p= 2 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(0.3286300651605581), 3: np.float64(0.3205161599416091), 4: np.float64(0.3126025877563094), 59: np.float64(0.009562796785380955), 40: np.float64(0.009562796785380955), 84: np.float64(0.009562796785380955), 0: np.float64(0.009562796785380955)}
err dic= {2: np.float64(0.05363006516055807), 3: np.float64(0.0735161599416091), 4: np.float64(0.06060258775630939), 59: np.float64(0.049437203214619044), 40: np.float64(0.06243720321461904), 84: np.float64(0.050437203214619045), 0: np.float64(0.02543720321461905)} 

err list= [np.float64(0.05363006516055807), np.float64(0.0735161599416091), np.float64(0.06060258775630939), np.float64(0.049437203214619044), np.float64(0.06243720321461904), np.float64(0.050437203214619045), np.float64(0.02543720321461905)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.3497941553897074), 3: np.float64(0.3327344931250646), 4: np.float64(0.3165068404068921), 59: np.float64(0.00024112776958401712), 40: np.float64(0.00024112776958401712), 84: np.float64(0.00024112776958401712), 0: np.float64(0.00024112776958401712)}
err dic= {2: np.float64(0.07479415538970735), 3: np.float64(0.08573449312506459), 4: np.float64(0.06450684040689209), 59: np.float64(0.05875887223041598), 40: np.float64(0.07175887223041598), 84: np.float64(0.05975887223041598), 0: np.float64(0.03475887223041599)} 

err list= [np.float64(0.07479415538970735), np.float64(0.08573449312506459), np.float64(0.06450684040689209), np.float64(0.05875887223041598), np.float64(0.07175887223041598), np.float64(0.05975887223041598), np.float64(0.03475887223041599)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.36716536918904563), 3: np.float64(0.3322249646492359), 4: np.float64(0.3006095792203026), 59: np.float64(2.173535405699907e-08), 40: np.float64(2.173535405699907e-08), 84: np.float64(2.173535405699907e-08), 0: np.float64(2.173535405699907e-08)}
err dic= {2: np.float64(0.09216536918904561), 3: np.float64(0.0852249646492359), 4: np.float64(0.04860957922030262), 59: np.float64(0.05899997826464594), 40: np.float64(0.07199997826464594), 84: np.float64(0.05999997826464594), 0: np.float64(0.034999978264645945)} 

err list= [np.float64(0.09216536918904561), np.float64(0.0852249646492359), np.float64(0.04860957922030262), np.float64(0.05899997826464594), np.float64(0.07199997826464594), np.float64(0.05999997826464594), np.float64(0.034999978264645945)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.41922895160969764), 3: np.float64(0.3264958357998366), 4: np.float64(0.25427521259046554), 59: np.float64(1.3354499888954436e-20), 40: np.float64(1.3354499888954436e-20), 84: np.float64(1.3354499888954436e-20), 0: np.float64(1.3354499888954436e-20)}
err dic= {2: np.float64(0.14422895160969762), 3: np.float64(0.0794958357998366), 4: np.float64(0.0022752125904655363), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.14422895160969762), np.float64(0.0794958357998366), np.float64(0.0022752125904655363), 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  0.5 

learned probs for this beta: {2: np.float64(0.5064803910556542), 3: np.float64(0.3071958857184985), 4: np.float64(0.18632372322584767), 59: np.float64(6.262123845733988e-41), 40: np.float64(6.262123845733988e-41), 84: np.float64(6.262123845733988e-41), 0: np.float64(6.262123845733988e-41)}
err dic= {2: np.float64(0.2314803910556542), 3: np.float64(0.06019588571849849), 4: np.float64(0.06567627677415233), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.2314803910556542), np.float64(0.06019588571849849), np.float64(0.06567627677415233), 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  0.75 

learned probs for this beta: {2: np.float64(0.5897976636568126), 3: np.float64(0.27860068919627307), 4: np.float64(0.13160164714691439), 59: np.float64(3.3107566130006916e-61), 40: np.float64(3.3107566130006916e-61), 84: np.float64(3.3107566130006916e-61), 0: np.float64(3.3107566130006916e-61)}
err dic= {2: np.float64(0.3147976636568126), 3: np.float64(0.03160068919627307), 4: np.float64(0.12039835285308562), 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(0.12039835285308562), 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(1.9030504710164814e-81), 40: np.float64(1.9030504710164814e-81), 84: np.float64(1.9030504710164814e-81), 0: np.float64(1.9030504710164814e-81)}
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(1.1451716530556965e-101), 40: np.float64(1.1451716530556965e-101), 84: np.float64(1.1451716530556965e-101), 0: np.float64(1.1451716530556965e-101)}
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(7.065865638929807e-122), 40: np.float64(7.065865638929807e-122), 84: np.float64(7.065865638929807e-122), 0: np.float64(7.065865638929807e-122)}
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(4.421913188198419e-142), 40: np.float64(4.421913188198419e-142), 84: np.float64(4.421913188198419e-142), 0: np.float64(4.421913188198419e-142)}
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(2.7901551230140706e-162), 40: np.float64(2.7901551230140706e-162), 84: np.float64(2.7901551230140706e-162), 0: np.float64(2.7901551230140706e-162)}
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(0.3340667008081574), 4: np.float64(0.3258185645767992), 8: np.float64(0.30010166197321597), 74: np.float64(0.010003268160456906), 40: np.float64(0.010003268160456906), 87: np.float64(0.010003268160456906), 0: np.float64(0.010003268160456906)}
err dic= {3: np.float64(0.07506670080815742), 4: np.float64(0.0798185645767992), 8: np.float64(0.044101661973215966), 74: np.float64(0.055996731839543096), 40: np.float64(0.06699673183954309), 87: np.float64(0.03699673183954309), 0: np.float64(0.038996731839543095)} 

