.float64(0.09663017641768684), np.float64(0.018952731287861957), np.float64(0.03045342808600124), np.float64(0.08676493955887535), np.float64(0.040258482885080216), np.float64(0.008235060441124653), np.float64(0.10776493955887535)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.16677931457601955), 2: np.float64(0.28582835447212973), 4: np.float64(0.2382392998136255), 95: np.float64(0.0570090667592262), 11: np.float64(0.1381258308605565), 22: np.float64(0.0570090667592262), 0: np.float64(0.0570090667592262)}
err dic= {8: np.float64(0.06822068542398044), 2: np.float64(0.08382835447212972), 4: np.float64(0.04123929981362548), 95: np.float64(0.015009066759226197), 11: np.float64(0.027874169139443516), 22: np.float64(0.0799909332407738), 0: np.float64(0.0360090667592262)} 

err list= [np.float64(0.06822068542398044), np.float64(0.08382835447212972), np.float64(0.04123929981362548), np.float64(0.015009066759226197), np.float64(0.027874169139443516), np.float64(0.0799909332407738), np.float64(0.0360090667592262)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.12928050978168432), 2: np.float64(0.4731030426314375), 4: np.float64(0.30696557842675704), 95: np.float64(0.0033469867989631454), 11: np.float64(0.08060990876323648), 22: np.float64(0.0033469867989631454), 0: np.float64(0.0033469867989631454)}
err dic= {8: np.float64(0.10571949021831567), 2: np.float64(0.2711030426314375), 4: np.float64(0.10996557842675703), 95: np.float64(0.038653013201036854), 11: np.float64(0.08539009123676353), 22: np.float64(0.13365301320103687), 0: np.float64(0.017653013201036856)} 

err list= [np.float64(0.10571949021831567), np.float64(0.2711030426314375), np.float64(0.10996557842675703), np.float64(0.038653013201036854), np.float64(0.08539009123676353), np.float64(0.13365301320103687), np.float64(0.017653013201036856)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.0470785013609871), 2: np.float64(0.6543392938080839), 4: np.float64(0.28061719004754343), 95: np.float64(7.043666829234368e-05), 11: np.float64(0.017753704778507275), 22: np.float64(7.043666829234368e-05), 0: np.float64(7.043666829234368e-05)}
err dic= {8: np.float64(0.1879214986390129), 2: np.float64(0.45233929380808385), 4: np.float64(0.08361719004754342), 95: np.float64(0.04192956333170766), 11: np.float64(0.14824629522149274), 22: np.float64(0.13692956333170767), 0: np.float64(0.020929563331707656)} 

err list= [np.float64(0.1879214986390129), np.float64(0.45233929380808385), np.float64(0.08361719004754342), np.float64(0.04192956333170766), np.float64(0.14824629522149274), np.float64(0.13692956333170767), np.float64(0.020929563331707656)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013536481371254223), 2: np.float64(0.766849839231136), 4: np.float64(0.2165497283674523), 95: np.float64(8.267204906416122e-07), 11: np.float64(0.0030614708686854085), 22: np.float64(8.267204906416122e-07), 0: np.float64(8.267204906416122e-07)}
err dic= {8: np.float64(0.22146351862874578), 2: np.float64(0.5648498392311361), 4: np.float64(0.01954972836745228), 95: np.float64(0.04199917327950936), 11: np.float64(0.1629385291313146), 22: np.float64(0.13699917327950936), 0: np.float64(0.02099917327950936)} 

err list= [np.float64(0.22146351862874578), np.float64(0.5648498392311361), np.float64(0.01954972836745228), np.float64(0.04199917327950936), np.float64(0.1629385291313146), np.float64(0.13699917327950936), np.float64(0.02099917327950936)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.003477553524834344), 2: np.float64(0.8410328182051247), 4: np.float64(0.1550162471584141), 95: np.float64(6.109695140123247e-09), 11: np.float64(0.0004733627825417179), 22: np.float64(6.109695140123247e-09), 0: np.float64(6.109695140123247e-09)}
err dic= {8: np.float64(0.23152244647516565), 2: np.float64(0.6390328182051246), 4: np.float64(0.0419837528415859), 95: np.float64(0.041999993890304864), 11: np.float64(0.16552663721745828), 22: np.float64(0.13699999389030487), 0: np.float64(0.020999993890304863)} 

