p= 0.5 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(0.19469110979957047), 3: np.float64(0.1898841691713173), 4: np.float64(0.18519591233005034), 59: np.float64(0.10755720217476343), 40: np.float64(0.10755720217476343), 84: np.float64(0.10755720217476343), 0: np.float64(0.10755720217476343)}
err dic= {2: np.float64(0.08030889020042956), 3: np.float64(0.057115830828682684), 4: np.float64(0.06680408766994966), 59: np.float64(0.048557202174763434), 40: np.float64(0.035557202174763436), 84: np.float64(0.04755720217476343), 0: np.float64(0.07255720217476343)} 

err list= [np.float64(0.08030889020042956), np.float64(0.057115830828682684), np.float64(0.06680408766994966), np.float64(0.048557202174763434), np.float64(0.035557202174763436), np.float64(0.04755720217476343), np.float64(0.07255720217476343)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.29388804327304135), 3: np.float64(0.2795549542702563), 4: np.float64(0.26592089826681925), 59: np.float64(0.04015902604747028), 40: np.float64(0.04015902604747028), 84: np.float64(0.04015902604747028), 0: np.float64(0.04015902604747028)}
err dic= {2: np.float64(0.018888043273041333), 3: np.float64(0.03255495427025629), 4: np.float64(0.013920898266819248), 59: np.float64(0.01884097395252972), 40: np.float64(0.031840973952529716), 84: np.float64(0.01984097395252972), 0: np.float64(0.005159026047470275)} 

err list= [np.float64(0.018888043273041333), np.float64(0.03255495427025629), np.float64(0.013920898266819248), np.float64(0.01884097395252972), np.float64(0.031840973952529716), np.float64(0.01984097395252972), np.float64(0.005159026047470275)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.36076153797774946), 3: np.float64(0.32643053855046866), 4: np.float64(0.2953665656700938), 59: np.float64(0.004360339450421464), 40: np.float64(0.004360339450421464), 84: np.float64(0.004360339450421464), 0: np.float64(0.004360339450421464)}
err dic= {2: np.float64(0.08576153797774944), 3: np.float64(0.07943053855046867), 4: np.float64(0.04336656567009378), 59: np.float64(0.054639660549578535), 40: np.float64(0.06763966054957853), 84: np.float64(0.055639660549578536), 0: np.float64(0.030639660549578538)} 

err list= [np.float64(0.08576153797774944), np.float64(0.07943053855046867), np.float64(0.04336656567009378), np.float64(0.054639660549578535), np.float64(0.06763966054957853), np.float64(0.055639660549578536), np.float64(0.030639660549578538)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.4192241579475863), 3: np.float64(0.3264921024920305), 4: np.float64(0.25427230508742266), 59: np.float64(2.8586182400662538e-06), 40: np.float64(2.8586182400662538e-06), 84: np.float64(2.8586182400662538e-06), 0: np.float64(2.8586182400662538e-06)}
err dic= {2: np.float64(0.14422415794758625), 3: np.float64(0.07949210249203048), 4: np.float64(0.0022723050874226547), 59: np.float64(0.05899714138175993), 40: np.float64(0.07199714138175993), 84: np.float64(0.05999714138175993), 0: np.float64(0.03499714138175994)} 

err list= [np.float64(0.14422415794758625), np.float64(0.07949210249203048), np.float64(0.0022723050874226547), np.float64(0.05899714138175993), np.float64(0.07199714138175993), np.float64(0.05999714138175993), np.float64(0.03499714138175994)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5064803910498094), 3: np.float64(0.3071958857149533), 4: np.float64(0.18632372322369742), 59: np.float64(2.8850772597895805e-12), 40: np.float64(2.8850772597895805e-12), 84: np.float64(2.8850772597895805e-12), 0: np.float64(2.8850772597895805e-12)}
err dic= {2: np.float64(0.23148039104980933), 3: np.float64(0.06019588571495332), 4: np.float64(0.06567627677630258), 59: np.float64(0.05899999999711492), 40: np.float64(0.07199999999711491), 84: np.float64(0.059999999997114924), 0: np.float64(0.03499999999711493)} 

err list= [np.float64(0.23148039104980933), np.float64(0.06019588571495332), np.float64(0.06567627677630258), np.float64(0.05899999999711492), np.float64(0.07199999999711491), np.float64(0.059999999997114924), np.float64(0.03499999999711493)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5897976636568126), 3: np.float64(0.27860068919627307), 4: np.float64(0.1316016471469144), 59: np.float64(3.274017252593395e-18), 40: np.float64(3.274017252593395e-18), 84: np.float64(3.274017252593395e-18), 0: np.float64(3.274017252593395e-18)}
err dic= {2: np.float64(0.3147976636568126), 3: np.float64(0.03160068919627307), 4: np.float64(0.12039835285308559), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.3147976636568126), np.float64(0.03160068919627307), np.float64(0.12039835285308559), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652409557748219), 3: np.float64(0.24472847105479767), 4: np.float64(0.09003057317038048), 59: np.float64(4.0394470311125845e-24), 40: np.float64(4.0394470311125845e-24), 84: np.float64(4.0394470311125845e-24), 0: np.float64(4.0394470311125845e-24)}
err dic= {2: np.float64(0.3902409557748219), 3: np.float64(0.002271528945202328), 4: np.float64(0.1619694268296195), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.3902409557748219), np.float64(0.002271528945202328), np.float64(0.1619694268296195), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.7306791292026885), 3: np.float64(0.20934307548219683), 4: np.float64(0.059977795315114234), 59: np.float64(5.217471713692847e-30), 40: np.float64(5.217471713692847e-30), 84: np.float64(5.217471713692847e-30), 0: np.float64(5.217471713692847e-30)}
err dic= {2: np.float64(0.4556791292026885), 3: np.float64(0.03765692451780317), 4: np.float64(0.19202220468488576), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.4556791292026885), np.float64(0.03765692451780317), np.float64(0.19202220468488576), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855970345892754), 3: np.float64(0.17529039214003653), 4: np.float64(0.039112573270687415), 59: np.float64(6.909916378006248e-36), 40: np.float64(6.909916378006248e-36), 84: np.float64(6.909916378006248e-36), 0: np.float64(6.909916378006248e-36)}
err dic= {2: np.float64(0.5105970345892754), 3: np.float64(0.07170960785996347), 4: np.float64(0.2128874267293126), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.5105970345892754), np.float64(0.07170960785996347), np.float64(0.2128874267293126), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845643329679), 3: np.float64(0.1443339551132097), 4: np.float64(0.025081480553821995), 59: np.float64(9.281871075985908e-42), 40: np.float64(9.281871075985908e-42), 84: np.float64(9.281871075985908e-42), 0: np.float64(9.281871075985908e-42)}
err dic= {2: np.float64(0.5555845643329679), 3: np.float64(0.10266604488679029), 4: np.float64(0.226918519446178), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.5555845643329679), np.float64(0.10266604488679029), np.float64(0.226918519446178), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973345), 3: np.float64(0.11731042782619833), 4: np.float64(0.015876239976466765), 59: np.float64(1.2571050518932684e-47), 40: np.float64(1.2571050518932684e-47), 84: np.float64(1.2571050518932684e-47), 0: np.float64(1.2571050518932684e-47)}
err dic= {2: np.float64(0.5918133321973345), 3: np.float64(0.12968957217380167), 4: np.float64(0.23612376002353325), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.5918133321973345), np.float64(0.12968957217380167), np.float64(0.23612376002353325), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
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(0.19377343934939203), 4: np.float64(0.18898915608528302), 8: np.float64(0.17247271400378128), 74: np.float64(0.11119117264038375), 40: np.float64(0.11119117264038375), 87: np.float64(0.11119117264038375), 0: np.float64(0.11119117264038375)}
err dic= {3: np.float64(0.06522656065060797), 4: np.float64(0.057010843914716974), 8: np.float64(0.08352728599621873), 74: np.float64(0.04519117264038375), 40: np.float64(0.03419117264038375), 87: np.float64(0.06419117264038375), 0: np.float64(0.06219117264038375)} 

err list= [np.float64(0.06522656065060797), np.float64(0.057010843914716974), np.float64(0.08352728599621873), np.float64(0.04519117264038375), np.float64(0.03419117264038375), np.float64(0.06419117264038375), np.float64(0.06219117264038375)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.29852480004715604), 4: np.float64(0.28396557374804676), 8: np.float64(0.23902990050991704), 74: np.float64(0.044619931423719665), 40: np.float64(0.044619931423719665), 87: np.float64(0.044619931423719665), 0: np.float64(0.044619931423719665)}
err dic= {3: np.float64(0.03952480004715603), 4: np.float64(0.037965573748046766), 8: np.float64(0.016970099490082963), 74: np.float64(0.021380068576280338), 40: np.float64(0.032380068576280334), 87: np.float64(0.002380068576280335), 0: np.float64(0.004380068576280337)} 

err list= [np.float64(0.03952480004715603), np.float64(0.037965573748046766), np.float64(0.016970099490082963), np.float64(0.021380068576280338), np.float64(0.032380068576280334), np.float64(0.002380068576280335), np.float64(0.004380068576280337)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.3833175897714758), 4: np.float64(0.3468400982165894), 8: np.float64(0.2491785358046002), 74: np.float64(0.0051659440518328015), 40: np.float64(0.0051659440518328015), 87: np.float64(0.0051659440518328015), 0: np.float64(0.0051659440518328015)}
err dic= {3: np.float64(0.12431758977147578), 4: np.float64(0.1008400982165894), 8: np.float64(0.006821464195399807), 74: np.float64(0.0608340559481672), 40: np.float64(0.07183405594816719), 87: np.float64(0.0418340559481672), 0: np.float64(0.0438340559481672)} 