err list= [np.float64(0.07506670080815742), np.float64(0.0798185645767992), np.float64(0.044101661973215966), np.float64(0.055996731839543096), np.float64(0.06699673183954309), np.float64(0.03699673183954309), np.float64(0.038996731839543095)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.36208492898054123), 4: np.float64(0.3444258386145423), 8: np.float64(0.29246038627617554), 74: np.float64(0.0002572115321852969), 40: np.float64(0.0002572115321852969), 87: np.float64(0.0002572115321852969), 0: np.float64(0.0002572115321852969)}
err dic= {3: np.float64(0.10308492898054122), 4: np.float64(0.0984258386145423), 8: np.float64(0.03646038627617554), 74: np.float64(0.0657427884678147), 40: np.float64(0.0767427884678147), 87: np.float64(0.046742788467814704), 0: np.float64(0.048742788467814706)} 

err list= [np.float64(0.10308492898054122), np.float64(0.0984258386145423), np.float64(0.03646038627617554), np.float64(0.0657427884678147), np.float64(0.0767427884678147), np.float64(0.046742788467814704), np.float64(0.048742788467814706)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.3912614013550087), 4: np.float64(0.35402795617919736), 8: np.float64(0.25471054276345634), 74: np.float64(2.4925584547324527e-08), 40: np.float64(2.4925584547324527e-08), 87: np.float64(2.4925584547324527e-08), 0: np.float64(2.4925584547324527e-08)}
err dic= {3: np.float64(0.1322614013550087), 4: np.float64(0.10802795617919736), 8: np.float64(0.0012894572365436674), 74: np.float64(0.06599997507441546), 40: np.float64(0.07699997507441546), 87: np.float64(0.04699997507441545), 0: np.float64(0.048999975074415454)} 

err list= [np.float64(0.1322614013550087), np.float64(0.10802795617919736), np.float64(0.0012894572365436674), np.float64(0.06599997507441546), np.float64(0.07699997507441546), np.float64(0.04699997507441545), np.float64(0.048999975074415454)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.4729190782429194), 4: np.float64(0.3683097484649926), 8: np.float64(0.15877117329208743), 74: np.float64(1.9507055279175452e-20), 40: np.float64(1.9507055279175452e-20), 87: np.float64(1.9507055279175452e-20), 0: np.float64(1.9507055279175452e-20)}
err dic= {3: np.float64(0.2139190782429194), 4: np.float64(0.1223097484649926), 8: np.float64(0.09722882670791258), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.2139190782429194), np.float64(0.1223097484649926), np.float64(0.09722882670791258), 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  0.5 

learned probs for this beta: {3: np.float64(0.5841457846018505), 4: np.float64(0.3543023281029142), 8: np.float64(0.06155188729523564), 74: np.float64(1.3306315028079632e-40), 40: np.float64(1.3306315028079632e-40), 87: np.float64(1.3306315028079632e-40), 0: np.float64(1.3306315028079632e-40)}
err dic= {3: np.float64(0.3251457846018505), 4: np.float64(0.10830232810291418), 8: np.float64(0.19444811270476436), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.3251457846018505), np.float64(0.10830232810291418), np.float64(0.19444811270476436), 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  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(9.35230395787871e-61), 40: np.float64(9.35230395787871e-61), 87: np.float64(9.35230395787871e-61), 0: np.float64(9.35230395787871e-61)}
err dic= {3: np.float64(0.4061469585882833), 4: np.float64(0.06819317589451784), 8: np.float64(0.235340134482801), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.4061469585882833), np.float64(0.06819317589451784), np.float64(0.235340134482801), 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 

learned probs for this beta: {3: np.float64(0.7263954957320881), 4: np.float64(0.26722596903937335), 8: np.float64(0.0063785352285387455), 74: np.float64(6.782089793771813e-81), 40: np.float64(6.782089793771813e-81), 87: np.float64(6.782089793771813e-81), 0: np.float64(6.782089793771813e-81)}
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(5.051723663845176e-101), 40: np.float64(5.051723663845176e-101), 87: np.float64(5.051723663845176e-101), 0: np.float64(5.051723663845176e-101)}
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(3.84542838474608e-121), 40: np.float64(3.84542838474608e-121), 87: np.float64(3.84542838474608e-121), 0: np.float64(3.84542838474608e-121)}
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(2.9782804218928433e-141), 40: np.float64(2.9782804218928433e-141), 87: np.float64(2.9782804218928433e-141), 0: np.float64(2.9782804218928433e-141)}
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(2.3380652962959335e-161), 40: np.float64(2.3380652962959335e-161), 87: np.float64(2.3380652962959335e-161), 0: np.float64(2.3380652962959335e-161)}
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(0.34090713475635787), 3: np.float64(0.32628721529697974), 9: np.float64(0.2948188875277115), 83: np.float64(0.009496690604737804), 79: np.float64(0.009496690604737804), 70: np.float64(0.009496690604737804), 0: np.float64(0.009496690604737804)}
err dic= {1: np.float64(0.07590713475635785), 3: np.float64(0.07528721529697974), 9: np.float64(0.05981888752771153), 83: np.float64(0.042503309395262194), 79: np.float64(0.0585033093952622), 70: np.float64(0.0715033093952622), 0: np.float64(0.0385033093952622)} 

err list= [np.float64(0.07590713475635785), np.float64(0.07528721529697974), np.float64(0.05981888752771153), np.float64(0.042503309395262194), np.float64(0.0585033093952622), np.float64(0.0715033093952622), np.float64(0.0385033093952622)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.374788105203058), 3: np.float64(0.3435873156613695), 9: np.float64(0.28074659201638746), 83: np.float64(0.00021949677979629775), 79: np.float64(0.00021949677979629775), 70: np.float64(0.00021949677979629775), 0: np.float64(0.00021949677979629775)}
err dic= {1: np.float64(0.10978810520305798), 3: np.float64(0.09258731566136952), 9: np.float64(0.04574659201638748), 83: np.float64(0.0517805032202037), 79: np.float64(0.06778050322020371), 70: np.float64(0.0807805032202037), 0: np.float64(0.047780503220203704)} 

