p= 0.075 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(0.11993065725032813), 3: np.float64(0.11696955877231784), 4: np.float64(0.11408157007622242), 59: np.float64(0.1622545534752819), 40: np.float64(0.1622545534752819), 84: np.float64(0.1622545534752819), 0: np.float64(0.1622545534752819)}
err dic= {2: np.float64(0.15506934274967188), 3: np.float64(0.13003044122768215), 4: np.float64(0.13791842992377756), 59: np.float64(0.1032545534752819), 40: np.float64(0.0902545534752819), 84: np.float64(0.1022545534752819), 0: np.float64(0.1272545534752819)} 

err list= [np.float64(0.15506934274967188), np.float64(0.13003044122768215), np.float64(0.13791842992377756), np.float64(0.1032545534752819), np.float64(0.0902545534752819), np.float64(0.1022545534752819), np.float64(0.1272545534752819)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.166094364146821), 3: np.float64(0.15799384642019262), 4: np.float64(0.15028839560493393), 59: np.float64(0.13140584845701223), 40: np.float64(0.13140584845701223), 84: np.float64(0.13140584845701223), 0: np.float64(0.13140584845701223)}
err dic= {2: np.float64(0.10890563585317903), 3: np.float64(0.08900615357980737), 4: np.float64(0.10171160439506607), 59: np.float64(0.07240584845701223), 40: np.float64(0.05940584845701223), 84: np.float64(0.07140584845701223), 0: np.float64(0.09640584845701222)} 

err list= [np.float64(0.10890563585317903), np.float64(0.08900615357980737), np.float64(0.10171160439506607), np.float64(0.07240584845701223), np.float64(0.05940584845701223), np.float64(0.07140584845701223), np.float64(0.09640584845701222)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.26238719149357426), 3: np.float64(0.23741774887675304), 4: np.float64(0.214824462889551), 59: np.float64(0.07134264918503223), 40: np.float64(0.07134264918503223), 84: np.float64(0.07134264918503223), 0: np.float64(0.07134264918503223)}
err dic= {2: np.float64(0.012612808506425766), 3: np.float64(0.009582251123246954), 4: np.float64(0.03717553711044899), 59: np.float64(0.012342649185032237), 40: np.float64(0.0006573508149677609), 84: np.float64(0.011342649185032236), 0: np.float64(0.03634264918503223)} 

err list= [np.float64(0.012612808506425766), np.float64(0.009582251123246954), np.float64(0.03717553711044899), np.float64(0.012342649185032237), np.float64(0.0006573508149677609), np.float64(0.011342649185032236), np.float64(0.03634264918503223)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.41032079947645567), 3: np.float64(0.31955815994274817), 4: np.float64(0.2488721452002685), 59: np.float64(0.0053122238451306205), 40: np.float64(0.0053122238451306205), 84: np.float64(0.0053122238451306205), 0: np.float64(0.0053122238451306205)}
err dic= {2: np.float64(0.13532079947645564), 3: np.float64(0.07255815994274817), 4: np.float64(0.0031278547997314887), 59: np.float64(0.053687776154869374), 40: np.float64(0.06668777615486937), 84: np.float64(0.054687776154869375), 0: np.float64(0.029687776154869384)} 

err list= [np.float64(0.13532079947645564), np.float64(0.07255815994274817), np.float64(0.0031278547997314887), np.float64(0.053687776154869374), np.float64(0.06668777615486937), np.float64(0.054687776154869375), np.float64(0.029687776154869384)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5062074001945954), 3: np.float64(0.30703030839144485), 4: np.float64(0.18622329550043631), 59: np.float64(0.00013474897838103246), 40: np.float64(0.00013474897838103246), 84: np.float64(0.00013474897838103246), 0: np.float64(0.00013474897838103246)}
err dic= {2: np.float64(0.2312074001945954), 3: np.float64(0.06003030839144485), 4: np.float64(0.06577670449956369), 59: np.float64(0.058865251021618964), 40: np.float64(0.07186525102161896), 84: np.float64(0.059865251021618965), 0: np.float64(0.03486525102161897)} 

err list= [np.float64(0.2312074001945954), np.float64(0.06003030839144485), np.float64(0.06577670449956369), np.float64(0.058865251021618964), np.float64(0.07186525102161896), np.float64(0.059865251021618965), np.float64(0.03486525102161897)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.589788961087491), 3: np.float64(0.27859657839360247), 4: np.float64(0.13159970534122797), 59: np.float64(3.6887944195868146e-06), 40: np.float64(3.6887944195868146e-06), 84: np.float64(3.6887944195868146e-06), 0: np.float64(3.6887944195868146e-06)}
err dic= {2: np.float64(0.314788961087491), 3: np.float64(0.03159657839360247), 4: np.float64(0.12040029465877203), 59: np.float64(0.05899631120558041), 40: np.float64(0.07199631120558041), 84: np.float64(0.05999631120558041), 0: np.float64(0.034996311205580416)} 

err list= [np.float64(0.314788961087491), np.float64(0.03159657839360247), np.float64(0.12040029465877203), np.float64(0.05899631120558041), np.float64(0.07199631120558041), np.float64(0.05999631120558041), np.float64(0.034996311205580416)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652407769874887), 3: np.float64(0.24472840528261347), 4: np.float64(0.09003054897414613), 59: np.float64(6.718893792176618e-08), 40: np.float64(6.718893792176618e-08), 84: np.float64(6.718893792176618e-08), 0: np.float64(6.718893792176618e-08)}
err dic= {2: np.float64(0.3902407769874887), 3: np.float64(0.002271594717386527), 4: np.float64(0.16196945102585386), 59: np.float64(0.05899993281106208), 40: np.float64(0.07199993281106207), 84: np.float64(0.05999993281106208), 0: np.float64(0.03499993281106208)} 

err list= [np.float64(0.3902407769874887), np.float64(0.002271594717386527), np.float64(0.16196945102585386), np.float64(0.05899993281106208), np.float64(0.07199993281106207), np.float64(0.05999993281106208), np.float64(0.03499993281106208)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.7306791261592259), 3: np.float64(0.20934307461023022), 4: np.float64(0.05997779506529161), 59: np.float64(1.0413129489791045e-09), 40: np.float64(1.0413129489791045e-09), 84: np.float64(1.0413129489791045e-09), 0: np.float64(1.0413129489791045e-09)}
err dic= {2: np.float64(0.4556791261592259), 3: np.float64(0.03765692538976978), 4: np.float64(0.1920222049347084), 59: np.float64(0.05899999895868705), 40: np.float64(0.07199999895868704), 84: np.float64(0.05999999895868705), 0: np.float64(0.03499999895868706)} 

err list= [np.float64(0.4556791261592259), np.float64(0.03765692538976978), np.float64(0.1920222049347084), np.float64(0.05899999895868705), np.float64(0.07199999895868704), np.float64(0.05999999895868705), np.float64(0.03499999895868706)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855970345391339), 3: np.float64(0.17529039212884848), 4: np.float64(0.039112573268191016), 59: np.float64(1.5956476777758862e-11), 40: np.float64(1.5956476777758862e-11), 84: np.float64(1.5956476777758862e-11), 0: np.float64(1.5956476777758862e-11)}
err dic= {2: np.float64(0.5105970345391339), 3: np.float64(0.07170960787115152), 4: np.float64(0.212887426731809), 59: np.float64(0.05899999998404352), 40: np.float64(0.07199999998404352), 84: np.float64(0.05999999998404352), 0: np.float64(0.034999999984043524)} 

err list= [np.float64(0.5105970345391339), np.float64(0.07170960787115152), np.float64(0.212887426731809), np.float64(0.05899999998404352), np.float64(0.07199999998404352), np.float64(0.05999999998404352), np.float64(0.034999999984043524)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845643321483), 3: np.float64(0.14433395511306732), 4: np.float64(0.025081480553797244), 59: np.float64(2.466848682643328e-13), 40: np.float64(2.466848682643328e-13), 84: np.float64(2.466848682643328e-13), 0: np.float64(2.466848682643328e-13)}
err dic= {2: np.float64(0.5555845643321483), 3: np.float64(0.10266604488693268), 4: np.float64(0.22691851944620275), 59: np.float64(0.05899999999975331), 40: np.float64(0.0719999999997533), 84: np.float64(0.05999999999975331), 0: np.float64(0.03499999999975332)} 

err list= [np.float64(0.5555845643321483), np.float64(0.10266604488693268), np.float64(0.22691851944620275), np.float64(0.05899999999975331), np.float64(0.0719999999997533), np.float64(0.05999999999975331), np.float64(0.03499999999975332)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973213), 3: np.float64(0.11731042782619654), 4: np.float64(0.015876239976466526), 59: np.float64(3.842279397258604e-15), 40: np.float64(3.842279397258604e-15), 84: np.float64(3.842279397258604e-15), 0: np.float64(3.842279397258604e-15)}
err dic= {2: np.float64(0.5918133321973212), 3: np.float64(0.12968957217380345), 4: np.float64(0.23612376002353347), 59: np.float64(0.05899999999999615), 40: np.float64(0.07199999999999615), 84: np.float64(0.059999999999996154), 0: np.float64(0.03499999999999616)} 

err list= [np.float64(0.5918133321973212), np.float64(0.12968957217380345), np.float64(0.23612376002353347), np.float64(0.05899999999999615), np.float64(0.07199999999999615), np.float64(0.059999999999996154), np.float64(0.03499999999999616)]
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(0.11831696976698795), 4: np.float64(0.11539571337489997), 8: np.float64(0.10491736322630041), 74: np.float64(0.16534248840795276), 40: np.float64(0.16534248840795276), 87: np.float64(0.16534248840795276), 0: np.float64(0.16534248840795276)}
err dic= {3: np.float64(0.14068303023301204), 4: np.float64(0.13060428662510004), 8: np.float64(0.1510826367736996), 74: np.float64(0.09934248840795276), 40: np.float64(0.08834248840795277), 87: np.float64(0.11834248840795276), 0: np.float64(0.11634248840795276)} 

err list= [np.float64(0.14068303023301204), np.float64(0.13060428662510004), np.float64(0.1510826367736996), np.float64(0.09934248840795276), np.float64(0.08834248840795277), np.float64(0.11834248840795276), np.float64(0.11634248840795276)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.16292818862658362), 4: np.float64(0.15498208710220868), 8: np.float64(0.12850570306809822), 74: np.float64(0.1383960053007768), 40: np.float64(0.1383960053007768), 87: np.float64(0.1383960053007768), 0: np.float64(0.1383960053007768)}
err dic= {3: np.float64(0.09607181137341639), 4: np.float64(0.09101791289779132), 8: np.float64(0.12749429693190178), 74: np.float64(0.0723960053007768), 40: np.float64(0.06139600530077681), 87: np.float64(0.09139600530077681), 0: np.float64(0.0893960053007768)} 

err list= [np.float64(0.09607181137341639), np.float64(0.09101791289779132), np.float64(0.12749429693190178), np.float64(0.0723960053007768), np.float64(0.06139600530077681), np.float64(0.09139600530077681), np.float64(0.0893960053007768)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.2612609659703066), 4: np.float64(0.2363986978821528), 8: np.float64(0.16468388498822345), 74: np.float64(0.08441411278983128), 40: np.float64(0.08441411278983128), 87: np.float64(0.08441411278983128), 0: np.float64(0.08441411278983128)}
err dic= {3: np.float64(0.0022609659703066165), 4: np.float64(0.00960130211784721), 8: np.float64(0.09131611501177656), 74: np.float64(0.01841411278983128), 40: np.float64(0.007414112789831284), 87: np.float64(0.03741411278983128), 0: np.float64(0.03541411278983128)} 