err list= [np.float64(0.23152244647516565), np.float64(0.6390328182051246), np.float64(0.0419837528415859), np.float64(0.041999993890304864), np.float64(0.16552663721745828), np.float64(0.13699999389030487), np.float64(0.020999993890304863)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467393106242881), 2: np.float64(0.8926352814859138), 4: np.float64(0.10644832520880987), 95: np.float64(4.2950419110944644e-11), 11: np.float64(6.96538658001623e-05), 22: np.float64(4.2950419110944644e-11), 0: np.float64(4.2950419110944644e-11)}
err dic= {8: np.float64(0.2341532606893757), 2: np.float64(0.6906352814859138), 4: np.float64(0.09055167479119014), 95: np.float64(0.04199999995704958), 11: np.float64(0.16593034613419985), 22: np.float64(0.1369999999570496), 0: np.float64(0.020999999957049584)} 

err list= [np.float64(0.2341532606893757), np.float64(0.6906352814859138), np.float64(0.09055167479119014), np.float64(0.04199999995704958), np.float64(0.16593034613419985), np.float64(0.1369999999570496), np.float64(0.020999999957049584)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066374506199876), 2: np.float64(0.9287259689191147), 4: np.float64(0.0710633695790275), 95: np.float64(3.039342870893817e-13), 11: np.float64(9.997755883424369e-06), 22: np.float64(3.039342870893817e-13), 0: np.float64(3.039342870893817e-13)}
err dic= {8: np.float64(0.23479933625493798), 2: np.float64(0.7267259689191148), 4: np.float64(0.12593663042097253), 95: np.float64(0.041999999999696065), 11: np.float64(0.16599000224411659), 22: np.float64(0.1369999999996961), 0: np.float64(0.020999999999696067)} 

err list= [np.float64(0.23479933625493798), np.float64(0.7267259689191148), np.float64(0.12593663042097253), np.float64(0.041999999999696065), np.float64(0.16599000224411659), np.float64(0.1369999999996961), np.float64(0.020999999999696067)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.6823878792683556e-05), 2: np.float64(0.9535067301964196), 4: np.float64(0.046445031633751556), 95: np.float64(2.169477445136238e-15), 11: np.float64(1.4142910286275055e-06), 22: np.float64(2.169477445136238e-15), 0: np.float64(2.169477445136238e-15)}
err dic= {8: np.float64(0.2349531761212073), 2: np.float64(0.7515067301964196), 4: np.float64(0.15055496836624846), 95: np.float64(0.04199999999999783), 11: np.float64(0.16599858570897139), 22: np.float64(0.13699999999999785), 0: np.float64(0.020999999999997833)} 

err list= [np.float64(0.2349531761212073), np.float64(0.7515067301964196), np.float64(0.15055496836624846), np.float64(0.04199999999999783), np.float64(0.16599858570897139), np.float64(0.13699999999999785), np.float64(0.020999999999997833)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.0815608602475046e-05), 2: np.float64(0.9701298210556255), 4: np.float64(0.02985916522652595), 95: np.float64(1.558329635992481e-17), 11: np.float64(1.9810924551184595e-07), 22: np.float64(1.558329635992481e-17), 0: np.float64(1.558329635992481e-17)}
err dic= {8: np.float64(0.23498918439139752), 2: np.float64(0.7681298210556256), 4: np.float64(0.16714083477347405), 95: np.float64(0.04199999999999999), 11: np.float64(0.1659998018907545), 22: np.float64(0.13699999999999998), 0: np.float64(0.020999999999999987)} 

err list= [np.float64(0.23498918439139752), np.float64(0.7681298210556256), np.float64(0.16714083477347405), np.float64(0.04199999999999999), np.float64(0.1659998018907545), np.float64(0.13699999999999998), np.float64(0.020999999999999987)]
results for assortment [8, 2, 4, 95, 11, 22] :

err MNL dic= {8: 0.235, 2: 0.202, 4: 0.197, 95: 0.042, 11: 0.166, 22: 0.137, 0: np.float64(0.2356339886054509)} 