err list= [np.float64(0.10978810520305798), np.float64(0.09258731566136952), np.float64(0.04574659201638748), np.float64(0.0517805032202037), np.float64(0.06778050322020371), np.float64(0.0807805032202037), np.float64(0.047780503220203704)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.41653656784102666), 3: np.float64(0.35045350154886956), 9: np.float64(0.23300985334328161), 83: np.float64(1.9316705713994527e-08), 79: np.float64(1.9316705713994527e-08), 70: np.float64(1.9316705713994527e-08), 0: np.float64(1.9316705713994527e-08)}
err dic= {1: np.float64(0.15153656784102665), 3: np.float64(0.09945350154886956), 9: np.float64(0.0019901466567183723), 83: np.float64(0.05199998068329428), 79: np.float64(0.0679999806832943), 70: np.float64(0.0809999806832943), 0: np.float64(0.04799998068329429)} 

err list= [np.float64(0.15153656784102665), np.float64(0.09945350154886956), np.float64(0.0019901466567183723), np.float64(0.05199998068329428), np.float64(0.0679999806832943), np.float64(0.0809999806832943), np.float64(0.04799998068329429)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.53166001008169), 3: np.float64(0.3473995733591339), 9: np.float64(0.12094041655917559), 83: np.float64(1.1024722609278642e-20), 79: np.float64(1.1024722609278642e-20), 70: np.float64(1.1024722609278642e-20), 0: np.float64(1.1024722609278642e-20)}
err dic= {1: np.float64(0.26666001008168994), 3: np.float64(0.0963995733591339), 9: np.float64(0.1140595834408244), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.26666001008168994), np.float64(0.0963995733591339), np.float64(0.1140595834408244), 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  0.5 

learned probs for this beta: {1: np.float64(0.6768077271813894), 3: np.float64(0.29176229833973133), 9: np.float64(0.03142997447887963), 83: np.float64(3.9866617070093293e-41), 79: np.float64(3.9866617070093293e-41), 70: np.float64(3.9866617070093293e-41), 0: np.float64(3.9866617070093293e-41)}
err dic= {1: np.float64(0.41180772718138936), 3: np.float64(0.04076229833973133), 9: np.float64(0.20357002552112036), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.41180772718138936), np.float64(0.04076229833973133), np.float64(0.20357002552112036), 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  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(1.4093736139696476e-61), 79: np.float64(1.4093736139696476e-61), 70: np.float64(1.4093736139696476e-61), 0: np.float64(1.4093736139696476e-61)}
err dic= {1: np.float64(0.509105702190221), 3: np.float64(0.031821361506595314), 9: np.float64(0.22828434068362594), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.509105702190221), np.float64(0.031821361506595314), np.float64(0.22828434068362594), 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 

learned probs for this beta: {1: np.float64(0.8431197129536219), 3: np.float64(0.1555712984978225), 9: np.float64(0.0013089885485560214), 83: np.float64(5.07686718614163e-82), 79: np.float64(5.07686718614163e-82), 70: np.float64(5.07686718614163e-82), 0: np.float64(5.07686718614163e-82)}
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(1.872001639545586e-102), 79: np.float64(1.872001639545586e-102), 70: np.float64(1.872001639545586e-102), 0: np.float64(1.872001639545586e-102)}
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(7.027475825616465e-123), 79: np.float64(7.027475825616465e-123), 70: np.float64(7.027475825616465e-123), 0: np.float64(7.027475825616465e-123)}
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(2.6699145917051407e-143), 79: np.float64(2.6699145917051407e-143), 70: np.float64(2.6699145917051407e-143), 0: np.float64(2.6699145917051407e-143)}
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(1.0220823209499084e-163), 79: np.float64(1.0220823209499084e-163), 70: np.float64(1.0220823209499084e-163), 0: np.float64(1.0220823209499084e-163)}
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(0.34295219634448054), 4: np.float64(0.3221115578758058), 8: np.float64(0.2966468233836659), 32: np.float64(0.009572355599011909), 27: np.float64(0.009572355599011909), 82: np.float64(0.009572355599011909), 0: np.float64(0.009572355599011909)}
err dic= {1: np.float64(0.12095219634448054), 4: np.float64(0.0921115578758058), 8: np.float64(0.06464682338366587), 32: np.float64(0.09242764440098808), 27: np.float64(0.11042764440098808), 82: np.float64(0.040427644400988096), 0: np.float64(0.03442764440098809)} 

err list= [np.float64(0.12095219634448054), np.float64(0.0921115578758058), np.float64(0.06464682338366587), np.float64(0.09242764440098808), np.float64(0.11042764440098808), np.float64(0.040427644400988096), np.float64(0.03442764440098809)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.37943513013648533), 4: np.float64(0.33520803193972865), 8: np.float64(0.2844689794537006), 32: np.float64(0.00022196461752141029), 27: np.float64(0.00022196461752141029), 82: np.float64(0.00022196461752141029), 0: np.float64(0.00022196461752141029)}
err dic= {1: np.float64(0.15743513013648533), 4: np.float64(0.10520803193972864), 8: np.float64(0.052468979453700576), 32: np.float64(0.10177803538247858), 27: np.float64(0.11977803538247858), 82: np.float64(0.049778035382478596), 0: np.float64(0.04377803538247859)} 