err list= [np.float64(0.0022609659703066165), np.float64(0.00960130211784721), np.float64(0.09131611501177656), np.float64(0.01841411278983128), np.float64(0.007414112789831284), np.float64(0.03741411278983128), np.float64(0.03541411278983128)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.455734486390001), 4: np.float64(0.3549263748731775), 8: np.float64(0.15131789582027702), 74: np.float64(0.009505310729134728), 40: np.float64(0.009505310729134728), 87: np.float64(0.009505310729134728), 0: np.float64(0.009505310729134728)}
err dic= {3: np.float64(0.19673448639000102), 4: np.float64(0.10892637487317752), 8: np.float64(0.10468210417972298), 74: np.float64(0.056494689270865275), 40: np.float64(0.06749468927086527), 87: np.float64(0.03749468927086527), 0: np.float64(0.039494689270865274)} 

err list= [np.float64(0.19673448639000102), np.float64(0.10892637487317752), np.float64(0.10468210417972298), np.float64(0.056494689270865275), np.float64(0.06749468927086527), np.float64(0.03749468927086527), np.float64(0.039494689270865274)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5834845491060661), 4: np.float64(0.3539012685014303), 8: np.float64(0.06145129657504427), 74: np.float64(0.00029072145436492304), 40: np.float64(0.00029072145436492304), 87: np.float64(0.00029072145436492304), 0: np.float64(0.00029072145436492304)}
err dic= {3: np.float64(0.32448454910606606), 4: np.float64(0.10790126850143028), 8: np.float64(0.19454870342495573), 74: np.float64(0.06570927854563507), 40: np.float64(0.07670927854563507), 87: np.float64(0.04670927854563508), 0: np.float64(0.04870927854563508)} 

err list= [np.float64(0.32448454910606606), np.float64(0.10790126850143028), np.float64(0.19454870342495573), np.float64(0.06570927854563507), np.float64(0.07670927854563507), np.float64(0.04670927854563508), np.float64(0.04870927854563508)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.6651196335078153), 4: np.float64(0.3141802684404537), 8: np.float64(0.020658392859112605), 74: np.float64(1.042629815458347e-05), 40: np.float64(1.042629815458347e-05), 87: np.float64(1.042629815458347e-05), 0: np.float64(1.042629815458347e-05)}
err dic= {3: np.float64(0.4061196335078153), 4: np.float64(0.06818026844045372), 8: np.float64(0.2353416071408874), 74: np.float64(0.06598957370184542), 40: np.float64(0.07698957370184542), 87: np.float64(0.046989573701845415), 0: np.float64(0.04898957370184542)} 

err list= [np.float64(0.4061196335078153), np.float64(0.06818026844045372), np.float64(0.2353416071408874), np.float64(0.06598957370184542), np.float64(0.07698957370184542), np.float64(0.046989573701845415), np.float64(0.04898957370184542)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.726394804716232), 4: np.float64(0.26722571482884633), 8: np.float64(0.006378522645130092), 74: np.float64(2.39452447936625e-07), 40: np.float64(2.39452447936625e-07), 87: np.float64(2.39452447936625e-07), 0: np.float64(2.39452447936625e-07)}
err dic= {3: np.float64(0.46739480471623196), 4: np.float64(0.02122571482884633), 8: np.float64(0.24962147735486992), 74: np.float64(0.06599976054755206), 40: np.float64(0.07699976054755206), 87: np.float64(0.04699976054755206), 0: np.float64(0.04899976054755206)} 

err list= [np.float64(0.46739480471623196), np.float64(0.02122571482884633), np.float64(0.24962147735486992), np.float64(0.06599976054755206), np.float64(0.07699976054755206), np.float64(0.04699976054755206), np.float64(0.04899976054755206)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.7758322063285901), 4: np.float64(0.2222796486717658), 8: np.float64(0.001888126625357154), 74: np.float64(4.593571590453131e-09), 40: np.float64(4.593571590453131e-09), 87: np.float64(4.593571590453131e-09), 0: np.float64(4.593571590453131e-09)}
err dic= {3: np.float64(0.5168322063285901), 4: np.float64(0.02372035132823419), 8: np.float64(0.25411187337464286), 74: np.float64(0.06599999540642841), 40: np.float64(0.0769999954064284), 87: np.float64(0.04699999540642841), 0: np.float64(0.04899999540642841)} 

err list= [np.float64(0.5168322063285901), np.float64(0.02372035132823419), np.float64(0.25411187337464286), np.float64(0.06599999540642841), np.float64(0.0769999954064284), np.float64(0.04699999540642841), np.float64(0.04899999540642841)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.8171262000293974), 4: np.float64(0.1823254998740373), 8: np.float64(0.0005482997492077225), 74: np.float64(8.683930976917985e-11), 40: np.float64(8.683930976917985e-11), 87: np.float64(8.683930976917985e-11), 0: np.float64(8.683930976917985e-11)}
err dic= {3: np.float64(0.5581262000293974), 4: np.float64(0.06367450012596271), 8: np.float64(0.2554517002507923), 74: np.float64(0.06599999991316069), 40: np.float64(0.07699999991316069), 87: np.float64(0.046999999913160694), 0: np.float64(0.048999999913160695)} 

err list= [np.float64(0.5581262000293974), np.float64(0.06367450012596271), np.float64(0.2554517002507923), np.float64(0.06599999991316069), np.float64(0.07699999991316069), np.float64(0.046999999913160694), np.float64(0.048999999913160695)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.8518182496374056), 4: np.float64(0.14802381634254766), 8: np.float64(0.00015793401340006124), 74: np.float64(1.6614905867168772e-12), 40: np.float64(1.6614905867168772e-12), 87: np.float64(1.6614905867168772e-12), 0: np.float64(1.6614905867168772e-12)}
err dic= {3: np.float64(0.5928182496374056), 4: np.float64(0.09797618365745234), 8: np.float64(0.2558420659865999), 74: np.float64(0.06599999999833851), 40: np.float64(0.07699999999833851), 87: np.float64(0.04699999999833851), 0: np.float64(0.04899999999833851)} 

err list= [np.float64(0.5928182496374056), np.float64(0.09797618365745234), np.float64(0.2558420659865999), np.float64(0.06599999999833851), np.float64(0.07699999999833851), np.float64(0.04699999999833851), np.float64(0.04899999999833851)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402410339), 4: np.float64(0.11919751703718935), 8: np.float64(4.534272164779054e-05), 74: np.float64(3.2197135002870207e-14), 40: np.float64(3.2197135002870207e-14), 87: np.float64(3.2197135002870207e-14), 0: np.float64(3.2197135002870207e-14)}
err dic= {3: np.float64(0.6217571402410339), 4: np.float64(0.12680248296281066), 8: np.float64(0.2559546572783522), 74: np.float64(0.0659999999999678), 40: np.float64(0.0769999999999678), 87: np.float64(0.046999999999967804), 0: np.float64(0.048999999999967805)} 

err list= [np.float64(0.6217571402410339), np.float64(0.12680248296281066), np.float64(0.2559546572783522), np.float64(0.0659999999999678), np.float64(0.0769999999999678), np.float64(0.046999999999967804), np.float64(0.048999999999967805)]
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(0.11387629639266175), 3: np.float64(0.10849284366187446), 9: np.float64(0.09630213496540435), 83: np.float64(0.1703321812450163), 79: np.float64(0.1703321812450163), 70: np.float64(0.1703321812450163), 0: np.float64(0.1703321812450163)}
err dic= {1: np.float64(0.15112370360733826), 3: np.float64(0.14250715633812555), 9: np.float64(0.13869786503459564), 83: np.float64(0.11833218124501632), 79: np.float64(0.10233218124501631), 70: np.float64(0.08933218124501631), 0: np.float64(0.12233218124501631)} 

err list= [np.float64(0.15112370360733826), np.float64(0.14250715633812555), np.float64(0.13869786503459564), np.float64(0.11833218124501632), np.float64(0.10233218124501631), np.float64(0.08933218124501631), np.float64(0.12233218124501631)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.16163379275220557), 3: np.float64(0.14690477262159637), 9: np.float64(0.1161726771176688), 83: np.float64(0.14382218937713226), 79: np.float64(0.14382218937713226), 70: np.float64(0.14382218937713226), 0: np.float64(0.14382218937713226)}
err dic= {1: np.float64(0.10336620724779444), 3: np.float64(0.10409522737840363), 9: np.float64(0.1188273228823312), 83: np.float64(0.09182218937713227), 79: np.float64(0.07582218937713225), 70: np.float64(0.06282218937713226), 0: np.float64(0.09582218937713226)} 

err list= [np.float64(0.10336620724779444), np.float64(0.10409522737840363), np.float64(0.1188273228823312), np.float64(0.09182218937713227), np.float64(0.07582218937713225), np.float64(0.06282218937713226), np.float64(0.09582218937713226)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.27443101217046006), 3: np.float64(0.22816987049037485), 9: np.float64(0.1450482068021531), 83: np.float64(0.08808772763425415), 79: np.float64(0.08808772763425415), 70: np.float64(0.08808772763425415), 0: np.float64(0.08808772763425415)}
err dic= {1: np.float64(0.009431012170460051), 3: np.float64(0.022830129509625152), 9: np.float64(0.08995179319784688), 83: np.float64(0.036087727634254156), 79: np.float64(0.02008772763425415), 70: np.float64(0.007087727634254151), 0: np.float64(0.04008772763425415)} 

err list= [np.float64(0.009431012170460051), np.float64(0.022830129509625152), np.float64(0.08995179319784688), np.float64(0.036087727634254156), np.float64(0.02008772763425415), np.float64(0.007087727634254151), np.float64(0.04008772763425415)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5141959665977676), 3: np.float64(0.33491413287171123), 9: np.float64(0.11479037325235728), 83: np.float64(0.009024881819540644), 79: np.float64(0.009024881819540644), 70: np.float64(0.009024881819540644), 0: np.float64(0.009024881819540644)}
err dic= {1: np.float64(0.24919596659776755), 3: np.float64(0.08391413287171123), 9: np.float64(0.12020962674764271), 83: np.float64(0.042975118180459355), 79: np.float64(0.05897511818045936), 70: np.float64(0.07197511818045936), 0: np.float64(0.03897511818045936)} 

err list= [np.float64(0.24919596659776755), np.float64(0.08391413287171123), np.float64(0.12020962674764271), np.float64(0.042975118180459355), np.float64(0.05897511818045936), np.float64(0.07197511818045936), np.float64(0.03897511818045936)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6762270946756677), 3: np.float64(0.2914696912606224), 9: np.float64(0.031378424980637185), 83: np.float64(0.00023119727076848848), 79: np.float64(0.00023119727076848848), 70: np.float64(0.00023119727076848848), 0: np.float64(0.00023119727076848848)}
err dic= {1: np.float64(0.41122709467566765), 3: np.float64(0.04046969126062239), 9: np.float64(0.2036215750193628), 83: np.float64(0.05176880272923151), 79: np.float64(0.06776880272923151), 70: np.float64(0.08076880272923151), 0: np.float64(0.047768802729231515)} 

err list= [np.float64(0.41122709467566765), np.float64(0.04046969126062239), np.float64(0.2036215750193628), np.float64(0.05176880272923151), np.float64(0.06776880272923151), np.float64(0.08076880272923151), np.float64(0.047768802729231515)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7740863441091225), 3: np.float64(0.2191715356039441), 9: np.float64(0.006715212758882388), 83: np.float64(6.726882012814456e-06), 79: np.float64(6.726882012814456e-06), 70: np.float64(6.726882012814456e-06), 0: np.float64(6.726882012814456e-06)}
err dic= {1: np.float64(0.5090863441091225), 3: np.float64(0.03182846439605591), 9: np.float64(0.2282847872411176), 83: np.float64(0.05199327311798718), 79: np.float64(0.0679932731179872), 70: np.float64(0.0809932731179872), 0: np.float64(0.047993273117987185)} 