err MNL list= [0.235, 0.202, 0.197, 0.042, 0.166, 0.137, np.float64(0.2356339886054509)]
sampled assortment [1, 3, 9, 100, 22, 58] number: 8
#  Learning probs for MM model, A = [1, 3, 9, 100, 22, 58]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 100]
#  Learning probs for MM model, A = [1, 3, 9, 100, 22, 58]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 100]
empirical probabilities from test set: {1: 0.218, 3: 0.181, 9: 0.197, 100: 0.222, 22: 0.113, 58: 0.041, 0: 0.028}
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.13403222283451285), 3: np.float64(0.12774859779979647), 9: np.float64(0.11095820061856827), 100: np.float64(0.10327983682958312), 22: np.float64(0.1746603806391724), 58: np.float64(0.1746603806391724), 0: np.float64(0.1746603806391724)}
err dic= {1: np.float64(0.08396777716548715), 3: np.float64(0.053251402200203524), 9: np.float64(0.08604179938143174), 100: np.float64(0.11872016317041688), 22: np.float64(0.06166038063917241), 58: np.float64(0.1336603806391724), 0: np.float64(0.14666038063917242)} 

err list= [np.float64(0.08396777716548715), np.float64(0.053251402200203524), np.float64(0.08604179938143174), np.float64(0.11872016317041688), np.float64(0.06166038063917241), np.float64(0.1336603806391724), np.float64(0.14666038063917242)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.19143983234258968), 3: np.float64(0.1742222986280127), 9: np.float64(0.13226195326419649), 100: np.float64(0.11476104631694235), 22: np.float64(0.12910495648275286), 58: np.float64(0.12910495648275286), 0: np.float64(0.12910495648275286)}
err dic= {1: np.float64(0.026560167657410316), 3: np.float64(0.006777701371987299), 9: np.float64(0.06473804673580352), 100: np.float64(0.10723895368305765), 22: np.float64(0.016104956482752855), 58: np.float64(0.08810495648275285), 0: np.float64(0.10110495648275286)} 

err list= [np.float64(0.026560167657410316), np.float64(0.006777701371987299), np.float64(0.06473804673580352), np.float64(0.10723895368305765), np.float64(0.016104956482752855), np.float64(0.08810495648275285), np.float64(0.10110495648275286)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.30747799734390785), 3: np.float64(0.2565761497573029), 9: np.float64(0.15136182113836877), 100: np.float64(0.11444225903575246), 22: np.float64(0.05671392424155927), 58: np.float64(0.05671392424155927), 0: np.float64(0.05671392424155927)}
err dic= {1: np.float64(0.08947799734390785), 3: np.float64(0.07557614975730292), 9: np.float64(0.04563817886163124), 100: np.float64(0.10755774096424754), 22: np.float64(0.05628607575844073), 58: np.float64(0.01571392424155927), 0: np.float64(0.02871392424155927)} 

err list= [np.float64(0.08947799734390785), np.float64(0.07557614975730292), np.float64(0.04563817886163124), np.float64(0.10755774096424754), np.float64(0.05628607575844073), np.float64(0.01571392424155927), np.float64(0.02871392424155927)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5155721582458953), 3: np.float64(0.3361177112440118), 9: np.float64(0.0932209254416666), 100: np.float64(0.045882310857573806), 22: np.float64(0.0030689647369518324), 58: np.float64(0.0030689647369518324), 0: np.float64(0.0030689647369518324)}
err dic= {1: np.float64(0.29757215824589534), 3: np.float64(0.1551177112440118), 9: np.float64(0.1037790745583334), 100: np.float64(0.1761176891424262), 22: np.float64(0.10993103526304818), 58: np.float64(0.03793103526304817), 0: np.float64(0.024931035263048167)} 

err list= [np.float64(0.29757215824589534), np.float64(0.1551177112440118), np.float64(0.1037790745583334), np.float64(0.1761176891424262), np.float64(0.10993103526304818), np.float64(0.03793103526304817), np.float64(0.024931035263048167)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6813909968496659), 3: np.float64(0.2940359187910665), 9: np.float64(0.019887008841826398), 100: np.float64(0.004541607673254051), 22: np.float64(4.8155948062123465e-05), 58: np.float64(4.8155948062123465e-05), 0: np.float64(4.8155948062123465e-05)}
err dic= {1: np.float64(0.4633909968496659), 3: np.float64(0.1130359187910665), 9: np.float64(0.1771129911581736), 100: np.float64(0.21745839232674596), 22: np.float64(0.11295184405193788), 58: np.float64(0.04095184405193788), 0: np.float64(0.027951844051937878)} 