err list= [np.float64(0.15743513013648533), np.float64(0.10520803193972864), np.float64(0.052468979453700576), np.float64(0.10177803538247858), np.float64(0.11977803538247858), np.float64(0.049778035382478596), np.float64(0.04377803538247859)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.42674102532007147), 4: np.float64(0.33372560518387484), 8: np.float64(0.23953329030804907), 32: np.float64(1.979700127870553e-08), 27: np.float64(1.979700127870553e-08), 82: np.float64(1.979700127870553e-08), 0: np.float64(1.979700127870553e-08)}
err dic= {1: np.float64(0.20474102532007146), 4: np.float64(0.10372560518387483), 8: np.float64(0.0075332903080490565), 32: np.float64(0.10199998020299872), 27: np.float64(0.11999998020299872), 82: np.float64(0.04999998020299872), 0: np.float64(0.043999980202998716)} 

err list= [np.float64(0.20474102532007146), np.float64(0.10372560518387483), np.float64(0.0075332903080490565), np.float64(0.10199998020299872), np.float64(0.11999998020299872), np.float64(0.04999998020299872), np.float64(0.043999980202998716)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5619787294115659), 4: np.float64(0.30746143031853845), 8: np.float64(0.13055984026989492), 32: np.float64(1.1878371092903467e-20), 27: np.float64(1.1878371092903467e-20), 82: np.float64(1.1878371092903467e-20), 0: np.float64(1.1878371092903467e-20)}
err dic= {1: np.float64(0.3399787294115659), 4: np.float64(0.07746143031853844), 8: np.float64(0.10144015973010509), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.3399787294115659), np.float64(0.07746143031853844), np.float64(0.10144015973010509), 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  0.5 

learned probs for this beta: {1: np.float64(0.7383008689607047), 4: np.float64(0.22465672961378827), 8: np.float64(0.03704240142550746), 32: np.float64(4.713084891349019e-41), 27: np.float64(4.713084891349019e-41), 82: np.float64(4.713084891349019e-41), 0: np.float64(4.713084891349019e-41)}
err dic= {1: np.float64(0.5163008689607047), 4: np.float64(0.00534327038621174), 8: np.float64(0.19495759857449255), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.5163008689607047), np.float64(0.00534327038621174), np.float64(0.19495759857449255), 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  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(1.801255224407622e-61), 27: np.float64(1.801255224407622e-61), 82: np.float64(1.801255224407622e-61), 0: np.float64(1.801255224407622e-61)}
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(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.6274867469393008), np.float64(0.0880374867598599), np.float64(0.22344926017944117), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
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(6.862445195046982e-82), 27: np.float64(6.862445195046982e-82), 82: np.float64(6.862445195046982e-82), 0: np.float64(6.862445195046982e-82)}
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(2.6275895703246578e-102), 27: np.float64(2.6275895703246578e-102), 82: np.float64(2.6275895703246578e-102), 0: np.float64(2.6275895703246578e-102)}
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(1.0108754497996606e-122), 27: np.float64(1.0108754497996606e-122), 82: np.float64(1.0108754497996606e-122), 0: np.float64(1.0108754497996606e-122)}
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(3.9011764478849493e-143), 27: np.float64(3.9011764478849493e-143), 82: np.float64(3.9011764478849493e-143), 0: np.float64(3.9011764478849493e-143)}
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(1.50827648018116e-163), 27: np.float64(1.50827648018116e-163), 82: np.float64(1.50827648018116e-163), 0: np.float64(1.50827648018116e-163)}
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(0.018466217046809882), 4: np.float64(0.46348523705340877), 6: np.float64(0.44418367771254175), 51: np.float64(0.018466217046809882), 82: np.float64(0.018466217046809882), 41: np.float64(0.018466217046809882), 0: np.float64(0.018466217046809882)}
err dic= {9: np.float64(0.20253378295319013), 4: np.float64(0.21848523705340878), 6: np.float64(0.18818367771254174), 51: np.float64(0.06753378295319011), 82: np.float64(0.02153378295319012), 41: np.float64(0.07453378295319012), 0: np.float64(0.040533782953190114)} 

err list= [np.float64(0.20253378295319013), np.float64(0.21848523705340878), np.float64(0.18818367771254174), np.float64(0.06753378295319011), np.float64(0.02153378295319012), np.float64(0.07453378295319012), np.float64(0.040533782953190114)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.00027953971432319704), 4: np.float64(0.5200974390998786), 6: np.float64(0.4785048623285057), 51: np.float64(0.00027953971432319704), 82: np.float64(0.00027953971432319704), 41: np.float64(0.00027953971432319704), 0: np.float64(0.00027953971432319704)}
err dic= {9: np.float64(0.2207204602856768), 4: np.float64(0.2750974390998786), 6: np.float64(0.2225048623285057), 51: np.float64(0.0857204602856768), 82: np.float64(0.0397204602856768), 41: np.float64(0.0927204602856768), 0: np.float64(0.0587204602856768)} 

err list= [np.float64(0.2207204602856768), np.float64(0.2750974390998786), np.float64(0.2225048623285057), np.float64(0.0857204602856768), np.float64(0.0397204602856768), np.float64(0.0927204602856768), np.float64(0.0587204602856768)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(2.4731538444431478e-08), 4: np.float64(0.5415765419029126), 6: np.float64(0.4584233344393954), 51: np.float64(2.4731538444431478e-08), 82: np.float64(2.4731538444431478e-08), 41: np.float64(2.4731538444431478e-08), 0: np.float64(2.4731538444431478e-08)}
err dic= {9: np.float64(0.22099997526846155), 4: np.float64(0.2965765419029126), 6: np.float64(0.20242333443939542), 51: np.float64(0.08599997526846155), 82: np.float64(0.03999997526846156), 41: np.float64(0.09299997526846156), 0: np.float64(0.058999975268461555)} 