err list= [np.float64(0.5090863441091225), np.float64(0.03182846439605591), np.float64(0.2282847872411176), np.float64(0.05199327311798718), np.float64(0.0679932731179872), np.float64(0.0809932731179872), np.float64(0.047993273117987185)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.843119325990245), 3: np.float64(0.15557119470573322), 9: np.float64(0.001308986334160457), 83: np.float64(1.2324246539482234e-07), 79: np.float64(1.2324246539482234e-07), 70: np.float64(1.2324246539482234e-07), 0: np.float64(1.2324246539482234e-07)}
err dic= {1: np.float64(0.578119325990245), 3: np.float64(0.09542880529426678), 9: np.float64(0.23369101366583953), 83: np.float64(0.051999876757534605), 79: np.float64(0.0679998767575346), 70: np.float64(0.0809998767575346), 0: np.float64(0.04799987675753461)} 

err list= [np.float64(0.578119325990245), np.float64(0.09542880529426678), np.float64(0.23369101366583953), np.float64(0.051999876757534605), np.float64(0.0679998767575346), np.float64(0.0809998767575346), np.float64(0.04799987675753461)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931967280832477), 3: np.float64(0.10655825217052345), 9: np.float64(0.00024501218928043943), 83: np.float64(1.889237015804495e-09), 79: np.float64(1.889237015804495e-09), 70: np.float64(1.889237015804495e-09), 0: np.float64(1.889237015804495e-09)}
err dic= {1: np.float64(0.6281967280832477), 3: np.float64(0.14444174782947655), 9: np.float64(0.23475498781071955), 83: np.float64(0.05199999811076298), 79: np.float64(0.06799999811076299), 70: np.float64(0.08099999811076299), 0: np.float64(0.047999998110762984)} 

err list= [np.float64(0.6281967280832477), np.float64(0.14444174782947655), np.float64(0.23475498781071955), np.float64(0.05199999811076298), np.float64(0.06799999811076299), np.float64(0.08099999811076299), np.float64(0.047999998110762984)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707239611623), 3: np.float64(0.0710843198560717), 9: np.float64(4.495606881969644e-05), 83: np.float64(2.8486576321314778e-11), 79: np.float64(2.8486576321314778e-11), 70: np.float64(2.8486576321314778e-11), 0: np.float64(2.8486576321314778e-11)}
err dic= {1: np.float64(0.6638707239611623), 3: np.float64(0.17991568014392828), 9: np.float64(0.2349550439311803), 83: np.float64(0.05199999997151342), 79: np.float64(0.06799999997151343), 70: np.float64(0.08099999997151343), 0: np.float64(0.04799999997151343)} 

err list= [np.float64(0.6638707239611623), np.float64(0.17991568014392828), np.float64(0.2349550439311803), np.float64(0.05199999997151342), np.float64(0.06799999997151343), np.float64(0.08099999997151343), np.float64(0.04799999997151343)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535429244132106), 3: np.float64(0.04644892580543504), 9: np.float64(8.14977962351865e-06), 83: np.float64(4.325803314938273e-13), 79: np.float64(4.325803314938273e-13), 70: np.float64(4.325803314938273e-13), 0: np.float64(4.325803314938273e-13)}
err dic= {1: np.float64(0.6885429244132106), 3: np.float64(0.20455107419456497), 9: np.float64(0.23499185022037647), 83: np.float64(0.05199999999956742), 79: np.float64(0.06799999999956742), 70: np.float64(0.08099999999956742), 0: np.float64(0.04799999999956742)} 

err list= [np.float64(0.6885429244132106), np.float64(0.20455107419456497), np.float64(0.23499185022037647), np.float64(0.05199999999956742), np.float64(0.06799999999956742), np.float64(0.08099999999956742), np.float64(0.04799999999956742)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386587635531), 3: np.float64(0.029859876603522014), 9: np.float64(1.4646328981749456e-06), 83: np.float64(6.614263688086996e-15), 79: np.float64(6.614263688086996e-15), 70: np.float64(6.614263688086996e-15), 0: np.float64(6.614263688086996e-15)}
err dic= {1: np.float64(0.7051386587635531), 3: np.float64(0.22114012339647798), 9: np.float64(0.2349985353671018), 83: np.float64(0.051999999999993385), 79: np.float64(0.06799999999999339), 70: np.float64(0.08099999999999338), 0: np.float64(0.04799999999999339)} 

err list= [np.float64(0.7051386587635531), np.float64(0.22114012339647798), np.float64(0.2349985353671018), np.float64(0.051999999999993385), np.float64(0.06799999999999339), np.float64(0.08099999999999338), np.float64(0.04799999999999339)]
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(0.11404732118935648), 4: np.float64(0.10613614536499998), 8: np.float64(0.09645045064712697), 32: np.float64(0.17084152069963057), 27: np.float64(0.17084152069963057), 82: np.float64(0.17084152069963057), 0: np.float64(0.17084152069963057)}
err dic= {1: np.float64(0.10795267881064352), 4: np.float64(0.12386385463500003), 8: np.float64(0.13554954935287306), 32: np.float64(0.06884152069963058), 27: np.float64(0.05084152069963058), 82: np.float64(0.12084152069963057), 0: np.float64(0.12684152069963056)} 

err list= [np.float64(0.10795267881064352), np.float64(0.12386385463500003), np.float64(0.13554954935287306), np.float64(0.06884152069963058), np.float64(0.05084152069963058), np.float64(0.12084152069963057), np.float64(0.12684152069963056)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1622933809646048), 4: np.float64(0.1409114473279883), 8: np.float64(0.11667136821774435), 32: np.float64(0.14503095087241508), 27: np.float64(0.14503095087241508), 82: np.float64(0.14503095087241508), 0: np.float64(0.14503095087241508)}
err dic= {1: np.float64(0.0597066190353952), 4: np.float64(0.08908855267201171), 8: np.float64(0.11532863178225566), 32: np.float64(0.04303095087241508), 27: np.float64(0.02503095087241508), 82: np.float64(0.09503095087241507), 0: np.float64(0.10103095087241508)} 

err list= [np.float64(0.0597066190353952), np.float64(0.08908855267201171), np.float64(0.11532863178225566), np.float64(0.04303095087241508), np.float64(0.02503095087241508), np.float64(0.09503095087241507), np.float64(0.10103095087241508)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.2780487397445854), 4: np.float64(0.2122189727388999), 8: np.float64(0.14717159055724727), 32: np.float64(0.09064017423981824), 27: np.float64(0.09064017423981824), 82: np.float64(0.09064017423981824), 0: np.float64(0.09064017423981824)}
err dic= {1: np.float64(0.05604873974458538), 4: np.float64(0.01778102726110012), 8: np.float64(0.08482840944275274), 32: np.float64(0.011359825760181755), 27: np.float64(0.029359825760181757), 82: np.float64(0.040640174239818236), 0: np.float64(0.04664017423981824)} 

err list= [np.float64(0.05604873974458538), np.float64(0.01778102726110012), np.float64(0.08482840944275274), np.float64(0.011359825760181755), np.float64(0.029359825760181757), np.float64(0.040640174239818236), np.float64(0.04664017423981824)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.541831137315798), 4: np.float64(0.2942267774239989), 8: np.float64(0.1232537353164064), 32: np.float64(0.010172087485949088), 27: np.float64(0.010172087485949088), 82: np.float64(0.010172087485949088), 0: np.float64(0.010172087485949088)}
err dic= {1: np.float64(0.31983113731579804), 4: np.float64(0.06422677742399888), 8: np.float64(0.10874626468359361), 32: np.float64(0.09182791251405091), 27: np.float64(0.10982791251405091), 82: np.float64(0.03982791251405091), 0: np.float64(0.03382791251405091)} 

err list= [np.float64(0.31983113731579804), np.float64(0.06422677742399888), np.float64(0.10874626468359361), np.float64(0.09182791251405091), np.float64(0.10982791251405091), np.float64(0.03982791251405091), np.float64(0.03382791251405091)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7375757948168502), 4: np.float64(0.22435419831276565), 8: np.float64(0.03697019670054493), 32: np.float64(0.00027495254246006007), 27: np.float64(0.00027495254246006007), 82: np.float64(0.00027495254246006007), 0: np.float64(0.00027495254246006007)}
err dic= {1: np.float64(0.5155757948168502), 4: np.float64(0.005645801687234359), 8: np.float64(0.19502980329945507), 32: np.float64(0.10172504745753994), 27: np.float64(0.11972504745753994), 82: np.float64(0.049725047457539945), 0: np.float64(0.04372504745753994)} 

err list= [np.float64(0.5155757948168502), np.float64(0.005645801687234359), np.float64(0.19502980329945507), np.float64(0.10172504745753994), np.float64(0.11972504745753994), np.float64(0.049725047457539945), np.float64(0.04372504745753994)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.849460600512508), 4: np.float64(0.14195503615491495), 8: np.float64(0.008549964687627691), 32: np.float64(8.599661237348688e-06), 27: np.float64(8.599661237348688e-06), 82: np.float64(8.599661237348688e-06), 0: np.float64(8.599661237348688e-06)}
err dic= {1: np.float64(0.6274606005125081), 4: np.float64(0.08804496384508506), 8: np.float64(0.2234500353123723), 32: np.float64(0.10199140033876264), 27: np.float64(0.11999140033876264), 82: np.float64(0.049991400338762655), 0: np.float64(0.04399140033876265)} 

err list= [np.float64(0.6274606005125081), np.float64(0.08804496384508506), np.float64(0.2234500353123723), np.float64(0.10199140033876264), np.float64(0.11999140033876264), np.float64(0.049991400338762655), np.float64(0.04399140033876265)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159706071511933), 4: np.float64(0.08226332861337066), 8: np.float64(0.001765397875620086), 32: np.float64(1.6658995403328835e-07), 27: np.float64(1.6658995403328835e-07), 82: np.float64(1.6658995403328835e-07), 0: np.float64(1.6658995403328835e-07)}
err dic= {1: np.float64(0.6939706071511933), 4: np.float64(0.14773667138662935), 8: np.float64(0.23023460212437993), 32: np.float64(0.10199983341004595), 27: np.float64(0.11999983341004596), 82: np.float64(0.04999983341004597), 0: np.float64(0.043999833410045965)} 

err list= [np.float64(0.6939706071511933), np.float64(0.14773667138662935), np.float64(0.23023460212437993), np.float64(0.10199983341004595), np.float64(0.11999983341004596), np.float64(0.04999983341004597), np.float64(0.043999833410045965)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545811560543421), 4: np.float64(0.0450752707787948), 8: np.float64(0.00034356255973174153), 32: np.float64(2.651782798984616e-09), 27: np.float64(2.651782798984616e-09), 82: np.float64(2.651782798984616e-09), 0: np.float64(2.651782798984616e-09)}
err dic= {1: np.float64(0.7325811560543422), 4: np.float64(0.1849247292212052), 8: np.float64(0.23165643744026826), 32: np.float64(0.1019999973482172), 27: np.float64(0.1199999973482172), 82: np.float64(0.0499999973482172), 0: np.float64(0.0439999973482172)} 

err list= [np.float64(0.7325811560543422), np.float64(0.1849247292212052), np.float64(0.23165643744026826), np.float64(0.1019999973482172), np.float64(0.1199999973482172), np.float64(0.0499999973482172), np.float64(0.0439999973482172)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9761795794170177), 4: np.float64(0.02375577728373647), 8: np.float64(6.464313533848215e-05), 32: np.float64(4.097684830321675e-11), 27: np.float64(4.097684830321675e-11), 82: np.float64(4.097684830321675e-11), 0: np.float64(4.097684830321675e-11)}
err dic= {1: np.float64(0.7541795794170177), 4: np.float64(0.20624422271626353), 8: np.float64(0.23193535686466152), 32: np.float64(0.10199999995902315), 27: np.float64(0.11999999995902315), 82: np.float64(0.049999999959023156), 0: np.float64(0.04399999995902315)} 