err list= [np.float64(0.12431758977147578), np.float64(0.1008400982165894), np.float64(0.006821464195399807), np.float64(0.0608340559481672), np.float64(0.07183405594816719), np.float64(0.0418340559481672), np.float64(0.0438340559481672)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.47291138160402446), 4: np.float64(0.36830375431659423), 8: np.float64(0.15876816140950295), 74: np.float64(4.175667469451702e-06), 40: np.float64(4.175667469451702e-06), 87: np.float64(4.175667469451702e-06), 0: np.float64(4.175667469451702e-06)}
err dic= {3: np.float64(0.21391138160402445), 4: np.float64(0.12230375431659424), 8: np.float64(0.09723183859049706), 74: np.float64(0.06599582433253055), 40: np.float64(0.07699582433253055), 87: np.float64(0.04699582433253055), 0: np.float64(0.04899582433253055)} 

err list= [np.float64(0.21391138160402445), np.float64(0.12230375431659424), np.float64(0.09723183859049706), np.float64(0.06599582433253055), np.float64(0.07699582433253055), np.float64(0.04699582433253055), np.float64(0.04899582433253055)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.584145784587888), 4: np.float64(0.35430232809444556), 8: np.float64(0.061551887293144904), 74: np.float64(6.130467529718647e-12), 40: np.float64(6.130467529718647e-12), 87: np.float64(6.130467529718647e-12), 0: np.float64(6.130467529718647e-12)}
err dic= {3: np.float64(0.325145784587888), 4: np.float64(0.10830232809444557), 8: np.float64(0.1944481127068551), 74: np.float64(0.06599999999386953), 40: np.float64(0.07699999999386953), 87: np.float64(0.046999999993869536), 0: np.float64(0.04899999999386954)} 

err list= [np.float64(0.325145784587888), np.float64(0.10830232809444557), np.float64(0.1944481127068551), np.float64(0.06599999999386953), np.float64(0.07699999999386953), np.float64(0.046999999993869536), np.float64(0.04899999999386954)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.6651469585882833), 4: np.float64(0.31419317589451784), 8: np.float64(0.02065986551719901), 74: np.float64(9.248521739518765e-18), 40: np.float64(9.248521739518765e-18), 87: np.float64(9.248521739518765e-18), 0: np.float64(9.248521739518765e-18)}
err dic= {3: np.float64(0.4061469585882833), 4: np.float64(0.06819317589451784), 8: np.float64(0.235340134482801), 74: np.float64(0.06599999999999999), 40: np.float64(0.07699999999999999), 87: np.float64(0.04699999999999999), 0: np.float64(0.048999999999999995)} 

err list= [np.float64(0.4061469585882833), np.float64(0.06819317589451784), np.float64(0.235340134482801), np.float64(0.06599999999999999), np.float64(0.07699999999999999), np.float64(0.04699999999999999), np.float64(0.048999999999999995)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.7263954957320881), 4: np.float64(0.26722596903937335), 8: np.float64(0.0063785352285387455), 74: np.float64(1.4395778198965726e-23), 40: np.float64(1.4395778198965726e-23), 87: np.float64(1.4395778198965726e-23), 0: np.float64(1.4395778198965726e-23)}
err dic= {3: np.float64(0.46739549573208805), 4: np.float64(0.02122596903937335), 8: np.float64(0.24962146477146127), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.46739549573208805), np.float64(0.02122596903937335), np.float64(0.24962146477146127), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.775832220546095), 4: np.float64(0.22227965274514916), 8: np.float64(0.001888126708755253), 74: np.float64(2.301596031579651e-29), 40: np.float64(2.301596031579651e-29), 87: np.float64(2.301596031579651e-29), 0: np.float64(2.301596031579651e-29)}
err dic= {3: np.float64(0.516832220546095), 4: np.float64(0.023720347254850838), 8: np.float64(0.25411187329124474), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.516832220546095), np.float64(0.023720347254850838), np.float64(0.25411187329124474), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.817126200312965), 4: np.float64(0.18232549993730982), 8: np.float64(0.0005482997497247672), 74: np.float64(3.7605567292150747e-35), 40: np.float64(3.7605567292150747e-35), 87: np.float64(3.7605567292150747e-35), 0: np.float64(3.7605567292150747e-35)}
err dic= {3: np.float64(0.558126200312965), 4: np.float64(0.06367450006269018), 8: np.float64(0.25545170025027525), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.558126200312965), np.float64(0.06367450006269018), np.float64(0.25545170025027525), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.851818249643065), 4: np.float64(0.1480238163435311), 8: np.float64(0.00015793401340318878), 74: np.float64(6.25159602362186e-41), 40: np.float64(6.25159602362186e-41), 87: np.float64(6.25159602362186e-41), 0: np.float64(6.25159602362186e-41)}
err dic= {3: np.float64(0.592818249643065), 4: np.float64(0.0979761836564689), 8: np.float64(0.2558420659865968), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.592818249643065), np.float64(0.0979761836564689), np.float64(0.2558420659865968), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402411473), 4: np.float64(0.11919751703720469), 8: np.float64(4.534272164780921e-05), 74: np.float64(1.0534158733278168e-46), 40: np.float64(1.0534158733278168e-46), 87: np.float64(1.0534158733278168e-46), 0: np.float64(1.0534158733278168e-46)}
err dic= {3: np.float64(0.6217571402411473), 4: np.float64(0.1268024829627953), 8: np.float64(0.2559546572783522), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.6217571402411473), np.float64(0.1268024829627953), np.float64(0.2559546572783522), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
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(0.19209800387721618), 3: np.float64(0.18325582684295735), 9: np.float64(0.1634645270769472), 83: np.float64(0.11529541055072007), 79: np.float64(0.11529541055072007), 70: np.float64(0.11529541055072007), 0: np.float64(0.11529541055072007)}
err dic= {1: np.float64(0.07290199612278384), 3: np.float64(0.06774417315704265), 9: np.float64(0.07153547292305279), 83: np.float64(0.06329541055072008), 79: np.float64(0.04729541055072006), 70: np.float64(0.034295410550720065), 0: np.float64(0.06729541055072007)} 

err list= [np.float64(0.07290199612278384), np.float64(0.06774417315704265), np.float64(0.07153547292305279), np.float64(0.06329541055072008), np.float64(0.04729541055072006), np.float64(0.034295410550720065), np.float64(0.06729541055072007)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.30833801299843994), 3: np.float64(0.2818119916089455), 9: np.float64(0.22747989022678358), 83: np.float64(0.045592526291458435), 79: np.float64(0.045592526291458435), 70: np.float64(0.045592526291458435), 0: np.float64(0.045592526291458435)}
err dic= {1: np.float64(0.04333801299843992), 3: np.float64(0.030811991608945488), 9: np.float64(0.007520109773216405), 83: np.float64(0.0064074737085415626), 79: np.float64(0.02240747370854157), 70: np.float64(0.03540747370854157), 0: np.float64(0.002407473708541566)} 

err list= [np.float64(0.04333801299843992), np.float64(0.030811991608945488), np.float64(0.007520109773216405), np.float64(0.0064074737085415626), np.float64(0.02240747370854157), np.float64(0.03540747370854157), np.float64(0.002407473708541566)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.408692845360513), 3: np.float64(0.3436972175487221), 9: np.float64(0.22809070188199548), 83: np.float64(0.0048798088021924785), 79: np.float64(0.0048798088021924785), 70: np.float64(0.0048798088021924785), 0: np.float64(0.0048798088021924785)}
err dic= {1: np.float64(0.14369284536051297), 3: np.float64(0.09269721754872212), 9: np.float64(0.006909298118004503), 83: np.float64(0.04712019119780752), 79: np.float64(0.06312019119780753), 70: np.float64(0.07612019119780752), 0: np.float64(0.04312019119780752)} 

err list= [np.float64(0.14369284536051297), np.float64(0.09269721754872212), np.float64(0.006909298118004503), np.float64(0.04712019119780752), np.float64(0.06312019119780753), np.float64(0.07612019119780752), np.float64(0.04312019119780752)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5316531054686952), 3: np.float64(0.34739477896361715), 9: np.float64(0.1209383761037711), 83: np.float64(3.4348659790337495e-06), 79: np.float64(3.4348659790337495e-06), 70: np.float64(3.4348659790337495e-06), 0: np.float64(3.4348659790337495e-06)}
err dic= {1: np.float64(0.26665310546869514), 3: np.float64(0.09639477896361714), 9: np.float64(0.11406162389622888), 83: np.float64(0.05199656513402096), 79: np.float64(0.06799656513402097), 70: np.float64(0.08099656513402097), 0: np.float64(0.047996565134020966)} 

err list= [np.float64(0.26665310546869514), np.float64(0.09639477896361714), np.float64(0.11406162389622888), np.float64(0.05199656513402096), np.float64(0.06799656513402097), np.float64(0.08099656513402097), np.float64(0.047996565134020966)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6768077271715972), 3: np.float64(0.29176229833481115), 9: np.float64(0.03142997447803851), 83: np.float64(3.888356210587007e-12), 79: np.float64(3.888356210587007e-12), 70: np.float64(3.888356210587007e-12), 0: np.float64(3.888356210587007e-12)}
err dic= {1: np.float64(0.4118077271715972), 3: np.float64(0.04076229833481115), 9: np.float64(0.20357002552196146), 83: np.float64(0.05199999999611164), 79: np.float64(0.06799999999611164), 70: np.float64(0.08099999999611164), 0: np.float64(0.047999999996111646)} 