err list= [np.float64(0.22099997526846155), np.float64(0.2965765419029126), np.float64(0.20242333443939542), np.float64(0.08599997526846155), np.float64(0.03999997526846156), np.float64(0.09299997526846156), np.float64(0.058999975268461555)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(1.6979880578716748e-20), 4: np.float64(0.6027772381334338), 6: np.float64(0.3972227618665658), 51: np.float64(1.6979880578716748e-20), 82: np.float64(1.6979880578716748e-20), 41: np.float64(1.6979880578716748e-20), 0: np.float64(1.6979880578716748e-20)}
err dic= {9: np.float64(0.221), 4: np.float64(0.35777723813343376), 6: np.float64(0.1412227618665658), 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(0.35777723813343376), np.float64(0.1412227618665658), 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  0.5 

learned probs for this beta: {9: np.float64(9.898192148618723e-41), 4: np.float64(0.6976973366279521), 6: np.float64(0.3023026633720482), 51: np.float64(9.898192148618723e-41), 82: np.float64(9.898192148618723e-41), 41: np.float64(9.898192148618723e-41), 0: np.float64(9.898192148618723e-41)}
err dic= {9: np.float64(0.221), 4: np.float64(0.4526973366279521), 6: np.float64(0.04630266337204819), 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(0.4526973366279521), np.float64(0.04630266337204819), 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  0.75 

learned probs for this beta: {9: np.float64(5.985903315870328e-61), 4: np.float64(0.7790173173345053), 6: np.float64(0.22098268266549476), 51: np.float64(5.985903315870328e-61), 82: np.float64(5.985903315870328e-61), 41: np.float64(5.985903315870328e-61), 0: np.float64(5.985903315870328e-61)}
err dic= {9: np.float64(0.221), 4: np.float64(0.5340173173345053), 6: np.float64(0.03501731733450525), 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(0.5340173173345053), np.float64(0.03501731733450525), 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 

learned probs for this beta: {9: np.float64(3.6581643629747807e-81), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(3.6581643629747807e-81), 82: np.float64(3.6581643629747807e-81), 41: np.float64(3.6581643629747807e-81), 0: np.float64(3.6581643629747807e-81)}
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(2.2566390697818353e-101), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(2.2566390697818353e-101), 82: np.float64(2.2566390697818353e-101), 41: np.float64(2.2566390697818353e-101), 0: np.float64(2.2566390697818353e-101)}
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(1.405673901621018e-121), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(1.405673901621018e-121), 82: np.float64(1.405673901621018e-121), 41: np.float64(1.405673901621018e-121), 0: np.float64(1.405673901621018e-121)}
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(8.828034391805506e-142), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(8.828034391805506e-142), 82: np.float64(8.828034391805506e-142), 41: np.float64(8.828034391805506e-142), 0: np.float64(8.828034391805506e-142)}
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(5.577556505356181e-162), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(5.577556505356181e-162), 82: np.float64(5.577556505356181e-162), 41: np.float64(5.577556505356181e-162), 0: np.float64(5.577556505356181e-162)}
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(0.33113004000029767), 9: np.float64(0.30319205728899123), 6: np.float64(0.3229544101826287), 39: np.float64(0.010680873132020747), 80: np.float64(0.010680873132020747), 68: np.float64(0.010680873132020747), 0: np.float64(0.010680873132020747)}
err dic= {5: np.float64(0.08613004000029767), 9: np.float64(0.07519205728899123), 6: np.float64(0.06495441018262871), 39: np.float64(0.08931912686797926), 80: np.float64(0.05231912686797925), 68: np.float64(0.04531912686797925), 0: np.float64(0.039319126867979254)} 

err list= [np.float64(0.08613004000029767), np.float64(0.07519205728899123), np.float64(0.06495441018262871), np.float64(0.08931912686797926), np.float64(0.05231912686797925), np.float64(0.04531912686797925), np.float64(0.039319126867979254)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.35796166882927316), 9: np.float64(0.3003129938458812), 6: np.float64(0.34050367223378464), 39: np.float64(0.0003054162727652451), 80: np.float64(0.0003054162727652451), 68: np.float64(0.0003054162727652451), 0: np.float64(0.0003054162727652451)}
err dic= {5: np.float64(0.11296166882927317), 9: np.float64(0.07231299384588122), 6: np.float64(0.08250367223378463), 39: np.float64(0.09969458372723476), 80: np.float64(0.06269458372723476), 68: np.float64(0.05569458372723476), 0: np.float64(0.04969458372723476)} 

err list= [np.float64(0.11296166882927317), np.float64(0.07231299384588122), np.float64(0.08250367223378463), np.float64(0.09969458372723476), np.float64(0.06269458372723476), np.float64(0.05569458372723476), np.float64(0.04969458372723476)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.38345890848563946), 9: np.float64(0.2695729894263373), 6: np.float64(0.3469679686770333), 39: np.float64(3.3352747626581264e-08), 80: np.float64(3.3352747626581264e-08), 68: np.float64(3.3352747626581264e-08), 0: np.float64(3.3352747626581264e-08)}
err dic= {5: np.float64(0.13845890848563946), 9: np.float64(0.041572989426337276), 6: np.float64(0.08896796867703327), 39: np.float64(0.09999996664725237), 80: np.float64(0.06299996664725237), 68: np.float64(0.055999966647252375), 0: np.float64(0.04999996664725238)} 

err list= [np.float64(0.13845890848563946), np.float64(0.041572989426337276), np.float64(0.08896796867703327), np.float64(0.09999996664725237), np.float64(0.06299996664725237), np.float64(0.055999966647252375), np.float64(0.04999996664725238)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.4568298022717689), 9: np.float64(0.18739078998862158), 6: np.float64(0.35577940773960876), 39: np.float64(3.838362389723928e-20), 80: np.float64(3.838362389723928e-20), 68: np.float64(3.838362389723928e-20), 0: np.float64(3.838362389723928e-20)}
err dic= {5: np.float64(0.2118298022717689), 9: np.float64(0.04060921001137843), 6: np.float64(0.09777940773960875), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.2118298022717689), np.float64(0.04060921001137843), np.float64(0.09777940773960875), 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  0.5 