err list= [np.float64(0.7541795794170177), np.float64(0.20624422271626353), np.float64(0.23193535686466152), np.float64(0.10199999995902315), np.float64(0.11999999995902315), np.float64(0.049999999959023156), np.float64(0.04399999995902315)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141691230163), 4: np.float64(0.012173924284485289), 8: np.float64(1.1906589969936729e-05), 32: np.float64(6.320697325165597e-13), 27: np.float64(6.320697325165597e-13), 82: np.float64(6.320697325165597e-13), 0: np.float64(6.320697325165597e-13)}
err dic= {1: np.float64(0.7658141691230164), 4: np.float64(0.2178260757155147), 8: np.float64(0.23198809341003007), 32: np.float64(0.10199999999936793), 27: np.float64(0.11999999999936793), 82: np.float64(0.04999999999936793), 0: np.float64(0.04399999999936793)} 

err list= [np.float64(0.7658141691230164), np.float64(0.2178260757155147), np.float64(0.23198809341003007), np.float64(0.10199999999936793), np.float64(0.11999999999936793), np.float64(0.04999999999936793), np.float64(0.04399999999936793)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855163026429), 4: np.float64(0.0061123224453527615), 8: np.float64(2.1612519648709597e-06), 32: np.float64(9.76060161702097e-15), 27: np.float64(9.76060161702097e-15), 82: np.float64(9.76060161702097e-15), 0: np.float64(9.76060161702097e-15)}
err dic= {1: np.float64(0.7718855163026429), 4: np.float64(0.22388767755464725), 8: np.float64(0.23199783874803515), 32: np.float64(0.10199999999999024), 27: np.float64(0.11999999999999024), 82: np.float64(0.04999999999999024), 0: np.float64(0.043999999999990234)} 

err list= [np.float64(0.7718855163026429), np.float64(0.22388767755464725), np.float64(0.23199783874803515), np.float64(0.10199999999999024), np.float64(0.11999999999999024), np.float64(0.04999999999999024), np.float64(0.043999999999990234)]
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(0.161336089836702), 4: np.float64(0.09901273229643949), 6: np.float64(0.09430681852005175), 51: np.float64(0.161336089836702), 82: np.float64(0.161336089836702), 41: np.float64(0.161336089836702), 0: np.float64(0.161336089836702)}
err dic= {9: np.float64(0.059663910163298), 4: np.float64(0.14598726770356052), 6: np.float64(0.16169318147994827), 51: np.float64(0.07533608983670201), 82: np.float64(0.121336089836702), 41: np.float64(0.068336089836702), 0: np.float64(0.102336089836702)} 

err list= [np.float64(0.059663910163298), np.float64(0.14598726770356052), np.float64(0.16169318147994827), np.float64(0.07533608983670201), np.float64(0.121336089836702), np.float64(0.068336089836702), np.float64(0.102336089836702)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.1487152098257343), 4: np.float64(0.13439572533783675), 6: np.float64(0.12202822553349081), 51: np.float64(0.1487152098257343), 82: np.float64(0.1487152098257343), 41: np.float64(0.1487152098257343), 0: np.float64(0.1487152098257343)}
err dic= {9: np.float64(0.0722847901742657), 4: np.float64(0.11060427466216324), 6: np.float64(0.1339717744665092), 51: np.float64(0.06271520982573431), 82: np.float64(0.1087152098257343), 41: np.float64(0.0557152098257343), 0: np.float64(0.0897152098257343)} 

err list= [np.float64(0.0722847901742657), np.float64(0.11060427466216324), np.float64(0.1339717744665092), np.float64(0.06271520982573431), np.float64(0.1087152098257343), np.float64(0.0557152098257343), np.float64(0.0897152098257343)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.11868050882362594), 4: np.float64(0.22243605549889348), 6: np.float64(0.18416140038298157), 51: np.float64(0.11868050882362594), 82: np.float64(0.11868050882362594), 41: np.float64(0.11868050882362594), 0: np.float64(0.11868050882362594)}
err dic= {9: np.float64(0.10231949117637407), 4: np.float64(0.02256394450110652), 6: np.float64(0.07183859961701844), 51: np.float64(0.03268050882362594), 82: np.float64(0.07868050882362593), 41: np.float64(0.025680508823625936), 0: np.float64(0.05968050882362594)} 

err list= [np.float64(0.10231949117637407), np.float64(0.02256394450110652), np.float64(0.07183859961701844), np.float64(0.03268050882362594), np.float64(0.07868050882362593), np.float64(0.025680508823625936), np.float64(0.05968050882362594)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.03913291423599177), 4: np.float64(0.48901684069581614), 6: np.float64(0.31531858812422386), 51: np.float64(0.03913291423599177), 82: np.float64(0.03913291423599177), 41: np.float64(0.03913291423599177), 0: np.float64(0.03913291423599177)}
err dic= {9: np.float64(0.18186708576400823), 4: np.float64(0.24401684069581614), 6: np.float64(0.05931858812422386), 51: np.float64(0.04686708576400822), 82: np.float64(0.0008670857640082283), 41: np.float64(0.05386708576400823), 0: np.float64(0.019867085764008224)} 

err list= [np.float64(0.18186708576400823), np.float64(0.24401684069581614), np.float64(0.05931858812422386), np.float64(0.04686708576400822), np.float64(0.0008670857640082283), np.float64(0.05386708576400823), np.float64(0.019867085764008224)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.002427512148430851), 4: np.float64(0.6897945004315673), 6: np.float64(0.29806793882627974), 51: np.float64(0.002427512148430851), 82: np.float64(0.002427512148430851), 41: np.float64(0.002427512148430851), 0: np.float64(0.002427512148430851)}
err dic= {9: np.float64(0.21857248785156916), 4: np.float64(0.4447945004315673), 6: np.float64(0.04206793882627974), 51: np.float64(0.08357248785156914), 82: np.float64(0.03757248785156915), 41: np.float64(0.09057248785156914), 0: np.float64(0.056572487851569146)} 

err list= [np.float64(0.21857248785156916), np.float64(0.4447945004315673), np.float64(0.04206793882627974), np.float64(0.08357248785156914), np.float64(0.03757248785156915), np.float64(0.09057248785156914), np.float64(0.056572487851569146)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.00013041704857630568), 4: np.float64(0.7785415446012882), 6: np.float64(0.22080637015583038), 51: np.float64(0.00013041704857630568), 82: np.float64(0.00013041704857630568), 41: np.float64(0.00013041704857630568), 0: np.float64(0.00013041704857630568)}
err dic= {9: np.float64(0.2208695829514237), 4: np.float64(0.5335415446012882), 6: np.float64(0.03519362984416963), 51: np.float64(0.08586958295142369), 82: np.float64(0.0398695829514237), 41: np.float64(0.0928695829514237), 0: np.float64(0.05886958295142369)} 

err list= [np.float64(0.2208695829514237), np.float64(0.5335415446012882), np.float64(0.03519362984416963), np.float64(0.08586958295142369), np.float64(0.0398695829514237), np.float64(0.0928695829514237), np.float64(0.05886958295142369)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(6.1318274601740225e-06), 4: np.float64(0.844127609210241), 6: np.float64(0.1558417316524583), 51: np.float64(6.1318274601740225e-06), 82: np.float64(6.1318274601740225e-06), 41: np.float64(6.1318274601740225e-06), 0: np.float64(6.1318274601740225e-06)}
err dic= {9: np.float64(0.22099386817253983), 4: np.float64(0.599127609210241), 6: np.float64(0.10015826834754171), 51: np.float64(0.08599386817253982), 82: np.float64(0.039993868172539825), 41: np.float64(0.09299386817253982), 0: np.float64(0.05899386817253982)} 

err list= [np.float64(0.22099386817253983), np.float64(0.599127609210241), np.float64(0.10015826834754171), np.float64(0.08599386817253982), np.float64(0.039993868172539825), np.float64(0.09299386817253982), np.float64(0.05899386817253982)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(2.528181310400578e-07), 4: np.float64(0.8934004158387185), 6: np.float64(0.10659832007062603), 51: np.float64(2.528181310400578e-07), 82: np.float64(2.528181310400578e-07), 41: np.float64(2.528181310400578e-07), 0: np.float64(2.528181310400578e-07)}
err dic= {9: np.float64(0.22099974718186896), 4: np.float64(0.6484004158387185), 6: np.float64(0.14940167992937398), 51: np.float64(0.08599974718186895), 82: np.float64(0.03999974718186896), 41: np.float64(0.09299974718186896), 0: np.float64(0.058999747181868956)} 

err list= [np.float64(0.22099974718186896), np.float64(0.6484004158387185), np.float64(0.14940167992937398), np.float64(0.08599974718186895), np.float64(0.03999974718186896), np.float64(0.09299974718186896), np.float64(0.058999747181868956)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(1.0228153862617576e-08), 4: np.float64(0.928909940452737), 6: np.float64(0.07109000840649413), 51: np.float64(1.0228153862617576e-08), 82: np.float64(1.0228153862617576e-08), 41: np.float64(1.0228153862617576e-08), 0: np.float64(1.0228153862617576e-08)}
err dic= {9: np.float64(0.22099998977184615), 4: np.float64(0.683909940452737), 6: np.float64(0.18490999159350588), 51: np.float64(0.08599998977184613), 82: np.float64(0.039999989771846135), 41: np.float64(0.09299998977184613), 0: np.float64(0.05899998977184613)} 

err list= [np.float64(0.22099998977184615), np.float64(0.683909940452737), np.float64(0.18490999159350588), np.float64(0.08599998977184613), np.float64(0.039999989771846135), np.float64(0.09299998977184613), np.float64(0.05899998977184613)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(4.154034008995082e-10), 4: np.float64(0.9535502799356103), 6: np.float64(0.046449717987372546), 51: np.float64(4.154034008995082e-10), 82: np.float64(4.154034008995082e-10), 41: np.float64(4.154034008995082e-10), 0: np.float64(4.154034008995082e-10)}
err dic= {9: np.float64(0.2209999995845966), 4: np.float64(0.7085502799356103), 6: np.float64(0.20955028201262746), 51: np.float64(0.08599999958459659), 82: np.float64(0.0399999995845966), 41: np.float64(0.0929999995845966), 0: np.float64(0.0589999995845966)} 

err list= [np.float64(0.2209999995845966), np.float64(0.7085502799356103), np.float64(0.20955028201262746), np.float64(0.08599999958459659), np.float64(0.0399999995845966), np.float64(0.0929999995845966), np.float64(0.0589999995845966)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(1.6961900013962673e-11), 4: np.float64(0.9701400141644945), 6: np.float64(0.029859985750695966), 51: np.float64(1.6961900013962673e-11), 82: np.float64(1.6961900013962673e-11), 41: np.float64(1.6961900013962673e-11), 0: np.float64(1.6961900013962673e-11)}
err dic= {9: np.float64(0.2209999999830381), 4: np.float64(0.7251400141644945), 6: np.float64(0.22614001424930405), 51: np.float64(0.08599999998303809), 82: np.float64(0.039999999983038104), 41: np.float64(0.0929999999830381), 0: np.float64(0.0589999999830381)} 