err list= [np.float64(0.4118077271715972), np.float64(0.04076229833481115), np.float64(0.20357002552196146), np.float64(0.05199999999611164), np.float64(0.06799999999611164), np.float64(0.08099999999611164), np.float64(0.047999999996111646)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.774105702190221), 3: np.float64(0.2191786384934047), 9: np.float64(0.006715659316374057), 83: np.float64(4.2930024568231626e-18), 79: np.float64(4.2930024568231626e-18), 70: np.float64(4.2930024568231626e-18), 0: np.float64(4.2930024568231626e-18)}
err dic= {1: np.float64(0.509105702190221), 3: np.float64(0.031821361506595314), 9: np.float64(0.22828434068362594), 83: np.float64(0.05199999999999999), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.047999999999999994)} 

err list= [np.float64(0.509105702190221), np.float64(0.031821361506595314), np.float64(0.22828434068362594), np.float64(0.05199999999999999), np.float64(0.068), np.float64(0.081), np.float64(0.047999999999999994)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8431197129536219), 3: np.float64(0.1555712984978225), 9: np.float64(0.0013089885485560214), 83: np.float64(4.8295774630104726e-24), 79: np.float64(4.8295774630104726e-24), 70: np.float64(4.8295774630104726e-24), 0: np.float64(4.8295774630104726e-24)}
err dic= {1: np.float64(0.5781197129536219), 3: np.float64(0.0954287015021775), 9: np.float64(0.23369101145144397), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.5781197129536219), np.float64(0.0954287015021775), np.float64(0.23369101145144397), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931967343909478), 3: np.float64(0.10655825341124762), 9: np.float64(0.0002450121978041865), 83: np.float64(5.5615762056378244e-30), 79: np.float64(5.5615762056378244e-30), 70: np.float64(5.5615762056378244e-30), 0: np.float64(5.5615762056378244e-30)}
err dic= {1: np.float64(0.6281967343909478), 3: np.float64(0.14444174658875236), 9: np.float64(0.2347549878021958), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.6281967343909478), np.float64(0.14444174658875236), np.float64(0.2347549878021958), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707240606471), 3: np.float64(0.07108431987050234), 9: np.float64(4.495606885052531e-05), 83: np.float64(6.52032677365536e-36), 79: np.float64(6.52032677365536e-36), 70: np.float64(6.52032677365536e-36), 0: np.float64(6.52032677365536e-36)}
err dic= {1: np.float64(0.6638707240606471), 3: np.float64(0.17991568012949766), 9: np.float64(0.23495504393114947), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.6638707240606471), np.float64(0.17991568012949766), np.float64(0.23495504393114947), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535429244147727), 3: np.float64(0.04644892580560327), 9: np.float64(8.149779623627911e-06), 83: np.float64(7.736520907369492e-42), 79: np.float64(7.736520907369492e-42), 70: np.float64(7.736520907369492e-42), 0: np.float64(7.736520907369492e-42)}
err dic= {1: np.float64(0.6885429244147727), 3: np.float64(0.20455107419439672), 9: np.float64(0.23499185022037636), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.6885429244147727), np.float64(0.20455107419439672), np.float64(0.23499185022037636), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386587635774), 3: np.float64(0.029859876603523985), 9: np.float64(1.4646328981753289e-06), 83: np.float64(9.249378342938049e-48), 79: np.float64(9.249378342938049e-48), 70: np.float64(9.249378342938049e-48), 0: np.float64(9.249378342938049e-48)}
err dic= {1: np.float64(0.7051386587635774), 3: np.float64(0.221140123396476), 9: np.float64(0.2349985353671018), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.7051386587635774), np.float64(0.221140123396476), np.float64(0.2349985353671018), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
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(0.19262853890834072), 4: np.float64(0.17973196886006815), 8: np.float64(0.1639278874899795), 32: np.float64(0.11592790118540305), 27: np.float64(0.11592790118540305), 82: np.float64(0.11592790118540305), 0: np.float64(0.11592790118540305)}
err dic= {1: np.float64(0.02937146109165928), 4: np.float64(0.05026803113993186), 8: np.float64(0.06807211251002052), 32: np.float64(0.01392790118540306), 27: np.float64(0.004072098814596942), 82: np.float64(0.06592790118540305), 0: np.float64(0.07192790118540306)} 

err list= [np.float64(0.02937146109165928), np.float64(0.05026803113993186), np.float64(0.06807211251002052), np.float64(0.01392790118540306), np.float64(0.004072098814596942), np.float64(0.06592790118540305), np.float64(0.07192790118540306)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3112343637013777), 4: np.float64(0.2732577198794345), 8: np.float64(0.22974392017093834), 32: np.float64(0.04644099906206293), 27: np.float64(0.04644099906206293), 82: np.float64(0.04644099906206293), 0: np.float64(0.04644099906206293)}
err dic= {1: np.float64(0.08923436370137769), 4: np.float64(0.04325771987943447), 8: np.float64(0.0022560798290616746), 32: np.float64(0.055559000937937066), 27: np.float64(0.07355900093793707), 82: np.float64(0.003559000937937075), 0: np.float64(0.0024409990620629304)} 

err list= [np.float64(0.08923436370137769), np.float64(0.04325771987943447), np.float64(0.0022560798290616746), np.float64(0.055559000937937066), np.float64(0.07355900093793707), np.float64(0.003559000937937075), np.float64(0.0024409990620629304)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.4185202136597351), 4: np.float64(0.3269855392090907), 8: np.float64(0.23435215001758294), 32: np.float64(0.005035524278397994), 27: np.float64(0.005035524278397994), 82: np.float64(0.005035524278397994), 0: np.float64(0.005035524278397994)}
err dic= {1: np.float64(0.19652021365973507), 4: np.float64(0.09698553920909067), 8: np.float64(0.0023521500175829324), 32: np.float64(0.096964475721602), 27: np.float64(0.114964475721602), 82: np.float64(0.04496447572160201), 0: np.float64(0.038964475721602006)} 

err list= [np.float64(0.19652021365973507), np.float64(0.09698553920909067), np.float64(0.0023521500175829324), np.float64(0.096964475721602), np.float64(0.114964475721602), np.float64(0.04496447572160201), np.float64(0.038964475721602006)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5619710209519264), 4: np.float64(0.30745667550599964), 8: np.float64(0.1305575001897369), 32: np.float64(3.7008380841008527e-06), 27: np.float64(3.7008380841008527e-06), 82: np.float64(3.7008380841008527e-06), 0: np.float64(3.7008380841008527e-06)}
err dic= {1: np.float64(0.33997102095192644), 4: np.float64(0.07745667550599963), 8: np.float64(0.1014424998102631), 32: np.float64(0.1019962991619159), 27: np.float64(0.1199962991619159), 82: np.float64(0.049996299161915905), 0: np.float64(0.0439962991619159)} 

err list= [np.float64(0.33997102095192644), np.float64(0.07745667550599963), np.float64(0.1014424998102631), np.float64(0.1019962991619159), np.float64(0.1199962991619159), np.float64(0.049996299161915905), np.float64(0.0439962991619159)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7383008689485275), 4: np.float64(0.2246567296087472), 8: np.float64(0.037042401424338296), 32: np.float64(4.596866816307202e-12), 27: np.float64(4.596866816307202e-12), 82: np.float64(4.596866816307202e-12), 0: np.float64(4.596866816307202e-12)}
err dic= {1: np.float64(0.5163008689485276), 4: np.float64(0.005343270391252819), 8: np.float64(0.19495759857566172), 32: np.float64(0.10199999999540313), 27: np.float64(0.11999999999540313), 82: np.float64(0.04999999999540314), 0: np.float64(0.04399999999540313)} 

err list= [np.float64(0.5163008689485276), np.float64(0.005343270391252819), np.float64(0.19495759857566172), np.float64(0.10199999999540313), np.float64(0.11999999999540313), np.float64(0.04999999999540314), np.float64(0.04399999999540313)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8494867469393008), 4: np.float64(0.14196251324014011), 8: np.float64(0.008550739820558834), 32: np.float64(5.486687864098196e-18), 27: np.float64(5.486687864098196e-18), 82: np.float64(5.486687864098196e-18), 0: np.float64(5.486687864098196e-18)}
err dic= {1: np.float64(0.6274867469393008), 4: np.float64(0.0880374867598599), 8: np.float64(0.22344926017944117), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.049999999999999996), 0: np.float64(0.04399999999999999)} 