err list= [np.float64(0.4633909968496659), np.float64(0.1130359187910665), np.float64(0.1771129911581736), np.float64(0.21745839232674596), np.float64(0.11295184405193788), np.float64(0.04095184405193788), np.float64(0.027951844051937878)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7763889396521734), 3: np.float64(0.22001274469443302), 9: np.float64(0.0032518368738513426), 100: np.float64(0.00034523149143693074), 22: np.float64(4.157627018630057e-07), 58: np.float64(4.157627018630057e-07), 0: np.float64(4.157627018630057e-07)}
err dic= {1: np.float64(0.5583889396521734), 3: np.float64(0.03901274469443303), 9: np.float64(0.19374816312614868), 100: np.float64(0.22165476850856308), 22: np.float64(0.11299958423729814), 58: np.float64(0.04099958423729814), 0: np.float64(0.027999584237298137)} 

err list= [np.float64(0.5583889396521734), np.float64(0.03901274469443303), np.float64(0.19374816312614868), np.float64(0.22165476850856308), np.float64(0.11299958423729814), np.float64(0.04099958423729814), np.float64(0.027999584237298137)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437493610429412), 3: np.float64(0.15573992430155875), 9: np.float64(0.00048644700818241957), 100: np.float64(2.4260714089034233e-05), 22: np.float64(2.3110763583072247e-09), 58: np.float64(2.3110763583072247e-09), 0: np.float64(2.3110763583072247e-09)}
err dic= {1: np.float64(0.6257493610429412), 3: np.float64(0.025260075698441242), 9: np.float64(0.19651355299181758), 100: np.float64(0.22197573928591097), 22: np.float64(0.11299999768892365), 58: np.float64(0.040999997688923644), 0: np.float64(0.027999997688923643)} 

err list= [np.float64(0.6257493610429412), np.float64(0.025260075698441242), np.float64(0.19651355299181758), np.float64(0.22197573928591097), np.float64(0.11299999768892365), np.float64(0.040999997688923644), np.float64(0.027999997688923643)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933412342259445), 3: np.float64(0.10658666254445416), 9: np.float64(7.044586738227353e-05), 100: np.float64(1.6573248782524142e-06), 22: np.float64(1.2446894165545682e-11), 58: np.float64(1.2446894165545682e-11), 0: np.float64(1.2446894165545682e-11)}
err dic= {1: np.float64(0.6753412342259445), 3: np.float64(0.07441333745554583), 9: np.float64(0.19692955413261773), 100: np.float64(0.22199834267512175), 22: np.float64(0.11299999998755311), 58: np.float64(0.04099999998755311), 0: np.float64(0.027999999987553106)} 

err list= [np.float64(0.6753412342259445), np.float64(0.07441333745554583), np.float64(0.19692955413261773), np.float64(0.22199834267512175), np.float64(0.11299999998755311), np.float64(0.04099999998755311), np.float64(0.027999999987553106)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011179584329), 3: np.float64(0.07108872798783236), 9: np.float64(1.004248385193081e-05), 100: np.float64(1.1156967800852119e-07), 22: np.float64(6.812185164751935e-14), 58: np.float64(6.812185164751935e-14), 0: np.float64(6.812185164751935e-14)}
err dic= {1: np.float64(0.7109011179584329), 3: np.float64(0.10991127201216763), 9: np.float64(0.1969899575161481), 100: np.float64(0.221999888430322), 22: np.float64(0.11299999999993188), 58: np.float64(0.04099999999993188), 0: np.float64(0.027999999999931878)} 

err list= [np.float64(0.7109011179584329), np.float64(0.10991127201216763), np.float64(0.1969899575161481), np.float64(0.221999888430322), np.float64(0.11299999999993188), np.float64(0.04099999999993188), np.float64(0.027999999999931878)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489961513715), 3: np.float64(0.04644957969911158), 9: np.float64(1.4167151805218192e-06), 100: np.float64(7.434334682403214e-09), 22: np.float64(3.776464225587867e-16), 58: np.float64(3.776464225587867e-16), 0: np.float64(3.776464225587867e-16)}
err dic= {1: np.float64(0.7355489961513715), 3: np.float64(0.13455042030088843), 9: np.float64(0.19699858328481948), 100: np.float64(0.22199999256566533), 22: np.float64(0.11299999999999963), 58: np.float64(0.04099999999999963), 0: np.float64(0.027999999999999622)} 