learned probs for this beta: {5: np.float64(0.5654187560796601), 9: np.float64(0.09163743278144765), 6: np.float64(0.3429438111388928), 39: np.float64(5.475125667128359e-40), 80: np.float64(5.475125667128359e-40), 68: np.float64(5.475125667128359e-40), 0: np.float64(5.475125667128359e-40)}
err dic= {5: np.float64(0.3204187560796601), 9: np.float64(0.13636256721855236), 6: np.float64(0.08494381113889277), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.3204187560796601), np.float64(0.13636256721855236), np.float64(0.08494381113889277), 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  0.75 

learned probs for this beta: {5: np.float64(0.6518852874465689), 9: np.float64(0.04018590653971), 6: np.float64(0.30792880601372125), 39: np.float64(8.301064387353442e-60), 80: np.float64(8.301064387353442e-60), 68: np.float64(8.301064387353442e-60), 0: np.float64(8.301064387353442e-60)}
err dic= {5: np.float64(0.40688528744656893), 9: np.float64(0.18781409346029002), 6: np.float64(0.04992880601372124), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.40688528744656893), np.float64(0.18781409346029002), np.float64(0.04992880601372124), 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 

learned probs for this beta: {5: np.float64(0.7191002954879085), 9: np.float64(0.016357489661781185), 6: np.float64(0.26454221485031076), 39: np.float64(1.3011381824080523e-79), 80: np.float64(1.3011381824080523e-79), 68: np.float64(1.3011381824080523e-79), 0: np.float64(1.3011381824080523e-79)}
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(2.0867992022929467e-99), 80: np.float64(2.0867992022929467e-99), 68: np.float64(2.0867992022929467e-99), 0: np.float64(2.0867992022929467e-99)}
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(3.4031002268375835e-119), 80: np.float64(3.4031002268375835e-119), 68: np.float64(3.4031002268375835e-119), 0: np.float64(3.4031002268375835e-119)}
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(5.621803953358164e-139), 80: np.float64(5.621803953358164e-139), 68: np.float64(5.621803953358164e-139), 0: np.float64(5.621803953358164e-139)}
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(9.384037954080152e-159), 80: np.float64(9.384037954080152e-159), 68: np.float64(9.384037954080152e-159), 0: np.float64(9.384037954080152e-159)}
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(0.3178550885873271), 3: np.float64(0.3384592067676306), 8: np.float64(0.30414093514938956), 15: np.float64(0.009886192373913225), 78: np.float64(0.009886192373913225), 97: np.float64(0.009886192373913225), 0: np.float64(0.009886192373913225)}
err dic= {6: np.float64(0.09685508858732708), 3: np.float64(0.1034592067676306), 8: np.float64(0.06614093514938957), 15: np.float64(0.16311380762608677), 78: np.float64(0.04611380762608677), 97: np.float64(0.029113807626086775), 0: np.float64(0.028113807626086774)} 

err list= [np.float64(0.09685508858732708), np.float64(0.1034592067676306), np.float64(0.06614093514938957), np.float64(0.16311380762608677), np.float64(0.04611380762608677), np.float64(0.029113807626086775), np.float64(0.028113807626086774)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.32776188858380634), 3: np.float64(0.37113937792050367), 8: np.float64(0.3001695104442979), 15: np.float64(0.00023230576284811427), 78: np.float64(0.00023230576284811427), 97: np.float64(0.00023230576284811427), 0: np.float64(0.00023230576284811427)}
err dic= {6: np.float64(0.10676188858380634), 3: np.float64(0.13613937792050368), 8: np.float64(0.062169510444297915), 15: np.float64(0.17276769423715188), 78: np.float64(0.05576769423715189), 97: np.float64(0.03876769423715189), 0: np.float64(0.037767694237151886)} 

err list= [np.float64(0.10676188858380634), np.float64(0.13613937792050368), np.float64(0.062169510444297915), np.float64(0.17276769423715188), np.float64(0.05576769423715189), np.float64(0.03876769423715189), np.float64(0.037767694237151886)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.3206755048483117), 3: np.float64(0.41060677516722544), 8: np.float64(0.26871763228764745), 15: np.float64(2.1924203970850212e-08), 78: np.float64(2.1924203970850212e-08), 97: np.float64(2.1924203970850212e-08), 0: np.float64(2.1924203970850212e-08)}
err dic= {6: np.float64(0.0996755048483117), 3: np.float64(0.17560677516722545), 8: np.float64(0.030717632287647456), 15: np.float64(0.172999978075796), 78: np.float64(0.05599997807579603), 97: np.float64(0.03899997807579603), 0: np.float64(0.037999978075796026)} 

err list= [np.float64(0.0996755048483117), np.float64(0.17560677516722545), np.float64(0.030717632287647456), np.float64(0.172999978075796), np.float64(0.05599997807579603), np.float64(0.03899997807579603), np.float64(0.037999978075796026)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2875137926500776), 3: np.float64(0.5289888465558913), 8: np.float64(0.1834973607940305), 15: np.float64(1.6540984098912337e-20), 78: np.float64(1.6540984098912337e-20), 97: np.float64(1.6540984098912337e-20), 0: np.float64(1.6540984098912337e-20)}
err dic= {6: np.float64(0.06651379265007759), 3: np.float64(0.2939888465558913), 8: np.float64(0.05450263920596948), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.06651379265007759), np.float64(0.2939888465558913), np.float64(0.05450263920596948), 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  0.5 