err list= [np.float64(0.6274867469393008), np.float64(0.0880374867598599), np.float64(0.22344926017944117), np.float64(0.102), np.float64(0.12), np.float64(0.049999999999999996), np.float64(0.04399999999999999)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159711584829692), 4: np.float64(0.08226343877516215), 8: np.float64(0.0017654027418688649), 32: np.float64(6.528181541879479e-24), 27: np.float64(6.528181541879479e-24), 82: np.float64(6.528181541879479e-24), 0: np.float64(6.528181541879479e-24)}
err dic= {1: np.float64(0.6939711584829692), 4: np.float64(0.14773656122483786), 8: np.float64(0.23023459725813114), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.6939711584829692), np.float64(0.14773656122483786), np.float64(0.23023459725813114), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545811653267549), 4: np.float64(0.045075272089623815), 8: np.float64(0.00034356258362130363), 32: np.float64(7.806371171793983e-30), 27: np.float64(7.806371171793983e-30), 82: np.float64(7.806371171793983e-30), 0: np.float64(7.806371171793983e-30)}
err dic= {1: np.float64(0.7325811653267549), 4: np.float64(0.1849247279103762), 8: np.float64(0.2316564374163787), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7325811653267549), np.float64(0.1849247279103762), np.float64(0.2316564374163787), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.976179579565728), 4: np.float64(0.023755777298822976), 8: np.float64(6.464313544905663e-05), 32: np.float64(9.379240034001018e-36), 27: np.float64(9.379240034001018e-36), 82: np.float64(9.379240034001018e-36), 0: np.float64(9.379240034001018e-36)}
err dic= {1: np.float64(0.754179579565728), 4: np.float64(0.20624422270117704), 8: np.float64(0.23193535686455097), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.754179579565728), np.float64(0.20624422270117704), np.float64(0.23193535686455097), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141691253702), 4: np.float64(0.012173924284659167), 8: np.float64(1.1906589970439095e-05), 32: np.float64(1.1304306604476038e-41), 27: np.float64(1.1304306604476038e-41), 82: np.float64(1.1304306604476038e-41), 0: np.float64(1.1304306604476038e-41)}
err dic= {1: np.float64(0.7658141691253703), 4: np.float64(0.21782607571534085), 8: np.float64(0.23198809341002957), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7658141691253703), np.float64(0.21782607571534085), np.float64(0.23198809341002957), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855163026799), 4: np.float64(0.00611232244535478), 8: np.float64(2.1612519648732226e-06), 32: np.float64(1.3649213497778672e-47), 27: np.float64(1.3649213497778672e-47), 82: np.float64(1.3649213497778672e-47), 0: np.float64(1.3649213497778672e-47)}
err dic= {1: np.float64(0.7718855163026799), 4: np.float64(0.22388767755464523), 8: np.float64(0.23199783874803515), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7718855163026799), np.float64(0.22388767755464523), np.float64(0.23199783874803515), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
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(0.1274131676387843), 4: np.float64(0.18577022703301857), 6: np.float64(0.1771639347730597), 51: np.float64(0.1274131676387843), 82: np.float64(0.1274131676387843), 41: np.float64(0.1274131676387843), 0: np.float64(0.1274131676387843)}
err dic= {9: np.float64(0.0935868323612157), 4: np.float64(0.059229772966981425), 6: np.float64(0.07883606522694031), 51: np.float64(0.041413167638784304), 82: np.float64(0.08741316763878429), 41: np.float64(0.0344131676387843), 0: np.float64(0.0684131676387843)} 

err list= [np.float64(0.0935868323612157), np.float64(0.059229772966981425), np.float64(0.07883606522694031), np.float64(0.041413167638784304), np.float64(0.08741316763878429), np.float64(0.0344131676387843), np.float64(0.0684131676387843)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.07211726337765927), 4: np.float64(0.33413909217716103), 6: np.float64(0.30527459093454123), 51: np.float64(0.07211726337765927), 82: np.float64(0.07211726337765927), 41: np.float64(0.07211726337765927), 0: np.float64(0.07211726337765927)}
err dic= {9: np.float64(0.14888273662234075), 4: np.float64(0.08913909217716104), 6: np.float64(0.04927459093454123), 51: np.float64(0.013882736622340727), 82: np.float64(0.032117263377659265), 41: np.float64(0.020882736622340733), 0: np.float64(0.013117263377659269)} 

err list= [np.float64(0.14888273662234075), np.float64(0.08913909217716104), np.float64(0.04927459093454123), np.float64(0.013882736622340727), np.float64(0.032117263377659265), np.float64(0.020882736622340733), np.float64(0.013117263377659269)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.012019217493283767), 4: np.float64(0.5095714642498725), 6: np.float64(0.430332448283709), 51: np.float64(0.012019217493283767), 82: np.float64(0.012019217493283767), 41: np.float64(0.012019217493283767), 0: np.float64(0.012019217493283767)}
err dic= {9: np.float64(0.20898078250671623), 4: np.float64(0.26457146424987255), 6: np.float64(0.17433244828370897), 51: np.float64(0.07398078250671622), 82: np.float64(0.027980782506716234), 41: np.float64(0.08098078250671623), 0: np.float64(0.04698078250671623)} 

err list= [np.float64(0.20898078250671623), np.float64(0.26457146424987255), np.float64(0.17433244828370897), np.float64(0.07398078250671622), np.float64(0.027980782506716234), np.float64(0.08098078250671623), np.float64(0.04698078250671623)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(7.708836391539542e-06), 4: np.float64(0.6027545492988734), 6: np.float64(0.3972069065191685), 51: np.float64(7.708836391539542e-06), 82: np.float64(7.708836391539542e-06), 41: np.float64(7.708836391539542e-06), 0: np.float64(7.708836391539542e-06)}
err dic= {9: np.float64(0.22099229116360847), 4: np.float64(0.3577545492988734), 6: np.float64(0.1412069065191685), 51: np.float64(0.08599229116360846), 82: np.float64(0.03999229116360846), 41: np.float64(0.09299229116360846), 0: np.float64(0.058992291163608455)} 

err list= [np.float64(0.22099229116360847), np.float64(0.3577545492988734), np.float64(0.1412069065191685), np.float64(0.08599229116360846), np.float64(0.03999229116360846), np.float64(0.09299229116360846), np.float64(0.058992291163608455)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(2.04377651744254e-11), 4: np.float64(0.6976973365598824), 6: np.float64(0.30230266333792905), 51: np.float64(2.04377651744254e-11), 82: np.float64(2.04377651744254e-11), 41: np.float64(2.04377651744254e-11), 0: np.float64(2.04377651744254e-11)}
err dic= {9: np.float64(0.22099999997956224), 4: np.float64(0.4526973365598824), 6: np.float64(0.04630266333792904), 51: np.float64(0.08599999997956223), 82: np.float64(0.03999999997956224), 41: np.float64(0.09299999997956224), 0: np.float64(0.058999999979562234)} 

err list= [np.float64(0.22099999997956224), np.float64(0.4526973365598824), np.float64(0.04630266333792904), np.float64(0.08599999997956223), np.float64(0.03999999997956224), np.float64(0.09299999997956224), np.float64(0.058999999979562234)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(5.616244296424671e-17), 4: np.float64(0.7790173173345051), 6: np.float64(0.22098268266549467), 51: np.float64(5.616244296424671e-17), 82: np.float64(5.616244296424671e-17), 41: np.float64(5.616244296424671e-17), 0: np.float64(5.616244296424671e-17)}
err dic= {9: np.float64(0.22099999999999995), 4: np.float64(0.5340173173345051), 6: np.float64(0.03501731733450533), 51: np.float64(0.08599999999999994), 82: np.float64(0.039999999999999945), 41: np.float64(0.09299999999999994), 0: np.float64(0.05899999999999994)} 

err list= [np.float64(0.22099999999999995), np.float64(0.5340173173345051), np.float64(0.03501731733450533), np.float64(0.08599999999999994), np.float64(0.039999999999999945), np.float64(0.09299999999999994), np.float64(0.05899999999999994)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(1.5596181174389799e-22), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(1.5596181174389799e-22), 82: np.float64(1.5596181174389799e-22), 41: np.float64(1.5596181174389799e-22), 0: np.float64(1.5596181174389799e-22)}
err dic= {9: np.float64(0.221), 4: np.float64(0.5991518039744367), 6: np.float64(0.10015180397443652), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.5991518039744367), np.float64(0.10015180397443652), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(4.371756094033142e-28), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(4.371756094033142e-28), 82: np.float64(4.371756094033142e-28), 41: np.float64(4.371756094033142e-28), 0: np.float64(4.371756094033142e-28)}
err dic= {9: np.float64(0.221), 4: np.float64(0.6484014727128832), 6: np.float64(0.14940147271288337), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.6484014727128832), np.float64(0.14940147271288337), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(1.2374201023249048e-33), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(1.2374201023249048e-33), 82: np.float64(1.2374201023249048e-33), 41: np.float64(1.2374201023249048e-33), 0: np.float64(1.2374201023249048e-33)}
err dic= {9: np.float64(0.221), 4: np.float64(0.6839099851249452), 6: np.float64(0.18490998512494472), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.6839099851249452), np.float64(0.18490998512494472), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(3.5313061114845655e-39), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(3.5313061114845655e-39), 82: np.float64(3.5313061114845655e-39), 41: np.float64(3.5313061114845655e-39), 0: np.float64(3.5313061114845655e-39)}
err dic= {9: np.float64(0.221), 4: np.float64(0.7085502818108356), 6: np.float64(0.20955028181083563), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.7085502818108356), np.float64(0.20955028181083563), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(1.013804215253925e-44), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(1.013804215253925e-44), 82: np.float64(1.013804215253925e-44), 41: np.float64(1.013804215253925e-44), 0: np.float64(1.013804215253925e-44)}
err dic= {9: np.float64(0.221), 4: np.float64(0.7251400142429856), 6: np.float64(0.22614001424298566), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.7251400142429856), np.float64(0.22614001424298566), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
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(0.19561932338760318), 9: np.float64(0.17805310358849355), 6: np.float64(0.1907894650842055), 39: np.float64(0.10888452698492644), 80: np.float64(0.10888452698492644), 68: np.float64(0.10888452698492644), 0: np.float64(0.10888452698492644)}
err dic= {5: np.float64(0.04938067661239681), 9: np.float64(0.04994689641150646), 6: np.float64(0.06721053491579451), 39: np.float64(0.008884526984926436), 80: np.float64(0.04588452698492644), 68: np.float64(0.05288452698492644), 0: np.float64(0.05888452698492644)} 

err list= [np.float64(0.04938067661239681), np.float64(0.04994689641150646), np.float64(0.06721053491579451), np.float64(0.008884526984926436), np.float64(0.04588452698492644), np.float64(0.05288452698492644), np.float64(0.05888452698492644)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.2937776682198875), 9: np.float64(0.2450415524495015), 6: np.float64(0.279449962271965), 39: np.float64(0.04543270426465911), 80: np.float64(0.04543270426465911), 68: np.float64(0.04543270426465911), 0: np.float64(0.04543270426465911)}
err dic= {5: np.float64(0.04877766821988749), 9: np.float64(0.01704155244950148), 6: np.float64(0.021449962271964995), 39: np.float64(0.054567295735340894), 80: np.float64(0.01756729573534089), 68: np.float64(0.01056729573534089), 0: np.float64(0.004567295735340891)} 