err list= [np.float64(0.7355489961513715), np.float64(0.13455042030088843), np.float64(0.19699858328481948), np.float64(0.22199999256566533), np.float64(0.11299999999999963), np.float64(0.04099999999999963), np.float64(0.027999999999999622)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303256956), 3: np.float64(0.029859970945651217), 9: np.float64(1.982372702720324e-07), 100: np.float64(4.913822077323317e-10), 22: np.float64(2.110334307912982e-18), 58: np.float64(2.110334307912982e-18), 0: np.float64(2.110334307912982e-18)}
err dic= {1: np.float64(0.7521398303256956), 3: np.float64(0.15114002905434878), 9: np.float64(0.19699980176272974), 100: np.float64(0.2219999995086178), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.027999999999999997)} 

err list= [np.float64(0.7521398303256956), np.float64(0.15114002905434878), np.float64(0.19699980176272974), np.float64(0.2219999995086178), np.float64(0.113), np.float64(0.041), np.float64(0.027999999999999997)]
results for assortment [1, 3, 9, 100, 22, 58] :

err MNL dic= {1: 0.218, 3: 0.181, 9: 0.197, 100: 0.222, 22: 0.113, 58: 0.041, 0: np.float64(0.22401612903225807)} 

err MNL list= [0.218, 0.181, 0.197, 0.222, 0.113, 0.041, np.float64(0.22401612903225807)]
sampled assortment [7, 6, 8, 16, 83, 70] number: 9
#  Learning probs for MM model, A = [7, 6, 8, 16, 83, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [7, 6, 8, 16, 83, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 12, 100]
empirical probabilities from test set: {7: 0.207, 6: 0.246, 8: 0.249, 16: 0.148, 83: 0.048, 70: 0.058, 0: 0.044}
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.10390553846622554), 6: np.float64(0.10653591969565371), 8: np.float64(0.10134010158075105), 16: np.float64(0.17205461006434275), 83: np.float64(0.17205461006434275), 70: np.float64(0.17205461006434275), 0: np.float64(0.17205461006434275)}
err dic= {7: np.float64(0.10309446153377445), 6: np.float64(0.1394640803043463), 8: np.float64(0.14765989841924895), 16: np.float64(0.024054610064342757), 83: np.float64(0.12405461006434275), 70: np.float64(0.11405461006434275), 0: np.float64(0.12805461006434277)} 

err list= [np.float64(0.10309446153377445), np.float64(0.1394640803043463), np.float64(0.14765989841924895), np.float64(0.024054610064342757), np.float64(0.12405461006434275), np.float64(0.11405461006434275), np.float64(0.12805461006434277)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.1351769553724767), 6: np.float64(0.14210762607919653), 8: np.float64(0.12858429746471964), 16: np.float64(0.14853278027090472), 83: np.float64(0.14853278027090472), 70: np.float64(0.14853278027090472), 0: np.float64(0.14853278027090472)}
err dic= {7: np.float64(0.07182304462752329), 6: np.float64(0.10389237392080347), 8: np.float64(0.12041570253528036), 16: np.float64(0.0005327802709047258), 83: np.float64(0.10053278027090472), 70: np.float64(0.09053278027090472), 0: np.float64(0.10453278027090472)} 

err list= [np.float64(0.07182304462752329), np.float64(0.10389237392080347), np.float64(0.12041570253528036), np.float64(0.0005327802709047258), np.float64(0.10053278027090472), np.float64(0.09053278027090472), np.float64(0.10453278027090472)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.19832795646497225), 6: np.float64(0.21918628972646034), 8: np.float64(0.1794545560521136), 16: np.float64(0.10075779943911412), 83: np.float64(0.10075779943911412), 70: np.float64(0.10075779943911412), 0: np.float64(0.10075779943911412)}
err dic= {7: np.float64(0.008672043535027735), 6: np.float64(0.026813710273539654), 8: np.float64(0.06954544394788639), 16: np.float64(0.04724220056088588), 83: np.float64(0.052757799439114114), 70: np.float64(0.04275779943911411), 0: np.float64(0.05675779943911412)} 