learned probs for this beta: {6: np.float64(0.21136722905274474), 3: np.float64(0.7045769546695909), 8: np.float64(0.08405581627766473), 15: np.float64(1.0855953385127866e-40), 78: np.float64(1.0855953385127866e-40), 97: np.float64(1.0855953385127866e-40), 0: np.float64(1.0855953385127866e-40)}
err dic= {6: np.float64(0.00963277094725526), 3: np.float64(0.46957695466959093), 8: np.float64(0.15394418372233526), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.00963277094725526), np.float64(0.46957695466959093), np.float64(0.15394418372233526), 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  0.75 

learned probs for this beta: {6: np.float64(0.13673323328089826), 3: np.float64(0.8300378726980453), 8: np.float64(0.033228894021056346), 15: np.float64(7.158547496468948e-61), 78: np.float64(7.158547496468948e-61), 97: np.float64(7.158547496468948e-61), 0: np.float64(7.158547496468948e-61)}
err dic= {6: np.float64(0.08426676671910174), 3: np.float64(0.5950378726980453), 8: np.float64(0.20477110597894366), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.08426676671910174), np.float64(0.5950378726980453), np.float64(0.20477110597894366), 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 

learned probs for this beta: {6: np.float64(0.0806651538227525), 3: np.float64(0.9074958368084762), 8: np.float64(0.011839009368771462), 15: np.float64(4.682526250461791e-81), 78: np.float64(4.682526250461791e-81), 97: np.float64(4.682526250461791e-81), 0: np.float64(4.682526250461791e-81)}
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(3.042441871206825e-101), 78: np.float64(3.042441871206825e-101), 97: np.float64(3.042441871206825e-101), 0: np.float64(3.042441871206825e-101)}
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(1.9669010556885784e-121), 78: np.float64(1.9669010556885784e-121), 97: np.float64(1.9669010556885784e-121), 0: np.float64(1.9669010556885784e-121)}
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(1.2667908274523504e-141), 78: np.float64(1.2667908274523504e-141), 97: np.float64(1.2667908274523504e-141), 0: np.float64(1.2667908274523504e-141)}
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(8.136455368482941e-162), 78: np.float64(8.136455368482941e-162), 97: np.float64(8.136455368482941e-162), 0: np.float64(8.136455368482941e-162)}
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(0.23364082202350417), 2: np.float64(0.2661224199862091), 4: np.float64(0.25444303094572035), 95: np.float64(0.007500984039302455), 11: np.float64(0.22329077492665972), 22: np.float64(0.007500984039302455), 0: np.float64(0.007500984039302455)}
err dic= {8: np.float64(0.0013591779764958178), 2: np.float64(0.0641224199862091), 4: np.float64(0.05744303094572034), 95: np.float64(0.03449901596069755), 11: np.float64(0.05729077492665971), 22: np.float64(0.12949901596069754), 0: np.float64(0.013499015960697545)} 

err list= [np.float64(0.0013591779764958178), np.float64(0.0641224199862091), np.float64(0.05744303094572034), np.float64(0.03449901596069755), np.float64(0.05729077492665971), np.float64(0.12949901596069754), np.float64(0.013499015960697545)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.22739483220509896), 2: np.float64(0.29470375769770385), 4: np.float64(0.2695657833911956), 95: np.float64(0.00023207382742613915), 11: np.float64(0.20763940522372326), 22: np.float64(0.00023207382742613915), 0: np.float64(0.00023207382742613915)}
err dic= {8: np.float64(0.00760516779490103), 2: np.float64(0.09270375769770384), 4: np.float64(0.07256578339119557), 95: np.float64(0.04176792617257386), 11: np.float64(0.04163940522372325), 22: np.float64(0.13676792617257388), 0: np.float64(0.02076792617257386)} 

err list= [np.float64(0.00760516779490103), np.float64(0.09270375769770384), np.float64(0.07256578339119557), np.float64(0.04176792617257386), np.float64(0.04163940522372325), np.float64(0.13676792617257388), np.float64(0.02076792617257386)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.20339912966047075), 2: np.float64(0.3412960210837011), 4: np.float64(0.2860132275789009), 95: np.float64(2.3761781523579736e-08), 11: np.float64(0.16929155039158336), 22: np.float64(2.3761781523579736e-08), 0: np.float64(2.3761781523579736e-08)}
err dic= {8: np.float64(0.03160087033952924), 2: np.float64(0.1392960210837011), 4: np.float64(0.0890132275789009), 95: np.float64(0.04199997623821848), 11: np.float64(0.0032915503915833533), 22: np.float64(0.1369999762382185), 0: np.float64(0.020999976238218476)} 