err list= [np.float64(0.2209999999830381), np.float64(0.7251400141644945), np.float64(0.22614001424930405), np.float64(0.08599999998303809), np.float64(0.039999999983038104), np.float64(0.0929999999830381), np.float64(0.0589999999830381)]
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(0.12237725115807059), 9: np.float64(0.11111136434642527), 6: np.float64(0.11935574606124708), 39: np.float64(0.16178890960856476), 80: np.float64(0.16178890960856476), 68: np.float64(0.16178890960856476), 0: np.float64(0.16178890960856476)}
err dic= {5: np.float64(0.1226227488419294), 9: np.float64(0.11688863565357474), 6: np.float64(0.13864425393875293), 39: np.float64(0.06178890960856476), 80: np.float64(0.09878890960856476), 68: np.float64(0.10578890960856477), 0: np.float64(0.11178890960856476)} 

err list= [np.float64(0.1226227488419294), np.float64(0.11688863565357474), np.float64(0.13864425393875293), np.float64(0.06178890960856476), np.float64(0.09878890960856476), np.float64(0.10578890960856477), np.float64(0.11178890960856476)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.1644369415039383), 9: np.float64(0.13582771463255558), 6: np.float64(0.156417257233449), 39: np.float64(0.13582952165751241), 80: np.float64(0.13582952165751241), 68: np.float64(0.13582952165751241), 0: np.float64(0.13582952165751241)}
err dic= {5: np.float64(0.08056305849606168), 9: np.float64(0.09217228536744443), 6: np.float64(0.10158274276655102), 39: np.float64(0.03582952165751241), 80: np.float64(0.07282952165751241), 68: np.float64(0.07982952165751242), 0: np.float64(0.08582952165751241)} 

err list= [np.float64(0.08056305849606168), np.float64(0.09217228536744443), np.float64(0.10158274276655102), np.float64(0.03582952165751241), np.float64(0.07282952165751241), np.float64(0.07982952165751242), np.float64(0.08582952165751241)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.2534658349780803), 9: np.float64(0.17438124148690787), 6: np.float64(0.22934537168189398), 39: np.float64(0.08570188796327957), 80: np.float64(0.08570188796327957), 68: np.float64(0.08570188796327957), 0: np.float64(0.08570188796327957)}
err dic= {5: np.float64(0.008465834978080289), 9: np.float64(0.05361875851309214), 6: np.float64(0.02865462831810603), 39: np.float64(0.014298112036720434), 80: np.float64(0.02270188796327957), 68: np.float64(0.02970188796327957), 0: np.float64(0.03570188796327957)} 

err list= [np.float64(0.008465834978080289), np.float64(0.05361875851309214), np.float64(0.02865462831810603), np.float64(0.014298112036720434), np.float64(0.02270188796327957), np.float64(0.02970188796327957), np.float64(0.03570188796327957)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.4353032594959314), 9: np.float64(0.17689755968214166), 6: np.float64(0.3390145193689654), 39: np.float64(0.012196165363238884), 80: np.float64(0.012196165363238884), 68: np.float64(0.012196165363238884), 0: np.float64(0.012196165363238884)}
err dic= {5: np.float64(0.1903032594959314), 9: np.float64(0.05110244031785835), 6: np.float64(0.08101451936896537), 39: np.float64(0.08780383463676113), 80: np.float64(0.050803834636761115), 68: np.float64(0.043803834636761116), 0: np.float64(0.03780383463676112)} 

err list= [np.float64(0.1903032594959314), np.float64(0.05110244031785835), np.float64(0.08101451936896537), np.float64(0.08780383463676113), np.float64(0.050803834636761115), np.float64(0.043803834636761116), np.float64(0.03780383463676112)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5644120517298055), 9: np.float64(0.09142895824045241), 6: np.float64(0.3423332140854401), 39: np.float64(0.0004564439860763787), 80: np.float64(0.0004564439860763787), 68: np.float64(0.0004564439860763787), 0: np.float64(0.0004564439860763787)}
err dic= {5: np.float64(0.31941205172980547), 9: np.float64(0.1365710417595476), 6: np.float64(0.08433321408544009), 39: np.float64(0.09954355601392363), 80: np.float64(0.06254355601392363), 68: np.float64(0.05554355601392362), 0: np.float64(0.04954355601392362)} 

err list= [np.float64(0.31941205172980547), np.float64(0.1365710417595476), np.float64(0.08433321408544009), np.float64(0.09954355601392363), np.float64(0.06254355601392363), np.float64(0.05554355601392362), np.float64(0.04954355601392362)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6518298889939405), 9: np.float64(0.040180984716371215), 6: np.float64(0.307902637637626), 39: np.float64(2.162216301546484e-05), 80: np.float64(2.162216301546484e-05), 68: np.float64(2.162216301546484e-05), 0: np.float64(2.162216301546484e-05)}
err dic= {5: np.float64(0.40682988899394046), 9: np.float64(0.1878190152836288), 6: np.float64(0.04990263763762598), 39: np.float64(0.09997837783698454), 80: np.float64(0.06297837783698454), 68: np.float64(0.05597837783698453), 0: np.float64(0.049978377836984535)} 

err list= [np.float64(0.40682988899394046), np.float64(0.1878190152836288), np.float64(0.04990263763762598), np.float64(0.09997837783698454), np.float64(0.06297837783698454), np.float64(0.05597837783698453), np.float64(0.049978377836984535)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7190983937190444), 9: np.float64(0.016357418876509565), 6: np.float64(0.2645415152286438), 39: np.float64(6.680439506211759e-07), 80: np.float64(6.680439506211759e-07), 68: np.float64(6.680439506211759e-07), 0: np.float64(6.680439506211759e-07)}
err dic= {5: np.float64(0.4740983937190444), 9: np.float64(0.21164258112349044), 6: np.float64(0.006541515228643768), 39: np.float64(0.09999933195604939), 80: np.float64(0.06299933195604938), 68: np.float64(0.05599933195604938), 0: np.float64(0.04999933195604938)} 

err list= [np.float64(0.4740983937190444), np.float64(0.21164258112349044), np.float64(0.006541515228643768), np.float64(0.09999933195604939), np.float64(0.06299933195604938), np.float64(0.05599933195604938), np.float64(0.04999933195604938)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723568628052531), 9: np.float64(0.006359122727984066), 6: np.float64(0.2212839460815928), 39: np.float64(1.7096292405147224e-08), 80: np.float64(1.7096292405147224e-08), 68: np.float64(1.7096292405147224e-08), 0: np.float64(1.7096292405147224e-08)}
err dic= {5: np.float64(0.5273568628052531), 9: np.float64(0.22164087727201595), 6: np.float64(0.03671605391840721), 39: np.float64(0.0999999829037076), 80: np.float64(0.06299998290370759), 68: np.float64(0.0559999829037076), 0: np.float64(0.0499999829037076)} 

err list= [np.float64(0.5273568628052531), np.float64(0.22164087727201595), np.float64(0.03671605391840721), np.float64(0.0999999829037076), np.float64(0.06299998290370759), np.float64(0.0559999829037076), np.float64(0.0499999829037076)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.815605720844507), 9: np.float64(0.0024080423329747125), 6: np.float64(0.18198623511001039), 39: np.float64(4.281268953977451e-10), 80: np.float64(4.281268953977451e-10), 68: np.float64(4.281268953977451e-10), 0: np.float64(4.281268953977451e-10)}
err dic= {5: np.float64(0.570605720844507), 9: np.float64(0.2255919576670253), 6: np.float64(0.07601376488998962), 39: np.float64(0.09999999957187311), 80: np.float64(0.0629999995718731), 68: np.float64(0.055999999571873106), 0: np.float64(0.04999999957187311)} 

err list= [np.float64(0.570605720844507), np.float64(0.2255919576670253), np.float64(0.07601376488998962), np.float64(0.09999999957187311), np.float64(0.0629999995718731), np.float64(0.055999999571873106), np.float64(0.04999999957187311)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511869020993253), 9: np.float64(0.0008989932663118152), 6: np.float64(0.14791410459116772), 39: np.float64(1.0798661754336789e-11), 80: np.float64(1.0798661754336789e-11), 68: np.float64(1.0798661754336789e-11), 0: np.float64(1.0798661754336789e-11)}
err dic= {5: np.float64(0.6061869020993254), 9: np.float64(0.2271010067336882), 6: np.float64(0.11008589540883229), 39: np.float64(0.09999999998920134), 80: np.float64(0.06299999998920133), 68: np.float64(0.05599999998920134), 0: np.float64(0.04999999998920134)} 

err list= [np.float64(0.6061869020993254), np.float64(0.2271010067336882), np.float64(0.11008589540883229), np.float64(0.09999999998920134), np.float64(0.06299999998920133), np.float64(0.05599999998920134), np.float64(0.04999999998920134)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036406456812), 9: np.float64(0.0003331497555666824), 6: np.float64(0.1191632095976519), 39: np.float64(2.7498887459297426e-13), 80: np.float64(2.7498887459297426e-13), 68: np.float64(2.7498887459297426e-13), 0: np.float64(2.7498887459297426e-13)}
err dic= {5: np.float64(0.6355036406456812), 9: np.float64(0.22766685024443334), 6: np.float64(0.1388367904023481), 39: np.float64(0.09999999999972502), 80: np.float64(0.06299999999972501), 68: np.float64(0.05599999999972501), 0: np.float64(0.049999999999725014)} 

err list= [np.float64(0.6355036406456812), np.float64(0.22766685024443334), np.float64(0.1388367904023481), np.float64(0.09999999999972502), np.float64(0.06299999999972501), np.float64(0.05599999999972501), np.float64(0.049999999999725014)]
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(0.10187942743519776), 3: np.float64(0.10948781770520172), 8: np.float64(0.09704700831711598), 15: np.float64(0.17289643663562265), 78: np.float64(0.17289643663562265), 97: np.float64(0.17289643663562265), 0: np.float64(0.17289643663562265)}
err dic= {6: np.float64(0.11912057256480224), 3: np.float64(0.12551218229479827), 8: np.float64(0.140952991682884), 15: np.float64(0.00010356336437733482), 78: np.float64(0.11689643663562266), 97: np.float64(0.13389643663562265), 0: np.float64(0.13489643663562265)} 

err list= [np.float64(0.11912057256480224), np.float64(0.12551218229479827), np.float64(0.140952991682884), np.float64(0.00010356336437733482), np.float64(0.11689643663562266), np.float64(0.13389643663562265), np.float64(0.13489643663562265)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.13071101012400513), 3: np.float64(0.15064816676729884), 8: np.float64(0.11869848024419793), 15: np.float64(0.1499855857161242), 78: np.float64(0.1499855857161242), 97: np.float64(0.1499855857161242), 0: np.float64(0.1499855857161242)}
err dic= {6: np.float64(0.09028898987599487), 3: np.float64(0.08435183323270115), 8: np.float64(0.11930151975580205), 15: np.float64(0.023014414283875795), 78: np.float64(0.0939855857161242), 97: np.float64(0.11098558571612419), 0: np.float64(0.11198558571612419)} 

err list= [np.float64(0.09028898987599487), np.float64(0.08435183323270115), np.float64(0.11930151975580205), np.float64(0.023014414283875795), np.float64(0.0939855857161242), np.float64(0.11098558571612419), np.float64(0.11198558571612419)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.18870547280520483), 3: np.float64(0.24815934042718668), 8: np.float64(0.15615145744976952), 15: np.float64(0.10174593232946078), 78: np.float64(0.10174593232946078), 97: np.float64(0.10174593232946078), 0: np.float64(0.10174593232946078)}
err dic= {6: np.float64(0.03229452719479517), 3: np.float64(0.013159340427186694), 8: np.float64(0.08184854255023047), 15: np.float64(0.07125406767053921), 78: np.float64(0.045745932329460774), 97: np.float64(0.06274593232946077), 0: np.float64(0.06374593232946077)} 