err list= [np.float64(0.008672043535027735), np.float64(0.026813710273539654), np.float64(0.06954544394788639), np.float64(0.04724220056088588), np.float64(0.052757799439114114), np.float64(0.04275779943911411), np.float64(0.05675779943911412)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.3024333174113124), 6: np.float64(0.3883320664093164), 8: np.float64(0.23553530442681275), 16: np.float64(0.01842482793813962), 83: np.float64(0.01842482793813962), 70: np.float64(0.01842482793813962), 0: np.float64(0.01842482793813962)}
err dic= {7: np.float64(0.09543331741131242), 6: np.float64(0.1423320664093164), 8: np.float64(0.013464695573187246), 16: np.float64(0.12957517206186037), 83: np.float64(0.02957517206186038), 70: np.float64(0.039575172061860384), 0: np.float64(0.025575172061860378)} 

err list= [np.float64(0.09543331741131242), np.float64(0.1423320664093164), np.float64(0.013464695573187246), np.float64(0.12957517206186037), np.float64(0.02957517206186038), np.float64(0.039575172061860384), np.float64(0.025575172061860378)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.3062733746816652), 6: np.float64(0.5049594274867715), 8: np.float64(0.18576419199808497), 16: np.float64(0.0007507514583700559), 83: np.float64(0.0007507514583700559), 70: np.float64(0.0007507514583700559), 0: np.float64(0.0007507514583700559)}
err dic= {7: np.float64(0.09927337468166522), 6: np.float64(0.2589594274867715), 8: np.float64(0.06323580800191503), 16: np.float64(0.14724924854162993), 83: np.float64(0.04724924854162994), 70: np.float64(0.057249248541629945), 0: np.float64(0.04324924854162994)} 

err list= [np.float64(0.09927337468166522), np.float64(0.2589594274867715), np.float64(0.06323580800191503), np.float64(0.14724924854162993), np.float64(0.04724924854162994), np.float64(0.057249248541629945), np.float64(0.04324924854162994)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.2785634998501392), 6: np.float64(0.5897189338104293), 8: np.float64(0.13158408014368236), 16: np.float64(3.337154893728073e-05), 83: np.float64(3.337154893728073e-05), 70: np.float64(3.337154893728073e-05), 0: np.float64(3.337154893728073e-05)}
err dic= {7: np.float64(0.07156349985013918), 6: np.float64(0.3437189338104293), 8: np.float64(0.11741591985631764), 16: np.float64(0.1479666284510627), 83: np.float64(0.04796662845106272), 70: np.float64(0.05796662845106272), 0: np.float64(0.043966628451062716)} 

err list= [np.float64(0.07156349985013918), np.float64(0.3437189338104293), np.float64(0.11741591985631764), np.float64(0.1479666284510627), np.float64(0.04796662845106272), np.float64(0.05796662845106272), np.float64(0.043966628451062716)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24472747009683854), 6: np.float64(0.6652382348889904), 8: np.float64(0.0900302049385258), 16: np.float64(1.0225189113482867e-06), 83: np.float64(1.0225189113482867e-06), 70: np.float64(1.0225189113482867e-06), 0: np.float64(1.0225189113482867e-06)}
err dic= {7: np.float64(0.03772747009683855), 6: np.float64(0.41923823488899037), 8: np.float64(0.15896979506147418), 16: np.float64(0.14799897748108864), 83: np.float64(0.04799897748108865), 70: np.float64(0.057998977481088655), 0: np.float64(0.04399897748108865)} 

err list= [np.float64(0.03772747009683855), np.float64(0.41923823488899037), np.float64(0.15896979506147418), np.float64(0.14799897748108864), np.float64(0.04799897748108865), np.float64(0.057998977481088655), np.float64(0.04399897748108865)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20934305003062412), 6: np.float64(0.7306790403679706), 8: np.float64(0.05997778802311656), 16: np.float64(3.039457213265352e-08), 83: np.float64(3.039457213265352e-08), 70: np.float64(3.039457213265352e-08), 0: np.float64(3.039457213265352e-08)}
err dic= {7: np.float64(0.0023430500306241275), 6: np.float64(0.4846790403679706), 8: np.float64(0.18902221197688343), 16: np.float64(0.14799996960542786), 83: np.float64(0.04799996960542787), 70: np.float64(0.05799996960542787), 0: np.float64(0.04399996960542787)} 