err list= [np.float64(0.04877766821988749), np.float64(0.01704155244950148), np.float64(0.021449962271964995), np.float64(0.054567295735340894), np.float64(0.01756729573534089), np.float64(0.01056729573534089), np.float64(0.004567295735340891)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.3747172692025088), 9: np.float64(0.2631432725028652), 6: np.float64(0.33905820635868356), 39: np.float64(0.00577031298398642), 80: np.float64(0.00577031298398642), 68: np.float64(0.00577031298398642), 0: np.float64(0.00577031298398642)}
err dic= {5: np.float64(0.1297172692025088), 9: np.float64(0.03514327250286517), 6: np.float64(0.08105820635868355), 39: np.float64(0.09422968701601359), 80: np.float64(0.05722968701601358), 68: np.float64(0.05022968701601358), 0: np.float64(0.04422968701601358)} 

err list= [np.float64(0.1297172692025088), np.float64(0.03514327250286517), np.float64(0.08105820635868355), np.float64(0.09422968701601359), np.float64(0.05722968701601358), np.float64(0.05022968701601358), np.float64(0.04422968701601358)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.4568196872406849), 9: np.float64(0.18738620281289506), 6: np.float64(0.3557715301454797), 39: np.float64(5.644950234885449e-06), 80: np.float64(5.644950234885449e-06), 68: np.float64(5.644950234885449e-06), 0: np.float64(5.644950234885449e-06)}
err dic= {5: np.float64(0.2118196872406849), 9: np.float64(0.04061379718710495), 6: np.float64(0.09777153014547968), 39: np.float64(0.09999435504976512), 80: np.float64(0.06299435504976511), 68: np.float64(0.05599435504976512), 0: np.float64(0.04999435504976512)} 

err list= [np.float64(0.2118196872406849), np.float64(0.04061379718710495), np.float64(0.09777153014547968), np.float64(0.09999435504976512), np.float64(0.06299435504976511), np.float64(0.05599435504976512), np.float64(0.04999435504976512)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5654187560533364), 9: np.float64(0.09163743277607579), 6: np.float64(0.3429438111229266), 39: np.float64(1.1915410882921904e-11), 80: np.float64(1.1915410882921904e-11), 68: np.float64(1.1915410882921904e-11), 0: np.float64(1.1915410882921904e-11)}
err dic= {5: np.float64(0.32041875605333636), 9: np.float64(0.1363625672239242), 6: np.float64(0.0849438111229266), 39: np.float64(0.09999999998808459), 80: np.float64(0.06299999998808459), 68: np.float64(0.05599999998808459), 0: np.float64(0.04999999998808459)} 

err list= [np.float64(0.32041875605333636), np.float64(0.1363625672239242), np.float64(0.0849438111229266), np.float64(0.09999999998808459), np.float64(0.06299999998808459), np.float64(0.05599999998808459), np.float64(0.04999999998808459)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6518852874465689), 9: np.float64(0.04018590653971), 6: np.float64(0.3079288060137212), 39: np.float64(2.665055138510608e-17), 80: np.float64(2.665055138510608e-17), 68: np.float64(2.665055138510608e-17), 0: np.float64(2.665055138510608e-17)}
err dic= {5: np.float64(0.40688528744656893), 9: np.float64(0.18781409346029002), 6: np.float64(0.04992880601372118), 39: np.float64(0.09999999999999998), 80: np.float64(0.06299999999999997), 68: np.float64(0.05599999999999997), 0: np.float64(0.049999999999999975)} 

err list= [np.float64(0.40688528744656893), np.float64(0.18781409346029002), np.float64(0.04992880601372118), np.float64(0.09999999999999998), np.float64(0.06299999999999997), np.float64(0.05599999999999997), np.float64(0.049999999999999975)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7191002954879085), 9: np.float64(0.016357489661781185), 6: np.float64(0.26454221485031076), 39: np.float64(6.16244860073076e-23), 80: np.float64(6.16244860073076e-23), 68: np.float64(6.16244860073076e-23), 0: np.float64(6.16244860073076e-23)}
err dic= {5: np.float64(0.47410029548790855), 9: np.float64(0.21164251033821882), 6: np.float64(0.006542214850310757), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.47410029548790855), np.float64(0.21164251033821882), np.float64(0.006542214850310757), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723569153432931), 9: np.float64(0.006359123522713147), 6: np.float64(0.22128396113399326), 39: np.float64(1.4580352457374973e-28), 80: np.float64(1.4580352457374973e-28), 68: np.float64(1.4580352457374973e-28), 0: np.float64(1.4580352457374973e-28)}
err dic= {5: np.float64(0.5273569153432931), 9: np.float64(0.22164087647728686), 6: np.float64(0.036716038866006745), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.5273569153432931), np.float64(0.22164087647728686), np.float64(0.036716038866006745), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.8156057222377775), 9: np.float64(0.002408042341331115), 6: np.float64(0.18198623542089104), 39: np.float64(3.5076768178502784e-34), 80: np.float64(3.5076768178502784e-34), 68: np.float64(3.5076768178502784e-34), 0: np.float64(3.5076768178502784e-34)}
err dic= {5: np.float64(0.5706057222377775), 9: np.float64(0.2255919576586689), 6: np.float64(0.07601376457910897), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.5706057222377775), np.float64(0.2255919576586689), np.float64(0.07601376457910897), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511869021360521), 9: np.float64(0.0008989932663974902), 6: np.float64(0.14791410459754986), 39: np.float64(8.548265476576235e-40), 80: np.float64(8.548265476576235e-40), 68: np.float64(8.548265476576235e-40), 0: np.float64(8.548265476576235e-40)}
err dic= {5: np.float64(0.6061869021360521), 9: np.float64(0.2271010067336025), 6: np.float64(0.11008589540245015), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.6061869021360521), np.float64(0.2271010067336025), np.float64(0.11008589540245015), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036406466493), 9: np.float64(0.00033314975556754796), 6: np.float64(0.11916320959778291), 39: np.float64(2.1049875540977585e-45), 80: np.float64(2.1049875540977585e-45), 68: np.float64(2.1049875540977585e-45), 0: np.float64(2.1049875540977585e-45)}
err dic= {5: np.float64(0.6355036406466493), 9: np.float64(0.22766685024443245), 6: np.float64(0.13883679040221708), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.6355036406466493), np.float64(0.22766685024443245), np.float64(0.13883679040221708), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
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(0.17384650357762865), 3: np.float64(0.18635897874268323), 8: np.float64(0.16579996852170287), 15: np.float64(0.11849863728949635), 78: np.float64(0.11849863728949635), 97: np.float64(0.11849863728949635), 0: np.float64(0.11849863728949635)}
err dic= {6: np.float64(0.04715349642237135), 3: np.float64(0.04864102125731676), 8: np.float64(0.07220003147829712), 15: np.float64(0.05450136271050364), 78: np.float64(0.062498637289496346), 97: np.float64(0.07949863728949635), 0: np.float64(0.08049863728949636)} 

err list= [np.float64(0.04715349642237135), np.float64(0.04864102125731676), np.float64(0.07220003147829712), np.float64(0.05450136271050364), np.float64(0.062498637289496346), np.float64(0.07949863728949635), np.float64(0.08049863728949636)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.2620006296696619), 3: np.float64(0.29867311622389325), 8: np.float64(0.2391441656781458), 15: np.float64(0.05004552210707558), 78: np.float64(0.05004552210707558), 97: np.float64(0.05004552210707558), 0: np.float64(0.05004552210707558)}
err dic= {6: np.float64(0.04100062966966192), 3: np.float64(0.06367311622389327), 8: np.float64(0.0011441656781458198), 15: np.float64(0.12295447789292441), 78: np.float64(0.005954477892924422), 97: np.float64(0.01104552210707558), 0: np.float64(0.01204552210707558)} 

err list= [np.float64(0.04100062966966192), np.float64(0.06367311622389327), np.float64(0.0011441656781458198), np.float64(0.12295447789292441), np.float64(0.005954477892924422), np.float64(0.01104552210707558), np.float64(0.01204552210707558)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.31319873086172956), 3: np.float64(0.4014856454360465), 8: np.float64(0.2623019781885204), 15: np.float64(0.0057534113784260075), 78: np.float64(0.0057534113784260075), 97: np.float64(0.0057534113784260075), 0: np.float64(0.0057534113784260075)}
err dic= {6: np.float64(0.09219873086172956), 3: np.float64(0.1664856454360465), 8: np.float64(0.024301978188520423), 15: np.float64(0.167246588621574), 78: np.float64(0.050246588621573995), 97: np.float64(0.033246588621573994), 0: np.float64(0.03224658862157399)} 

err list= [np.float64(0.09219873086172956), np.float64(0.1664856454360465), np.float64(0.024301978188520423), np.float64(0.167246588621574), np.float64(0.050246588621573995), np.float64(0.033246588621573994), np.float64(0.03224658862157399)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.28750757716439157), 3: np.float64(0.5289786061477847), 8: np.float64(0.18349320235143218), 15: np.float64(5.153584097750477e-06), 78: np.float64(5.153584097750477e-06), 97: np.float64(5.153584097750477e-06), 0: np.float64(5.153584097750477e-06)}
err dic= {6: np.float64(0.06650757716439157), 3: np.float64(0.2939786061477847), 8: np.float64(0.054506797648567806), 15: np.float64(0.17299484641590224), 78: np.float64(0.05599484641590225), 97: np.float64(0.03899484641590225), 0: np.float64(0.03799484641590225)} 