err list= [np.float64(0.03229452719479517), np.float64(0.013159340427186694), np.float64(0.08184854255023047), np.float64(0.07125406767053921), np.float64(0.045745932329460774), np.float64(0.06274593232946077), np.float64(0.06374593232946077)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2660915093506935), 3: np.float64(0.49629883825510746), 8: np.float64(0.16856761740888515), 15: np.float64(0.017260508746327983), 78: np.float64(0.017260508746327983), 97: np.float64(0.017260508746327983), 0: np.float64(0.017260508746327983)}
err dic= {6: np.float64(0.045091509350693476), 3: np.float64(0.26129883825510747), 8: np.float64(0.06943238259111484), 15: np.float64(0.155739491253672), 78: np.float64(0.038739491253672015), 97: np.float64(0.021739491253672017), 0: np.float64(0.020739491253672016)} 

err list= [np.float64(0.045091509350693476), np.float64(0.26129883825510747), np.float64(0.06943238259111484), np.float64(0.155739491253672), np.float64(0.038739491253672015), np.float64(0.021739491253672017), np.float64(0.020739491253672016)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.21069529867306339), 3: np.float64(0.7029205149163066), 8: np.float64(0.08375231580735497), 15: np.float64(0.0006579676508191666), 78: np.float64(0.0006579676508191666), 97: np.float64(0.0006579676508191666), 0: np.float64(0.0006579676508191666)}
err dic= {6: np.float64(0.010304701326936616), 3: np.float64(0.4679205149163066), 8: np.float64(0.154247684192645), 15: np.float64(0.17234203234918083), 78: np.float64(0.055342032349180836), 97: np.float64(0.038342032349180835), 0: np.float64(0.037342032349180834)} 

err list= [np.float64(0.010304701326936616), np.float64(0.4679205149163066), np.float64(0.154247684192645), np.float64(0.17234203234918083), np.float64(0.055342032349180836), np.float64(0.038342032349180835), np.float64(0.037342032349180834)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.1367057120102478), 3: np.float64(0.8299364331712576), 8: np.float64(0.03322090096305703), 15: np.float64(3.4238463859505134e-05), 78: np.float64(3.4238463859505134e-05), 97: np.float64(3.4238463859505134e-05), 0: np.float64(3.4238463859505134e-05)}
err dic= {6: np.float64(0.08429428798975219), 3: np.float64(0.5949364331712577), 8: np.float64(0.20477909903694297), 15: np.float64(0.1729657615361405), 78: np.float64(0.055965761536140496), 97: np.float64(0.038965761536140495), 0: np.float64(0.037965761536140494)} 

err list= [np.float64(0.08429428798975219), np.float64(0.5949364331712577), np.float64(0.20477909903694297), np.float64(0.1729657615361405), np.float64(0.055965761536140496), np.float64(0.038965761536140495), np.float64(0.037965761536140494)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.08066445013165915), 3: np.float64(0.9074921254304275), 8: np.float64(0.011838877130646913), 15: np.float64(1.1368268166770173e-06), 78: np.float64(1.1368268166770173e-06), 97: np.float64(1.1368268166770173e-06), 0: np.float64(1.1368268166770173e-06)}
err dic= {6: np.float64(0.14033554986834085), 3: np.float64(0.6724921254304275), 8: np.float64(0.22616112286935308), 15: np.float64(0.1729988631731833), 78: np.float64(0.055998863173183325), 97: np.float64(0.038998863173183324), 0: np.float64(0.03799886317318332)} 

err list= [np.float64(0.14033554986834085), np.float64(0.6724921254304275), np.float64(0.22616112286935308), np.float64(0.1729988631731833), np.float64(0.055998863173183325), np.float64(0.038998863173183324), np.float64(0.03799886317318332)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.04464838627369278), 3: np.float64(0.9514152815740159), 8: np.float64(0.003936209333466424), 15: np.float64(3.07047062007245e-08), 78: np.float64(3.07047062007245e-08), 97: np.float64(3.07047062007245e-08), 0: np.float64(3.07047062007245e-08)}
err dic= {6: np.float64(0.17635161372630723), 3: np.float64(0.7164152815740159), 8: np.float64(0.23406379066653357), 15: np.float64(0.1729999692952938), 78: np.float64(0.0559999692952938), 97: np.float64(0.0389999692952938), 0: np.float64(0.0379999692952938)} 

err list= [np.float64(0.17635161372630723), np.float64(0.7164152815740159), np.float64(0.23406379066653357), np.float64(0.1729999692952938), np.float64(0.0559999692952938), np.float64(0.0389999692952938), np.float64(0.0379999692952938)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023650013241487456), 3: np.float64(0.9750994279084243), 8: np.float64(0.0012505556608757645), 15: np.float64(7.973032259259149e-10), 78: np.float64(7.973032259259149e-10), 97: np.float64(7.973032259259149e-10), 0: np.float64(7.973032259259149e-10)}
err dic= {6: np.float64(0.19734998675851254), 3: np.float64(0.7400994279084243), 8: np.float64(0.23674944433912423), 15: np.float64(0.17299999920269676), 78: np.float64(0.05599999920269678), 97: np.float64(0.038999999202696777), 0: np.float64(0.037999999202696776)} 

err list= [np.float64(0.19734998675851254), np.float64(0.7400994279084243), np.float64(0.23674944433912423), np.float64(0.17299999920269676), np.float64(0.05599999920269678), np.float64(0.038999999202696777), np.float64(0.037999999202696776)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.01214882045438794), 3: np.float64(0.9874656934198339), 8: np.float64(0.00038548604367916195), 15: np.float64(2.0524581723734864e-11), 78: np.float64(2.0524581723734864e-11), 97: np.float64(2.0524581723734864e-11), 0: np.float64(2.0524581723734864e-11)}
err dic= {6: np.float64(0.20885117954561205), 3: np.float64(0.7524656934198339), 8: np.float64(0.23761451395632083), 15: np.float64(0.1729999999794754), 78: np.float64(0.05599999997947542), 97: np.float64(0.03899999997947542), 0: np.float64(0.03799999997947542)} 

err list= [np.float64(0.20885117954561205), np.float64(0.7524656934198339), np.float64(0.23761451395632083), np.float64(0.1729999999794754), np.float64(0.05599999997947542), np.float64(0.03899999997947542), np.float64(0.03799999997947542)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.006106510940501774), 3: np.float64(0.9937770715374855), 8: np.float64(0.00011641751990615653), 15: np.float64(5.265394011537013e-13), 78: np.float64(5.265394011537013e-13), 97: np.float64(5.265394011537013e-13), 0: np.float64(5.265394011537013e-13)}
err dic= {6: np.float64(0.21489348905949823), 3: np.float64(0.7587770715374855), 8: np.float64(0.23788358248009384), 15: np.float64(0.17299999999947344), 78: np.float64(0.055999999999473464), 97: np.float64(0.03899999999947346), 0: np.float64(0.03799999999947346)} 

err list= [np.float64(0.21489348905949823), np.float64(0.7587770715374855), np.float64(0.23788358248009384), np.float64(0.17299999999947344), np.float64(0.055999999999473464), np.float64(0.03899999999947346), np.float64(0.03799999999947346)]
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(0.11015961396720315), 2: np.float64(0.12707741107721127), 4: np.float64(0.12110647957068117), 95: np.float64(0.17889916449920693), 11: np.float64(0.10495900188728587), 22: np.float64(0.17889916449920693), 0: np.float64(0.17889916449920693)}
err dic= {8: np.float64(0.12484038603279683), 2: np.float64(0.07492258892278875), 4: np.float64(0.07589352042931884), 95: np.float64(0.13689916449920692), 11: np.float64(0.06104099811271414), 22: np.float64(0.041899164499206915), 0: np.float64(0.15789916449920693)} 

err list= [np.float64(0.12484038603279683), np.float64(0.07492258892278875), np.float64(0.07589352042931884), np.float64(0.13689916449920692), np.float64(0.06104099811271414), np.float64(0.041899164499206915), np.float64(0.15789916449920693)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.13229564270770236), 2: np.float64(0.17520972083855021), 4: np.float64(0.15936718635799835), 95: np.float64(0.13764522031331436), 11: np.float64(0.12019178915580044), 22: np.float64(0.13764522031331436), 0: np.float64(0.13764522031331436)}
err dic= {8: np.float64(0.10270435729229763), 2: np.float64(0.026790279161449798), 4: np.float64(0.03763281364200166), 95: np.float64(0.09564522031331435), 11: np.float64(0.04580821084419957), 22: np.float64(0.0006452203133143486), 0: np.float64(0.11664522031331435)} 

err list= [np.float64(0.10270435729229763), np.float64(0.026790279161449798), np.float64(0.03763281364200166), np.float64(0.09564522031331435), np.float64(0.04580821084419957), np.float64(0.0006452203133143486), np.float64(0.11664522031331435)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.15973543297939477), 2: np.float64(0.27479617055786887), 4: np.float64(0.22880956215969595), 95: np.float64(0.06815768713827883), 11: np.float64(0.1321857728882034), 22: np.float64(0.06815768713827883), 0: np.float64(0.06815768713827883)}
err dic= {8: np.float64(0.07526456702060522), 2: np.float64(0.07279617055786886), 4: np.float64(0.03180956215969594), 95: np.float64(0.026157687138278825), 11: np.float64(0.0338142271117966), 22: np.float64(0.06884231286172118), 0: np.float64(0.04715768713827882)} 

err list= [np.float64(0.07526456702060522), np.float64(0.07279617055786886), np.float64(0.03180956215969594), np.float64(0.026157687138278825), np.float64(0.0338142271117966), np.float64(0.06884231286172118), np.float64(0.04715768713827882)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.12851729907068452), 2: np.float64(0.4711219008889947), 4: np.float64(0.30556265817981243), 95: np.float64(0.004900778190123568), 11: np.float64(0.08009580729013506), 22: np.float64(0.004900778190123568), 0: np.float64(0.004900778190123568)}
err dic= {8: np.float64(0.10648270092931547), 2: np.float64(0.2691219008889947), 4: np.float64(0.10856265817981242), 95: np.float64(0.03709922180987643), 11: np.float64(0.08590419270986495), 22: np.float64(0.13209922180987643), 0: np.float64(0.016099221809876434)} 

err list= [np.float64(0.10648270092931547), np.float64(0.2691219008889947), np.float64(0.10856265817981242), np.float64(0.03709922180987643), np.float64(0.08590419270986495), np.float64(0.13209922180987643), np.float64(0.016099221809876434)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04706506486429958), 2: np.float64(0.6542239331254407), 4: np.float64(0.2805598867293658), 95: np.float64(0.00013426643791769003), 11: np.float64(0.017748315967144154), 22: np.float64(0.00013426643791769003), 0: np.float64(0.00013426643791769003)}
err dic= {8: np.float64(0.18793493513570042), 2: np.float64(0.4522239331254407), 4: np.float64(0.08355988672936582), 95: np.float64(0.04186573356208231), 11: np.float64(0.14825168403285585), 22: np.float64(0.13686573356208231), 0: np.float64(0.020865733562082312)} 

err list= [np.float64(0.18793493513570042), np.float64(0.4522239331254407), np.float64(0.08355988672936582), np.float64(0.04186573356208231), np.float64(0.14825168403285585), np.float64(0.13686573356208231), np.float64(0.020865733562082312)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013536275957069698), 2: np.float64(0.7668445030382744), 4: np.float64(0.21654779102542066), 95: np.float64(3.3362718791955294e-06), 11: np.float64(0.003061421163597211), 22: np.float64(3.3362718791955294e-06), 0: np.float64(3.3362718791955294e-06)}
err dic= {8: np.float64(0.2214637240429303), 2: np.float64(0.5648445030382745), 4: np.float64(0.019547791025420647), 95: np.float64(0.04199666372812081), 11: np.float64(0.1629385788364028), 22: np.float64(0.1369966637281208), 0: np.float64(0.020996663728120805)} 