err list= [np.float64(0.0023430500306241275), np.float64(0.4846790403679706), np.float64(0.18902221197688343), np.float64(0.14799996960542786), np.float64(0.04799996960542787), np.float64(0.05799996960542787), np.float64(0.04399996960542787)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17529039149902784), 6: np.float64(0.7855970317164733), 8: np.float64(0.03911257312765905), 16: np.float64(9.142098842961157e-10), 83: np.float64(9.142098842961157e-10), 70: np.float64(9.142098842961157e-10), 0: np.float64(9.142098842961157e-10)}
err dic= {7: np.float64(0.03170960850097215), 6: np.float64(0.5395970317164733), 8: np.float64(0.20988742687234097), 16: np.float64(0.14799999908579012), 83: np.float64(0.04799999908579012), 70: np.float64(0.05799999908579012), 0: np.float64(0.043999999085790116)} 

err list= [np.float64(0.03170960850097215), np.float64(0.5395970317164733), np.float64(0.20988742687234097), np.float64(0.14799999908579012), np.float64(0.04799999908579012), np.float64(0.05799999908579012), np.float64(0.043999999085790116)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.14433395509716723), 6: np.float64(0.8305845642406492), 8: np.float64(0.025081480551034225), 16: np.float64(2.77872088317674e-11), 83: np.float64(2.77872088317674e-11), 70: np.float64(2.77872088317674e-11), 0: np.float64(2.77872088317674e-11)}
err dic= {7: np.float64(0.06266604490283276), 6: np.float64(0.5845845642406492), 8: np.float64(0.22391851944896576), 16: np.float64(0.14799999997221278), 83: np.float64(0.04799999997221279), 70: np.float64(0.05799999997221279), 0: np.float64(0.04399999997221279)} 

err list= [np.float64(0.06266604490283276), np.float64(0.5845845642406492), np.float64(0.22391851944896576), np.float64(0.14799999997221278), np.float64(0.04799999997221279), np.float64(0.05799999997221279), np.float64(0.04399999997221279)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11731042782579924), 6: np.float64(0.8668133321943855), 8: np.float64(0.015876239976412746), 16: np.float64(8.505077346357908e-13), 83: np.float64(8.505077346357908e-13), 70: np.float64(8.505077346357908e-13), 0: np.float64(8.505077346357908e-13)}
err dic= {7: np.float64(0.08968957217420075), 6: np.float64(0.6208133321943855), 8: np.float64(0.23312376002358726), 16: np.float64(0.14799999999914948), 83: np.float64(0.047999999999149494), 70: np.float64(0.057999999999149496), 0: np.float64(0.04399999999914949)} 

err list= [np.float64(0.08968957217420075), np.float64(0.6208133321943855), np.float64(0.23312376002358726), np.float64(0.14799999999914948), np.float64(0.047999999999149494), np.float64(0.057999999999149496), np.float64(0.04399999999914949)]
results for assortment [7, 6, 8, 16, 83, 70] :

err MNL dic= {7: 0.207, 6: 0.246, 8: 0.249, 16: 0.148, 83: 0.048, 70: 0.058, 0: np.float64(0.21812319790301443)} 

err MNL list= [0.207, 0.246, 0.249, 0.148, 0.048, 0.058, np.float64(0.21812319790301443)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2]
 mean error for all betas:

mean_err= [0.11149098 0.09804994 0.07986885 0.07688488 0.08197835 0.08809065
 0.09415793 0.09978183 0.10582503 0.11194494 0.11789315]
mean_std= [0.         0.01344105 0.02795612 0.02475623 0.02437356 0.02611244
 0.0283782  0.03043116 0.03339643 0.03661789 0.03965834]
MNL: [0.17062606 0.16668406 0.16718534 0.16743585 0.16353078 0.16596076
 0.16918108 0.17351914 0.17085945 0.16773189]
 mean error for MNL:

mean_err_MNL= 0.16827143997207789
mean_std_MNL= 0.0027038801497929975