err list= [np.float64(0.06650757716439157), np.float64(0.2939786061477847), np.float64(0.054506797648567806), np.float64(0.17299484641590224), np.float64(0.05599484641590225), np.float64(0.03899484641590225), np.float64(0.03799484641590225)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.21136722904205038), 3: np.float64(0.7045769546426739), 8: np.float64(0.08405581627292316), 15: np.float64(1.0588260774604237e-11), 78: np.float64(1.0588260774604237e-11), 97: np.float64(1.0588260774604237e-11), 0: np.float64(1.0588260774604237e-11)}
err dic= {6: np.float64(0.009632770957949621), 3: np.float64(0.4695769546426739), 8: np.float64(0.15394418372707683), 15: np.float64(0.17299999998941173), 78: np.float64(0.05599999998941174), 97: np.float64(0.03899999998941174), 0: np.float64(0.03799999998941174)} 

err list= [np.float64(0.009632770957949621), np.float64(0.4695769546426739), np.float64(0.15394418372707683), np.float64(0.17299999998941173), np.float64(0.05599999998941174), np.float64(0.03899999998941174), np.float64(0.03799999998941174)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13673323328089826), 3: np.float64(0.8300378726980452), 8: np.float64(0.03322889402105634), 15: np.float64(2.180519181359413e-17), 78: np.float64(2.180519181359413e-17), 97: np.float64(2.180519181359413e-17), 0: np.float64(2.180519181359413e-17)}
err dic= {6: np.float64(0.08426676671910174), 3: np.float64(0.5950378726980452), 8: np.float64(0.20477110597894366), 15: np.float64(0.17299999999999996), 78: np.float64(0.05599999999999998), 97: np.float64(0.03899999999999998), 0: np.float64(0.03799999999999998)} 

err list= [np.float64(0.08426676671910174), np.float64(0.5950378726980452), np.float64(0.20477110597894366), np.float64(0.17299999999999996), np.float64(0.05599999999999998), np.float64(0.03899999999999998), np.float64(0.03799999999999998)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.0806651538227525), 3: np.float64(0.9074958368084762), 8: np.float64(0.011839009368771462), 15: np.float64(4.454444526521499e-23), 78: np.float64(4.454444526521499e-23), 97: np.float64(4.454444526521499e-23), 0: np.float64(4.454444526521499e-23)}
err dic= {6: np.float64(0.1403348461772475), 3: np.float64(0.6724958368084762), 8: np.float64(0.22616099063122852), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.1403348461772475), np.float64(0.6724958368084762), np.float64(0.22616099063122852), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.04464840069712358), 3: np.float64(0.9514153882278131), 8: np.float64(0.00393621107506327), 15: np.float64(9.038866184993028e-29), 78: np.float64(9.038866184993028e-29), 97: np.float64(9.038866184993028e-29), 0: np.float64(9.038866184993028e-29)}
err dic= {6: np.float64(0.17635159930287642), 3: np.float64(0.7164153882278131), 8: np.float64(0.23406378892493673), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.17635159930287642), np.float64(0.7164153882278131), np.float64(0.23406378892493673), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023650013524335572), 3: np.float64(0.975099430792984), 8: np.float64(0.0012505556826808662), 15: np.float64(1.8249564897524513e-34), 78: np.float64(1.8249564897524513e-34), 97: np.float64(1.8249564897524513e-34), 0: np.float64(1.8249564897524513e-34)}
err dic= {6: np.float64(0.19734998647566443), 3: np.float64(0.740099430792984), 8: np.float64(0.23674944431731912), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.19734998647566443), np.float64(0.740099430792984), np.float64(0.23674944431731912), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.012148820459890007), 3: np.float64(0.9874656934961611), 8: np.float64(0.0003854860439483042), 15: np.float64(3.6707367914678812e-40), 78: np.float64(3.6707367914678812e-40), 97: np.float64(3.6707367914678812e-40), 0: np.float64(3.6707367914678812e-40)}
err dic= {6: np.float64(0.20885117954010998), 3: np.float64(0.7524656934961611), 8: np.float64(0.23761451395605168), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.20885117954010998), np.float64(0.7524656934961611), np.float64(0.23761451395605168), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.00610651094060876), 3: np.float64(0.9937770715394815), 8: np.float64(0.00011641751990945703), 15: np.float64(7.363120614745125e-46), 78: np.float64(7.363120614745125e-46), 97: np.float64(7.363120614745125e-46), 0: np.float64(7.363120614745125e-46)}
err dic= {6: np.float64(0.21489348905939124), 3: np.float64(0.7587770715394815), 8: np.float64(0.23788358248009053), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.21489348905939124), np.float64(0.7587770715394815), np.float64(0.23788358248009053), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
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(0.16469699198038232), 2: np.float64(0.18909510428903223), 4: np.float64(0.18043103580314923), 95: np.float64(0.10289370642580918), 11: np.float64(0.15709574865001324), 22: np.float64(0.10289370642580918), 0: np.float64(0.10289370642580918)}
err dic= {8: np.float64(0.07030300801961767), 2: np.float64(0.012904895710967784), 4: np.float64(0.016568964196850777), 95: np.float64(0.06089370642580918), 11: np.float64(0.008904251349986764), 22: np.float64(0.03410629357419083), 0: np.float64(0.08189370642580918)} 

err list= [np.float64(0.07030300801961767), np.float64(0.012904895710967784), np.float64(0.016568964196850777), np.float64(0.06089370642580918), np.float64(0.008904251349986764), np.float64(0.03410629357419083), np.float64(0.08189370642580918)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.20518375975598335), 2: np.float64(0.26735766705735076), 4: np.float64(0.24422175122153036), 95: np.float64(0.032043086779035126), 11: np.float64(0.18710756162802025), 22: np.float64(0.032043086779035126), 0: np.float64(0.032043086779035126)}
err dic= {8: np.float64(0.029816240244016634), 2: np.float64(0.06535766705735074), 4: np.float64(0.047221751221530356), 95: np.float64(0.009956913220964876), 11: np.float64(0.021107561628020244), 22: np.float64(0.10495691322096488), 0: np.float64(0.011043086779035125)} 

err list= [np.float64(0.029816240244016634), np.float64(0.06535766705735074), np.float64(0.047221751221530356), np.float64(0.009956913220964876), np.float64(0.021107561628020244), np.float64(0.10495691322096488), np.float64(0.011043086779035125)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.20102589633449805), 2: np.float64(0.3375777368312185), 4: np.float64(0.28283968750236926), 95: np.float64(0.003756854405442523), 11: np.float64(0.16728611611559033), 22: np.float64(0.003756854405442523), 0: np.float64(0.003756854405442523)}
err dic= {8: np.float64(0.03397410366550194), 2: np.float64(0.1355777368312185), 4: np.float64(0.08583968750236926), 95: np.float64(0.03824314559455748), 11: np.float64(0.001286116115590319), 22: np.float64(0.1332431455945575), 0: np.float64(0.017243145594557478)} 

err list= [np.float64(0.03397410366550194), np.float64(0.1355777368312185), np.float64(0.08583968750236926), np.float64(0.03824314559455748), np.float64(0.001286116115590319), np.float64(0.1332431455945575), np.float64(0.017243145594557478)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.13082438043755187), 2: np.float64(0.4775163065034913), 4: np.float64(0.31002667107418486), 95: np.float64(3.0860801901927647e-06), 11: np.float64(0.0816233837442005), 22: np.float64(3.0860801901927647e-06), 0: np.float64(3.0860801901927647e-06)}
err dic= {8: np.float64(0.10417561956244811), 2: np.float64(0.2755163065034913), 4: np.float64(0.11302667107418485), 95: np.float64(0.04199691391980981), 11: np.float64(0.08437661625579951), 22: np.float64(0.1369969139198098), 0: np.float64(0.020996913919809807)} 

err list= [np.float64(0.10417561956244811), np.float64(0.2755163065034913), np.float64(0.11302667107418485), np.float64(0.04199691391980981), np.float64(0.08437661625579951), np.float64(0.1369969139198098), np.float64(0.020996913919809807)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04709325965806872), 2: np.float64(0.6544667084378497), 4: np.float64(0.2806804187852727), 95: np.float64(3.5997216719411573e-12), 11: np.float64(0.01775961310800998), 22: np.float64(3.5997216719411573e-12), 0: np.float64(3.5997216719411573e-12)}
err dic= {8: np.float64(0.18790674034193128), 2: np.float64(0.4524667084378497), 4: np.float64(0.08368041878527271), 95: np.float64(0.04199999999640028), 11: np.float64(0.14824038689199004), 22: np.float64(0.13699999999640028), 0: np.float64(0.02099999999640028)} 

err list= [np.float64(0.18790674034193128), np.float64(0.4524667084378497), np.float64(0.08368041878527271), np.float64(0.04199999999640028), np.float64(0.14824038689199004), np.float64(0.13699999999640028), np.float64(0.02099999999640028)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013536549016638748), 2: np.float64(0.7668515971786537), 4: np.float64(0.2165503665695186), 95: np.float64(4.116697924253048e-18), 11: np.float64(0.003061487235188769), 22: np.float64(4.116697924253048e-18), 0: np.float64(4.116697924253048e-18)}
err dic= {8: np.float64(0.22146345098336123), 2: np.float64(0.5648515971786536), 4: np.float64(0.019550366569518585), 95: np.float64(0.041999999999999996), 11: np.float64(0.16293851276481125), 22: np.float64(0.137), 0: np.float64(0.020999999999999998)} 