err list= [np.float64(0.2214637240429303), np.float64(0.5648445030382745), np.float64(0.019547791025420647), np.float64(0.04199666372812081), np.float64(0.1629385788364028), np.float64(0.1369966637281208), np.float64(0.020996663728120805)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034775522367853275), 2: np.float64(0.8410327122631517), 4: np.float64(0.15501621893580547), 95: np.float64(5.132287909687641e-08), 11: np.float64(0.0004733625956200577), 22: np.float64(5.132287909687641e-08), 0: np.float64(5.132287909687641e-08)}
err dic= {8: np.float64(0.23152244776321465), 2: np.float64(0.6390327122631516), 4: np.float64(0.041983781064194536), 95: np.float64(0.0419999486771209), 11: np.float64(0.16552663740437995), 22: np.float64(0.13699994867712093), 0: np.float64(0.020999948677120905)} 

err list= [np.float64(0.23152244776321465), np.float64(0.6390327122631516), np.float64(0.041983781064194536), np.float64(0.0419999486771209), np.float64(0.16552663740437995), np.float64(0.13699994867712093), np.float64(0.020999948677120905)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467393050557736), 2: np.float64(0.8926352799771938), 4: np.float64(0.10644832491316357), 95: np.float64(6.464234379745054e-10), 11: np.float64(6.965386531588674e-05), 22: np.float64(6.464234379745054e-10), 0: np.float64(6.464234379745054e-10)}
err dic= {8: np.float64(0.23415326069494422), 2: np.float64(0.6906352799771938), 4: np.float64(0.09055167508683644), 95: np.float64(0.04199999935357657), 11: np.float64(0.16593034613468413), 22: np.float64(0.13699999935357657), 0: np.float64(0.020999999353576562)} 

err list= [np.float64(0.23415326069494422), np.float64(0.6906352799771938), np.float64(0.09055167508683644), np.float64(0.04199999935357657), np.float64(0.16593034613468413), np.float64(0.13699999935357657), np.float64(0.020999999353576562)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066374504021243), 2: np.float64(0.9287259688991545), 4: np.float64(0.07106336957613762), 95: np.float64(7.928298672638632e-12), 11: np.float64(9.997755882287503e-06), 22: np.float64(7.928298672638632e-12), 0: np.float64(7.928298672638632e-12)}
err dic= {8: np.float64(0.23479933625495977), 2: np.float64(0.7267259688991545), 4: np.float64(0.12593663042386238), 95: np.float64(0.041999999992071706), 11: np.float64(0.16599000224411772), 22: np.float64(0.1369999999920717), 0: np.float64(0.0209999999920717)} 

err list= [np.float64(0.23479933625495977), np.float64(0.7267259688991545), np.float64(0.12593663042386238), np.float64(0.041999999992071706), np.float64(0.16599000224411772), np.float64(0.1369999999920717), np.float64(0.0209999999920717)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.6823878792601476e-05), 2: np.float64(0.9535067301961612), 4: np.float64(0.04644503163372375), 95: np.float64(9.756966270620554e-14), 11: np.float64(1.4142910286249312e-06), 22: np.float64(9.756966270620554e-14), 0: np.float64(9.756966270620554e-14)}
err dic= {8: np.float64(0.2349531761212074), 2: np.float64(0.7515067301961611), 4: np.float64(0.15055496836627624), 95: np.float64(0.041999999999902435), 11: np.float64(0.16599858570897139), 22: np.float64(0.13699999999990245), 0: np.float64(0.02099999999990243)} 

err list= [np.float64(0.2349531761212074), np.float64(0.7515067301961611), np.float64(0.15055496836627624), np.float64(0.041999999999902435), np.float64(0.16599858570897139), np.float64(0.13699999999990245), np.float64(0.02099999999990243)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.081560860247474e-05), 2: np.float64(0.9701298210556221), 4: np.float64(0.029859165226525684), 95: np.float64(1.2073387154830707e-15), 11: np.float64(1.9810924551184023e-07), 22: np.float64(1.2073387154830707e-15), 0: np.float64(1.2073387154830707e-15)}
err dic= {8: np.float64(0.23498918439139752), 2: np.float64(0.768129821055622), 4: np.float64(0.16714083477347433), 95: np.float64(0.041999999999998795), 11: np.float64(0.1659998018907545), 22: np.float64(0.13699999999999882), 0: np.float64(0.020999999999998794)} 

err list= [np.float64(0.23498918439139752), np.float64(0.768129821055622), np.float64(0.16714083477347433), np.float64(0.041999999999998795), np.float64(0.1659998018907545), np.float64(0.13699999999999882), np.float64(0.020999999999998794)]
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(0.13016645442125904), 3: np.float64(0.12405558528843558), 9: np.float64(0.10771640502990368), 100: np.float64(0.10025071019799485), 22: np.float64(0.1792702816874696), 58: np.float64(0.1792702816874696), 0: np.float64(0.1792702816874696)}
err dic= {1: np.float64(0.08783354557874096), 3: np.float64(0.05694441471156442), 9: np.float64(0.08928359497009633), 100: np.float64(0.12174928980200515), 22: np.float64(0.06627028168746961), 58: np.float64(0.1382702816874696), 0: np.float64(0.15127028168746962)} 

err list= [np.float64(0.08783354557874096), np.float64(0.05694441471156442), np.float64(0.08928359497009633), np.float64(0.12174928980200515), np.float64(0.06627028168746961), np.float64(0.1382702816874696), np.float64(0.15127028168746962)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1832872047620885), 3: np.float64(0.16675077071541985), 9: np.float64(0.1264153992619414), 100: np.float64(0.1096362201906402), 22: np.float64(0.13797013502330133), 58: np.float64(0.13797013502330133), 0: np.float64(0.13797013502330133)}
err dic= {1: np.float64(0.03471279523791149), 3: np.float64(0.01424922928458014), 9: np.float64(0.07058460073805861), 100: np.float64(0.1123637798093598), 22: np.float64(0.024970135023301324), 58: np.float64(0.09697013502330132), 0: np.float64(0.10997013502330133)} 

err list= [np.float64(0.03471279523791149), np.float64(0.01424922928458014), np.float64(0.07058460073805861), np.float64(0.1123637798093598), np.float64(0.024970135023301324), np.float64(0.09697013502330132), np.float64(0.10997013502330133)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.29594032239578455), 3: np.float64(0.24669153326283605), 9: np.float64(0.1448642579811597), 100: np.float64(0.1093664859308943), 22: np.float64(0.06771246680977555), 58: np.float64(0.06771246680977555), 0: np.float64(0.06771246680977555)}
err dic= {1: np.float64(0.07794032239578455), 3: np.float64(0.06569153326283605), 9: np.float64(0.0521357420188403), 100: np.float64(0.1126335140691057), 22: np.float64(0.04528753319022445), 58: np.float64(0.02671246680977555), 0: np.float64(0.039712466809775554)} 

err list= [np.float64(0.07794032239578455), np.float64(0.06569153326283605), np.float64(0.0521357420188403), np.float64(0.1126335140691057), np.float64(0.04528753319022445), np.float64(0.02671246680977555), np.float64(0.039712466809775554)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5136203291895352), 3: np.float64(0.33472393641707826), 9: np.float64(0.09261531177788032), 100: np.float64(0.04553606773697417), 22: np.float64(0.004501451626176618), 58: np.float64(0.004501451626176618), 0: np.float64(0.004501451626176618)}
err dic= {1: np.float64(0.2956203291895352), 3: np.float64(0.15372393641707827), 9: np.float64(0.10438468822211969), 100: np.float64(0.17646393226302584), 22: np.float64(0.10849854837382339), 58: np.float64(0.03649854837382338), 0: np.float64(0.023498548373823383)} 

err list= [np.float64(0.2956203291895352), np.float64(0.15372393641707827), np.float64(0.10438468822211969), np.float64(0.17646393226302584), np.float64(0.10849854837382339), np.float64(0.03649854837382338), np.float64(0.023498548373823383)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.681308318303542), 3: np.float64(0.2939941269354523), 9: np.float64(0.019881935426477516), 100: np.float64(0.0045403277014733545), 22: np.float64(9.176387768596154e-05), 58: np.float64(9.176387768596154e-05), 0: np.float64(9.176387768596154e-05)}
err dic= {1: np.float64(0.463308318303542), 3: np.float64(0.1129941269354523), 9: np.float64(0.1771180645735225), 100: np.float64(0.21745967229852664), 22: np.float64(0.11290823612231404), 58: np.float64(0.04090823612231404), 0: np.float64(0.02790823612231404)} 

err list= [np.float64(0.463308318303542), np.float64(0.1129941269354523), np.float64(0.1771180645735225), np.float64(0.21745967229852664), np.float64(0.11290823612231404), np.float64(0.04090823612231404), np.float64(0.02790823612231404)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7763862029556592), 3: np.float64(0.22001173567330343), 9: np.float64(0.003251800870007816), 100: np.float64(0.00034522731781108434), 22: np.float64(1.6777277394202914e-06), 58: np.float64(1.6777277394202914e-06), 0: np.float64(1.6777277394202914e-06)}
err dic= {1: np.float64(0.5583862029556592), 3: np.float64(0.03901173567330343), 9: np.float64(0.1937481991299922), 100: np.float64(0.22165477268218892), 22: np.float64(0.11299832227226059), 58: np.float64(0.04099832227226058), 0: np.float64(0.02799832227226058)} 

err list= [np.float64(0.5583862029556592), np.float64(0.03901173567330343), np.float64(0.1937481991299922), np.float64(0.22165477268218892), np.float64(0.11299832227226059), np.float64(0.04099832227226058), np.float64(0.02799832227226058)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437493206975359), 3: np.float64(0.15573991344880617), 9: np.float64(0.00048644690450756913), 100: np.float64(2.426070853045383e-05), 22: np.float64(1.9413540002128164e-08), 58: np.float64(1.9413540002128164e-08), 0: np.float64(1.9413540002128164e-08)}
err dic= {1: np.float64(0.625749320697536), 3: np.float64(0.025260086551193828), 9: np.float64(0.19651355309549243), 100: np.float64(0.22197573929146955), 22: np.float64(0.11299998058646), 58: np.float64(0.04099998058646), 0: np.float64(0.02799998058646)} 

err list= [np.float64(0.625749320697536), np.float64(0.025260086551193828), np.float64(0.19651355309549243), np.float64(0.22197573929146955), np.float64(0.11299998058646), np.float64(0.04099998058646), np.float64(0.02799998058646)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933412337877992), 3: np.float64(0.10658666245815765), 9: np.float64(7.044586717543178e-05), 100: np.float64(1.6573248731031903e-06), 22: np.float64(1.8733143437349076e-10), 58: np.float64(1.8733143437349076e-10), 0: np.float64(1.8733143437349076e-10)}
err dic= {1: np.float64(0.6753412337877992), 3: np.float64(0.07441333754184234), 9: np.float64(0.19692955413282456), 100: np.float64(0.2219983426751269), 22: np.float64(0.11299999981266858), 58: np.float64(0.04099999981266857), 0: np.float64(0.027999999812668565)} 

err list= [np.float64(0.6753412337877992), np.float64(0.07441333754184234), np.float64(0.19692955413282456), np.float64(0.2219983426751269), np.float64(0.11299999981266858), np.float64(0.04099999981266857), np.float64(0.027999999812668565)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011179539564), 3: np.float64(0.07108872798718269), 9: np.float64(1.004248385155474e-05), 100: np.float64(1.1156967800415795e-07), 22: np.float64(1.7769972267094923e-12), 58: np.float64(1.7769972267094923e-12), 0: np.float64(1.7769972267094923e-12)}
err dic= {1: np.float64(0.7109011179539564), 3: np.float64(0.10991127201281731), 9: np.float64(0.19698995751614845), 100: np.float64(0.221999888430322), 22: np.float64(0.11299999999822301), 58: np.float64(0.040999999998223007), 0: np.float64(0.027999999998223002)} 