err list= [np.float64(0.22146345098336123), np.float64(0.5648515971786536), np.float64(0.019550366569518585), np.float64(0.041999999999999996), np.float64(0.16293851276481125), np.float64(0.137), np.float64(0.020999999999999998)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034775536988864626), 2: np.float64(0.8410328325211592), 4: np.float64(0.15501625097215452), 95: np.float64(4.73455015179951e-24), 11: np.float64(0.00047336280779999217), 22: np.float64(4.73455015179951e-24), 0: np.float64(4.73455015179951e-24)}
err dic= {8: np.float64(0.23152244630111352), 2: np.float64(0.6390328325211592), 4: np.float64(0.04198374902784549), 95: np.float64(0.042), 11: np.float64(0.1655266371922), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23152244630111352), np.float64(0.6390328325211592), np.float64(0.04198374902784549), np.float64(0.042), np.float64(0.1655266371922), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467393110206104), 2: np.float64(0.8926352815932924), 4: np.float64(0.10644832522985162), 95: np.float64(5.512947412007942e-30), 11: np.float64(6.965386583462914e-05), 22: np.float64(5.512947412007942e-30), 0: np.float64(5.512947412007942e-30)}
err dic= {8: np.float64(0.23415326068897938), 2: np.float64(0.6906352815932923), 4: np.float64(0.09055167477014839), 95: np.float64(0.042), 11: np.float64(0.16593034613416538), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23415326068897938), np.float64(0.6906352815932923), np.float64(0.09055167477014839), np.float64(0.042), np.float64(0.16593034613416538), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066374506286724), 2: np.float64(0.9287259689199104), 4: np.float64(0.07106336957914271), 95: np.float64(6.495716835629265e-36), 11: np.float64(9.99775588346969e-06), 22: np.float64(6.495716835629265e-36), 0: np.float64(6.495716835629265e-36)}
err dic= {8: np.float64(0.23479933625493712), 2: np.float64(0.7267259689199104), 4: np.float64(0.1259366304208573), 95: np.float64(0.042), 11: np.float64(0.16599000224411653), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23479933625493712), np.float64(0.7267259689199104), np.float64(0.1259366304208573), np.float64(0.042), np.float64(0.16599000224411653), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.682387879268542e-05), 2: np.float64(0.9535067301964254), 4: np.float64(0.04644503163375219), 95: np.float64(7.723655018421982e-42), 11: np.float64(1.414291028627564e-06), 22: np.float64(7.723655018421982e-42), 0: np.float64(7.723655018421982e-42)}
err dic= {8: np.float64(0.2349531761212073), 2: np.float64(0.7515067301964253), 4: np.float64(0.15055496836624782), 95: np.float64(0.042), 11: np.float64(0.16599858570897139), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.2349531761212073), np.float64(0.7515067301964253), np.float64(0.15055496836624782), np.float64(0.042), np.float64(0.16599858570897139), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.0815608602475049e-05), 2: np.float64(0.9701298210556255), 4: np.float64(0.02985916522652595), 95: np.float64(9.241948328071718e-48), 11: np.float64(1.9810924551184603e-07), 22: np.float64(9.241948328071718e-48), 0: np.float64(9.241948328071718e-48)}
err dic= {8: np.float64(0.23498918439139752), 2: np.float64(0.7681298210556256), 4: np.float64(0.16714083477347405), 95: np.float64(0.042), 11: np.float64(0.1659998018907545), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23498918439139752), np.float64(0.7681298210556256), np.float64(0.16714083477347405), np.float64(0.042), np.float64(0.1659998018907545), np.float64(0.137), np.float64(0.021)]
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(0.19359075777502327), 3: np.float64(0.18473224595249968), 9: np.float64(0.16134076004222156), 100: np.float64(0.15048401310116083), 22: np.float64(0.10328407437636668), 58: np.float64(0.10328407437636668), 0: np.float64(0.10328407437636668)}
err dic= {1: np.float64(0.02440924222497673), 3: np.float64(0.0037322459524996854), 9: np.float64(0.03565923995777845), 100: np.float64(0.07151598689883917), 22: np.float64(0.009715925623633326), 58: np.float64(0.062284074376366676), 0: np.float64(0.07528407437636668)} 

err list= [np.float64(0.02440924222497673), np.float64(0.0037322459524996854), np.float64(0.03565923995777845), np.float64(0.07151598689883917), np.float64(0.009715925623633326), np.float64(0.062284074376366676), np.float64(0.07528407437636668)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.2789223469633934), 3: np.float64(0.2548634585023713), 9: np.float64(0.19713141103355364), 100: np.float64(0.1722071934305231), 22: np.float64(0.03229186335671673), 58: np.float64(0.03229186335671673), 0: np.float64(0.03229186335671673)}
err dic= {1: np.float64(0.06092234696339341), 3: np.float64(0.0738634585023713), 9: np.float64(0.00013141103355363004), 100: np.float64(0.049792806569476905), 22: np.float64(0.08070813664328327), 58: np.float64(0.008708136643283272), 0: np.float64(0.004291863356716729)} 

err list= [np.float64(0.06092234696339341), np.float64(0.0738634585023713), np.float64(0.00013141103355363004), np.float64(0.049792806569476905), np.float64(0.08070813664328327), np.float64(0.008708136643283272), np.float64(0.004291863356716729)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.36167260890313946), 3: np.float64(0.30337798653102704), 9: np.float64(0.18359473409321636), 100: np.float64(0.1401289511490222), 22: np.float64(0.0037419064411996273), 58: np.float64(0.0037419064411996273), 0: np.float64(0.0037419064411996273)}
err dic= {1: np.float64(0.14367260890313946), 3: np.float64(0.12237798653102705), 9: np.float64(0.013405265906783648), 100: np.float64(0.08187104885097779), 22: np.float64(0.10925809355880038), 58: np.float64(0.03725809355880037), 0: np.float64(0.024258093558800372)} 

err list= [np.float64(0.14367260890313946), np.float64(0.12237798653102705), np.float64(0.013405265906783648), np.float64(0.08187104885097779), np.float64(0.10925809355880038), np.float64(0.03725809355880037), np.float64(0.024258093558800372)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5199232963448555), 3: np.float64(0.33916373005480155), 9: np.float64(0.0943853551959308), 100: np.float64(0.046519214459323464), 22: np.float64(2.801315029310719e-06), 58: np.float64(2.801315029310719e-06), 0: np.float64(2.801315029310719e-06)}
err dic= {1: np.float64(0.3019232963448555), 3: np.float64(0.15816373005480155), 9: np.float64(0.1026146448040692), 100: np.float64(0.17548078554067653), 22: np.float64(0.1129971986849707), 58: np.float64(0.04099719868497069), 0: np.float64(0.02799719868497069)} 

err list= [np.float64(0.3019232963448555), np.float64(0.15816373005480155), np.float64(0.1026146448040692), np.float64(0.17548078554067653), np.float64(0.1129971986849707), np.float64(0.04099719868497069), np.float64(0.02799719868497069)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.681482384970784), 3: np.float64(0.2940820686842336), 9: np.float64(0.019892551347935054), 100: np.float64(0.004542994989661499), 22: np.float64(2.4621110499094864e-12), 58: np.float64(2.4621110499094864e-12), 0: np.float64(2.4621110499094864e-12)}
err dic= {1: np.float64(0.463482384970784), 3: np.float64(0.1130820686842336), 9: np.float64(0.17710744865206496), 100: np.float64(0.21745700501033852), 22: np.float64(0.11299999999753789), 58: np.float64(0.04099999999753789), 0: np.float64(0.02799999999753789)} 

err list= [np.float64(0.463482384970784), np.float64(0.1130820686842336), np.float64(0.17710744865206496), np.float64(0.21745700501033852), np.float64(0.11299999999753789), np.float64(0.04099999999753789), np.float64(0.02799999999753789)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.776389841292173), 3: np.float64(0.22001307711622545), 9: np.float64(0.003251848726695263), 100: np.float64(0.00034523286490644345), 22: np.float64(2.070346510193318e-18), 58: np.float64(2.070346510193318e-18), 0: np.float64(2.070346510193318e-18)}
err dic= {1: np.float64(0.5583898412921731), 3: np.float64(0.03901307711622545), 9: np.float64(0.19374815127330475), 100: np.float64(0.22165476713509355), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.027999999999999997)} 