err list= [np.float64(0.7109011179539564), np.float64(0.10991127201281731), np.float64(0.19698995751614845), np.float64(0.221999888430322), np.float64(0.11299999999822301), np.float64(0.040999999998223007), np.float64(0.027999999998223002)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489961513264), 3: np.float64(0.04644957969910673), 9: np.float64(1.416715180521157e-06), 100: np.float64(7.434334682399622e-09), 22: np.float64(1.6984197808961042e-14), 58: np.float64(1.6984197808961042e-14), 0: np.float64(1.6984197808961042e-14)}
err dic= {1: np.float64(0.7355489961513264), 3: np.float64(0.13455042030089326), 9: np.float64(0.19699858328481948), 100: np.float64(0.22199999256566533), 22: np.float64(0.11299999999998302), 58: np.float64(0.040999999999983015), 0: np.float64(0.027999999999983018)} 

err list= [np.float64(0.7355489961513264), np.float64(0.13455042030089326), np.float64(0.19699858328481948), np.float64(0.22199999256566533), np.float64(0.11299999999998302), np.float64(0.040999999999983015), np.float64(0.027999999999983018)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303256952), 3: np.float64(0.02985997094565118), 9: np.float64(1.9823727027203125e-07), 100: np.float64(4.913822077323287e-10), 22: np.float64(1.6350124220871414e-16), 58: np.float64(1.6350124220871414e-16), 0: np.float64(1.6350124220871414e-16)}
err dic= {1: np.float64(0.7521398303256952), 3: np.float64(0.1511400290543488), 9: np.float64(0.19699980176272974), 100: np.float64(0.2219999995086178), 22: np.float64(0.11299999999999984), 58: np.float64(0.040999999999999835), 0: np.float64(0.027999999999999838)} 

err list= [np.float64(0.7521398303256952), np.float64(0.1511400290543488), np.float64(0.19699980176272974), np.float64(0.2219999995086178), np.float64(0.11299999999999984), np.float64(0.040999999999999835), np.float64(0.027999999999999838)]
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(0.1000990482797207), 6: np.float64(0.10263306775130245), 8: np.float64(0.09762759397181418), 16: np.float64(0.174910072499292), 83: np.float64(0.174910072499292), 70: np.float64(0.174910072499292), 0: np.float64(0.174910072499292)}
err dic= {7: np.float64(0.10690095172027929), 6: np.float64(0.14336693224869757), 8: np.float64(0.1513724060281858), 16: np.float64(0.026910072499292004), 83: np.float64(0.12691007249929198), 70: np.float64(0.116910072499292), 0: np.float64(0.13091007249929199)} 

err list= [np.float64(0.10690095172027929), np.float64(0.14336693224869757), np.float64(0.1513724060281858), np.float64(0.026910072499292004), np.float64(0.12691007249929198), np.float64(0.116910072499292), np.float64(0.13091007249929199)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.12681861390260774), 6: np.float64(0.1333207432782822), 8: np.float64(0.12063359711855558), 16: np.float64(0.15480676142513874), 83: np.float64(0.15480676142513874), 70: np.float64(0.15480676142513874), 0: np.float64(0.15480676142513874)}
err dic= {7: np.float64(0.08018138609739225), 6: np.float64(0.1126792567217178), 8: np.float64(0.1283664028814444), 16: np.float64(0.006806761425138752), 83: np.float64(0.10680676142513874), 70: np.float64(0.09680676142513875), 0: np.float64(0.11080676142513875)} 

err list= [np.float64(0.08018138609739225), np.float64(0.1126792567217178), np.float64(0.1283664028814444), np.float64(0.006806761425138752), np.float64(0.10680676142513874), np.float64(0.09680676142513875), np.float64(0.11080676142513875)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.1820127178080714), 6: np.float64(0.20115516244139), 8: np.float64(0.1646919176311633), 16: np.float64(0.11303505052984533), 83: np.float64(0.11303505052984533), 70: np.float64(0.11303505052984533), 0: np.float64(0.11303505052984533)}
err dic= {7: np.float64(0.024987282191928584), 6: np.float64(0.04484483755860999), 8: np.float64(0.08430808236883669), 16: np.float64(0.03496494947015466), 83: np.float64(0.06503505052984533), 70: np.float64(0.05503505052984533), 0: np.float64(0.06903505052984533)} 

err list= [np.float64(0.024987282191928584), np.float64(0.04484483755860999), np.float64(0.08430808236883669), np.float64(0.03496494947015466), np.float64(0.06503505052984533), np.float64(0.05503505052984533), np.float64(0.06903505052984533)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.2880106263032868), 6: np.float64(0.3698129644495755), 8: np.float64(0.2243029012978853), 16: np.float64(0.029468376987312476), 83: np.float64(0.029468376987312476), 70: np.float64(0.029468376987312476), 0: np.float64(0.029468376987312476)}
err dic= {7: np.float64(0.08101062630328679), 6: np.float64(0.12381296444957551), 8: np.float64(0.0246970987021147), 16: np.float64(0.11853162301268752), 83: np.float64(0.018531623012687525), 70: np.float64(0.028531623012687527), 0: np.float64(0.014531623012687522)} 

err list= [np.float64(0.08101062630328679), np.float64(0.12381296444957551), np.float64(0.0246970987021147), np.float64(0.11853162301268752), np.float64(0.018531623012687525), np.float64(0.028531623012687527), np.float64(0.014531623012687522)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.30518796430445355), 6: np.float64(0.503169888310424), 8: np.float64(0.18510585732593593), 16: np.float64(0.0016340725147969762), 83: np.float64(0.0016340725147969762), 70: np.float64(0.0016340725147969762), 0: np.float64(0.0016340725147969762)}
err dic= {7: np.float64(0.09818796430445356), 6: np.float64(0.257169888310424), 8: np.float64(0.06389414267406407), 16: np.float64(0.14636592748520302), 83: np.float64(0.046365927485203025), 70: np.float64(0.05636592748520303), 0: np.float64(0.04236592748520302)} 

err list= [np.float64(0.09818796430445356), np.float64(0.257169888310424), np.float64(0.06389414267406407), np.float64(0.14636592748520302), np.float64(0.046365927485203025), np.float64(0.05636592748520303), np.float64(0.04236592748520302)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.27844193125742905), 6: np.float64(0.5894615730976424), 8: np.float64(0.13152665520662235), 16: np.float64(0.0001424601095766617), 83: np.float64(0.0001424601095766617), 70: np.float64(0.0001424601095766617), 0: np.float64(0.0001424601095766617)}
err dic= {7: np.float64(0.07144193125742906), 6: np.float64(0.34346157309764236), 8: np.float64(0.11747334479337765), 16: np.float64(0.14785753989042333), 83: np.float64(0.04785753989042334), 70: np.float64(0.05785753989042334), 0: np.float64(0.04385753989042333)} 

err list= [np.float64(0.07144193125742906), np.float64(0.34346157309764236), np.float64(0.11747334479337765), np.float64(0.14785753989042333), np.float64(0.04785753989042334), np.float64(0.05785753989042334), np.float64(0.04385753989042333)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24471958271907815), 6: np.float64(0.66521679477335), 8: np.float64(0.09002730333440301), 16: np.float64(9.079793292208228e-06), 83: np.float64(9.079793292208228e-06), 70: np.float64(9.079793292208228e-06), 0: np.float64(9.079793292208228e-06)}
err dic= {7: np.float64(0.03771958271907816), 6: np.float64(0.41921679477335005), 8: np.float64(0.158972696665597), 16: np.float64(0.1479909202067078), 83: np.float64(0.047990920206707796), 70: np.float64(0.0579909202067078), 0: np.float64(0.04399092020670779)} 

err list= [np.float64(0.03771958271907816), np.float64(0.41921679477335005), np.float64(0.158972696665597), np.float64(0.1479909202067078), np.float64(0.047990920206707796), np.float64(0.0579909202067078), np.float64(0.04399092020670779)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20934266726585288), 6: np.float64(0.730677704387647), 8: np.float64(0.05997767835917354), 16: np.float64(4.874968315731538e-07), 83: np.float64(4.874968315731538e-07), 70: np.float64(4.874968315731538e-07), 0: np.float64(4.874968315731538e-07)}
err dic= {7: np.float64(0.002342667265852888), 6: np.float64(0.484677704387647), 8: np.float64(0.18902232164082647), 16: np.float64(0.14799951250316842), 83: np.float64(0.047999512503168425), 70: np.float64(0.05799951250316843), 0: np.float64(0.04399951250316842)} 

err list= [np.float64(0.002342667265852888), np.float64(0.484677704387647), np.float64(0.18902232164082647), np.float64(0.14799951250316842), np.float64(0.047999512503168425), np.float64(0.05799951250316843), np.float64(0.04399951250316842)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17529037411297566), 6: np.float64(0.7855969537975934), 8: np.float64(0.039112569248306445), 16: np.float64(2.5710281079393798e-08), 83: np.float64(2.5710281079393798e-08), 70: np.float64(2.5710281079393798e-08), 0: np.float64(2.5710281079393798e-08)}
err dic= {7: np.float64(0.031709625887024334), 6: np.float64(0.5395969537975934), 8: np.float64(0.20988743075169355), 16: np.float64(0.14799997428971892), 83: np.float64(0.04799997428971892), 70: np.float64(0.057999974289718925), 0: np.float64(0.04399997428971892)} 

err list= [np.float64(0.031709625887024334), np.float64(0.5395969537975934), np.float64(0.20988743075169355), np.float64(0.14799997428971892), np.float64(0.04799997428971892), np.float64(0.057999974289718925), np.float64(0.04399997428971892)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.14433395432571167), 6: np.float64(0.8305845598012291), 8: np.float64(0.02508148041697535), 16: np.float64(1.3640208742751618e-09), 83: np.float64(1.3640208742751618e-09), 70: np.float64(1.3640208742751618e-09), 0: np.float64(1.3640208742751618e-09)}
err dic= {7: np.float64(0.06266604567428832), 6: np.float64(0.5845845598012291), 8: np.float64(0.22391851958302464), 16: np.float64(0.14799999863597912), 83: np.float64(0.047999998635979126), 70: np.float64(0.05799999863597913), 0: np.float64(0.04399999863597912)} 

err list= [np.float64(0.06266604567428832), np.float64(0.5845845598012291), np.float64(0.22391851958302464), np.float64(0.14799999863597912), np.float64(0.047999998635979126), np.float64(0.05799999863597913), np.float64(0.04399999863597912)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11731042779202583), 6: np.float64(0.8668133319448319), 8: np.float64(0.015876239971842013), 16: np.float64(7.28249539981153e-11), 83: np.float64(7.28249539981153e-11), 70: np.float64(7.28249539981153e-11), 0: np.float64(7.28249539981153e-11)}
err dic= {7: np.float64(0.08968957220797416), 6: np.float64(0.6208133319448319), 8: np.float64(0.233123760028158), 16: np.float64(0.14799999992717505), 83: np.float64(0.04799999992717505), 70: np.float64(0.05799999992717505), 0: np.float64(0.04399999992717504)} 

err list= [np.float64(0.08968957220797416), np.float64(0.6208133319448319), np.float64(0.233123760028158), np.float64(0.14799999992717505), np.float64(0.04799999992717505), np.float64(0.05799999992717505), np.float64(0.04399999992717504)]
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= [0.11475437 0.10326676 0.08685452 0.07977115 0.08412308 0.08985988
 0.09567322 0.10110765 0.10700353 0.11300559 0.11885738]
mean_std= [0.         0.01148761 0.02503398 0.02491079 0.0239206  0.02532555
 0.02743222 0.02941415 0.03235971 0.03559015 0.03865155]
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