err list= [np.float64(0.5583898412921731), np.float64(0.03901307711622545), np.float64(0.19374815127330475), np.float64(0.22165476713509355), np.float64(0.113), np.float64(0.041), np.float64(0.027999999999999997)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437493664948656), 3: np.float64(0.15573992576810317), 9: np.float64(0.00048644702219156026), 100: np.float64(2.426071484012091e-05), 22: np.float64(1.790909373544205e-24), 58: np.float64(1.790909373544205e-24), 0: np.float64(1.790909373544205e-24)}
err dic= {1: np.float64(0.6257493664948657), 3: np.float64(0.02526007423189683), 9: np.float64(0.19651355297780845), 100: np.float64(0.22197573928515987), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.6257493664948657), np.float64(0.02526007423189683), np.float64(0.19651355297780845), np.float64(0.22197573928515987), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933412342571281), 3: np.float64(0.10658666255059607), 9: np.float64(7.044586739699485e-05), 100: np.float64(1.6573248786188935e-06), 22: np.float64(1.5976345446501956e-30), 58: np.float64(1.5976345446501956e-30), 0: np.float64(1.5976345446501956e-30)}
err dic= {1: np.float64(0.6753412342571281), 3: np.float64(0.07441333744940393), 9: np.float64(0.19692955413260302), 100: np.float64(0.2219983426751214), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.6753412342571281), np.float64(0.07441333744940393), np.float64(0.19692955413260302), np.float64(0.2219983426751214), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011179586114), 3: np.float64(0.07108872798785826), 9: np.float64(1.00424838519458e-05), 100: np.float64(1.1156967800869512e-07), 22: np.float64(1.4559076663663147e-36), 58: np.float64(1.4559076663663147e-36), 0: np.float64(1.4559076663663147e-36)}
err dic= {1: np.float64(0.7109011179586114), 3: np.float64(0.10991127201214174), 9: np.float64(0.19698995751614806), 100: np.float64(0.221999888430322), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.7109011179586114), np.float64(0.10991127201214174), np.float64(0.19698995751614806), np.float64(0.221999888430322), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489961513725), 3: np.float64(0.04644957969911168), 9: np.float64(1.416715180521834e-06), 100: np.float64(7.434334682403295e-09), 22: np.float64(1.3444761517693017e-42), 58: np.float64(1.3444761517693017e-42), 0: np.float64(1.3444761517693017e-42)}
err dic= {1: np.float64(0.7355489961513725), 3: np.float64(0.13455042030088832), 9: np.float64(0.19699858328481948), 100: np.float64(0.22199999256566533), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.7355489961513725), np.float64(0.13455042030088832), np.float64(0.19699858328481948), np.float64(0.22199999256566533), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303256955), 3: np.float64(0.029859970945651217), 9: np.float64(1.9823727027203242e-07), 100: np.float64(4.913822077323317e-10), 22: np.float64(1.2515709242908226e-48), 58: np.float64(1.2515709242908226e-48), 0: np.float64(1.2515709242908226e-48)}
err dic= {1: np.float64(0.7521398303256955), 3: np.float64(0.15114002905434878), 9: np.float64(0.19699980176272974), 100: np.float64(0.2219999995086178), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.7521398303256955), np.float64(0.15114002905434878), np.float64(0.19699980176272974), np.float64(0.2219999995086178), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
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(0.17188422130204928), 6: np.float64(0.17623549108055822), 8: np.float64(0.16764038475716023), 16: np.float64(0.12105997571505821), 83: np.float64(0.12105997571505821), 70: np.float64(0.12105997571505821), 0: np.float64(0.12105997571505821)}
err dic= {7: np.float64(0.03511577869795071), 6: np.float64(0.06976450891944178), 8: np.float64(0.08135961524283977), 16: np.float64(0.026940024284941785), 83: np.float64(0.0730599757150582), 70: np.float64(0.0630599757150582), 0: np.float64(0.07705997571505821)} 

err list= [np.float64(0.03511577869795071), np.float64(0.06976450891944178), np.float64(0.08135961524283977), np.float64(0.026940024284941785), np.float64(0.0730599757150582), np.float64(0.0630599757150582), np.float64(0.07705997571505821)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.26131383908472516), 6: np.float64(0.27471168611282704), 8: np.float64(0.24856941276663533), 16: np.float64(0.053851265508953826), 83: np.float64(0.053851265508953826), 70: np.float64(0.053851265508953826), 0: np.float64(0.053851265508953826)}
err dic= {7: np.float64(0.054313839084725174), 6: np.float64(0.02871168611282704), 8: np.float64(0.000430587233364671), 16: np.float64(0.09414873449104616), 83: np.float64(0.005851265508953825), 70: np.float64(0.004148734491046177), 0: np.float64(0.009851265508953828)} 

err list= [np.float64(0.054313839084725174), np.float64(0.02871168611282704), np.float64(0.000430587233364671), np.float64(0.09414873449104616), np.float64(0.005851265508953825), np.float64(0.004148734491046177), np.float64(0.009851265508953828)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.3234542143778789), 6: np.float64(0.3574721910594379), 8: np.float64(0.29267347619052964), 16: np.float64(0.006600029593038627), 83: np.float64(0.006600029593038627), 70: np.float64(0.006600029593038627), 0: np.float64(0.006600029593038627)}
err dic= {7: np.float64(0.11645421437787892), 6: np.float64(0.1114721910594379), 8: np.float64(0.043673476190529636), 16: np.float64(0.14139997040696137), 83: np.float64(0.041399970406961376), 70: np.float64(0.05139997040696138), 0: np.float64(0.03739997040696137)} 

err list= [np.float64(0.11645421437787892), np.float64(0.1114721910594379), np.float64(0.043673476190529636), np.float64(0.14139997040696137), np.float64(0.041399970406961376), np.float64(0.05139997040696138), np.float64(0.03739997040696137)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.32648662062228806), 6: np.float64(0.41921711908750603), 8: np.float64(0.25426803580297463), 16: np.float64(7.0561218076794755e-06), 83: np.float64(7.0561218076794755e-06), 70: np.float64(7.0561218076794755e-06), 0: np.float64(7.0561218076794755e-06)}
err dic= {7: np.float64(0.11948662062228807), 6: np.float64(0.17321711908750603), 8: np.float64(0.0052680358029746355), 16: np.float64(0.1479929438781923), 83: np.float64(0.04799294387819232), 70: np.float64(0.05799294387819232), 0: np.float64(0.04399294387819232)} 

err list= [np.float64(0.11948662062228807), np.float64(0.17321711908750603), np.float64(0.0052680358029746355), np.float64(0.1479929438781923), np.float64(0.04799294387819232), np.float64(0.05799294387819232), np.float64(0.04399294387819232)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.3071958856890672), 6: np.float64(0.5064803910071303), 8: np.float64(0.18632372320799667), 16: np.float64(2.3951593814335325e-11), 83: np.float64(2.3951593814335325e-11), 70: np.float64(2.3951593814335325e-11), 0: np.float64(2.3951593814335325e-11)}
err dic= {7: np.float64(0.1001958856890672), 6: np.float64(0.2604803910071303), 8: np.float64(0.06267627679200333), 16: np.float64(0.1479999999760484), 83: np.float64(0.04799999997604841), 70: np.float64(0.05799999997604841), 0: np.float64(0.04399999997604841)} 

err list= [np.float64(0.1001958856890672), np.float64(0.2604803910071303), np.float64(0.06267627679200333), np.float64(0.1479999999760484), np.float64(0.04799999997604841), np.float64(0.05799999997604841), np.float64(0.04399999997604841)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.27860068919627295), 6: np.float64(0.5897976636568124), 8: np.float64(0.13160164714691427), 16: np.float64(9.031528939781169e-17), 83: np.float64(9.031528939781169e-17), 70: np.float64(9.031528939781169e-17), 0: np.float64(9.031528939781169e-17)}
err dic= {7: np.float64(0.07160068919627297), 6: np.float64(0.3437976636568124), 8: np.float64(0.11739835285308572), 16: np.float64(0.1479999999999999), 83: np.float64(0.04799999999999991), 70: np.float64(0.05799999999999991), 0: np.float64(0.04399999999999991)} 

err list= [np.float64(0.07160068919627297), np.float64(0.3437976636568124), np.float64(0.11739835285308572), np.float64(0.1479999999999999), np.float64(0.04799999999999991), np.float64(0.05799999999999991), np.float64(0.04399999999999991)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24472847105479775), 6: np.float64(0.6652409557748219), 8: np.float64(0.09003057317038048), 16: np.float64(3.5565985405436305e-22), 83: np.float64(3.5565985405436305e-22), 70: np.float64(3.5565985405436305e-22), 0: np.float64(3.5565985405436305e-22)}
err dic= {7: np.float64(0.03772847105479776), 6: np.float64(0.4192409557748219), 8: np.float64(0.1589694268296195), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.03772847105479776), np.float64(0.4192409557748219), np.float64(0.1589694268296195), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20934307548219694), 6: np.float64(0.7306791292026886), 8: np.float64(0.05997779531511427), 16: np.float64(1.4350636504646715e-27), 83: np.float64(1.4350636504646715e-27), 70: np.float64(1.4350636504646715e-27), 0: np.float64(1.4350636504646715e-27)}
err dic= {7: np.float64(0.002343075482196949), 6: np.float64(0.48467912920268863), 8: np.float64(0.18902220468488573), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.002343075482196949), np.float64(0.48467912920268863), np.float64(0.18902220468488573), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17529039214003667), 6: np.float64(0.7855970345892757), 8: np.float64(0.03911257327068745), 16: np.float64(5.8848474390130264e-33), 83: np.float64(5.8848474390130264e-33), 70: np.float64(5.8848474390130264e-33), 0: np.float64(5.8848474390130264e-33)}
err dic= {7: np.float64(0.031709607859963324), 6: np.float64(0.5395970345892757), 8: np.float64(0.20988742672931254), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.031709607859963324), np.float64(0.5395970345892757), np.float64(0.20988742672931254), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.1443339551132098), 6: np.float64(0.8305845643329679), 8: np.float64(0.025081480553822005), 16: np.float64(2.439494871545051e-38), 83: np.float64(2.439494871545051e-38), 70: np.float64(2.439494871545051e-38), 0: np.float64(2.439494871545051e-38)}
err dic= {7: np.float64(0.0626660448867902), 6: np.float64(0.5845845643329679), 8: np.float64(0.223918519446178), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.0626660448867902), np.float64(0.5845845643329679), np.float64(0.223918519446178), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11731042782619833), 6: np.float64(0.8668133321973345), 8: np.float64(0.01587623997646676), 16: np.float64(1.0183832705494185e-43), 83: np.float64(1.0183832705494185e-43), 70: np.float64(1.0183832705494185e-43), 0: np.float64(1.0183832705494185e-43)}
err dic= {7: np.float64(0.08968957217380166), 6: np.float64(0.6208133321973345), 8: np.float64(0.23312376002353324), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.08968957217380166), np.float64(0.6208133321973345), np.float64(0.23312376002353324), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
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= [0.06090855 0.04455828 0.05557218 0.06296283 0.07098034 0.07893116
 0.08630709 0.09291235 0.09971882 0.10644936 0.11289716]
mean_std= [0.         0.01635027 0.0205142  0.02189725 0.02531232 0.02915485
 0.0324808  0.03505045 0.03824466 0.04152216 0.04453197]
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