err list= [np.float64(0.03160087033952924), np.float64(0.1392960210837011), np.float64(0.0890132275789009), np.float64(0.04199997623821848), np.float64(0.0032915503915833533), np.float64(0.1369999762382185), np.float64(0.020999976238218476)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.1308257606990439), 2: np.float64(0.4775204477078609), 4: np.float64(0.31002951642583915), 95: np.float64(2.098470778568317e-20), 11: np.float64(0.0816242751672552), 22: np.float64(2.098470778568317e-20), 0: np.float64(2.098470778568317e-20)}
err dic= {8: np.float64(0.1041742393009561), 2: np.float64(0.2755204477078609), 4: np.float64(0.11302951642583914), 95: np.float64(0.042), 11: np.float64(0.0843757248327448), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.1041742393009561), np.float64(0.2755204477078609), np.float64(0.11302951642583914), np.float64(0.042), np.float64(0.0843757248327448), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04709325965882175), 2: np.float64(0.6544667084443634), 4: np.float64(0.2806804187885039), 95: np.float64(1.6540704066747368e-40), 11: np.float64(0.017759613108311294), 22: np.float64(1.6540704066747368e-40), 0: np.float64(1.6540704066747368e-40)}
err dic= {8: np.float64(0.18790674034117824), 2: np.float64(0.4524667084443634), 4: np.float64(0.08368041878850391), 95: np.float64(0.042), 11: np.float64(0.14824038689168872), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.18790674034117824), np.float64(0.4524667084443634), np.float64(0.08368041878850391), np.float64(0.042), np.float64(0.14824038689168872), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013536549016638746), 2: np.float64(0.7668515971786537), 4: np.float64(0.2165503665695186), 95: np.float64(1.282261445127427e-60), 11: np.float64(0.003061487235188769), 22: np.float64(1.282261445127427e-60), 0: np.float64(1.282261445127427e-60)}
err dic= {8: np.float64(0.22146345098336123), 2: np.float64(0.5648515971786536), 4: np.float64(0.019550366569518585), 95: np.float64(0.042), 11: np.float64(0.16293851276481125), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.22146345098336123), np.float64(0.5648515971786536), np.float64(0.019550366569518585), np.float64(0.042), np.float64(0.16293851276481125), np.float64(0.137), np.float64(0.021)]
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(9.996519854626743e-81), 11: np.float64(0.00047336280779999217), 22: np.float64(9.996519854626743e-81), 0: np.float64(9.996519854626743e-81)}
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(7.890354019420172e-101), 11: np.float64(6.965386583462914e-05), 22: np.float64(7.890354019420172e-101), 0: np.float64(7.890354019420172e-101)}
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(6.302055914703775e-121), 11: np.float64(9.99775588346969e-06), 22: np.float64(6.302055914703775e-121), 0: np.float64(6.302055914703775e-121)}
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(5.079495300645519e-141), 11: np.float64(1.414291028627564e-06), 22: np.float64(5.079495300645519e-141), 0: np.float64(5.079495300645519e-141)}
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(4.1200620740698645e-161), 11: np.float64(1.9810924551184603e-07), 22: np.float64(4.1200620740698645e-161), 0: np.float64(4.1200620740698645e-161)}
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(0.2723036796596198), 3: np.float64(0.26037401984825126), 9: np.float64(0.2296817709313497), 100: np.float64(0.21505729842535443), 22: np.float64(0.007527743711808536), 58: np.float64(0.007527743711808536), 0: np.float64(0.007527743711808536)}
err dic= {1: np.float64(0.054303679659619825), 3: np.float64(0.07937401984825126), 9: np.float64(0.03268177093134969), 100: np.float64(0.006942701574645577), 22: np.float64(0.10547225628819147), 58: np.float64(0.03347225628819146), 0: np.float64(0.020472256288191465)} 

err list= [np.float64(0.054303679659619825), np.float64(0.07937401984825126), np.float64(0.03268177093134969), np.float64(0.006942701574645577), np.float64(0.10547225628819147), np.float64(0.03347225628819146), np.float64(0.020472256288191465)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.30731187784342895), 3: np.float64(0.2811871847856256), 9: np.float64(0.21898440896650206), 100: np.float64(0.1918181994644311), 22: np.float64(0.00023277631333742412), 58: np.float64(0.00023277631333742412), 0: np.float64(0.00023277631333742412)}
err dic= {1: np.float64(0.08931187784342895), 3: np.float64(0.1001871847856256), 9: np.float64(0.021984408966502056), 100: np.float64(0.030181800535568903), 22: np.float64(0.11276722368666257), 58: np.float64(0.04076722368666258), 0: np.float64(0.027767223686662578)} 

err list= [np.float64(0.08931187784342895), np.float64(0.1001871847856256), np.float64(0.021984408966502056), np.float64(0.030181800535568903), np.float64(0.11276722368666257), np.float64(0.04076722368666258), np.float64(0.027767223686662578)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.365594499479859), 3: np.float64(0.3067314403006975), 9: np.float64(0.18580621518668622), 100: np.float64(0.14186777412628385), 22: np.float64(2.3635491213211316e-08), 58: np.float64(2.3635491213211316e-08), 0: np.float64(2.3635491213211316e-08)}
err dic= {1: np.float64(0.147594499479859), 3: np.float64(0.1257314403006975), 9: np.float64(0.01119378481331379), 100: np.float64(0.08013222587371616), 22: np.float64(0.11299997636450879), 58: np.float64(0.04099997636450879), 0: np.float64(0.027999976364508787)} 

err list= [np.float64(0.147594499479859), np.float64(0.1257314403006975), np.float64(0.01119378481331379), np.float64(0.08013222587371616), np.float64(0.11299997636450879), np.float64(0.04099997636450879), np.float64(0.027999976364508787)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5199273620382431), 3: np.float64(0.33916654873196656), 9: np.float64(0.09438635240642483), 100: np.float64(0.04651973682336486), 22: np.float64(1.904838127757517e-20), 58: np.float64(1.904838127757517e-20), 0: np.float64(1.904838127757517e-20)}
err dic= {1: np.float64(0.3019273620382431), 3: np.float64(0.15816654873196656), 9: np.float64(0.10261364759357518), 100: np.float64(0.17548026317663515), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.3019273620382431), np.float64(0.15816654873196656), np.float64(0.10261364759357518), np.float64(0.17548026317663515), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6814823849754578), 3: np.float64(0.29408206868659303), 9: np.float64(0.019892551348217543), 100: np.float64(0.004542994989732106), 22: np.float64(1.1313388636160772e-40), 58: np.float64(1.1313388636160772e-40), 0: np.float64(1.1313388636160772e-40)}
err dic= {1: np.float64(0.4634823849754578), 3: np.float64(0.11308206868659304), 9: np.float64(0.17710744865178246), 100: np.float64(0.2174570050102679), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.4634823849754578), np.float64(0.11308206868659304), np.float64(0.17710744865178246), np.float64(0.2174570050102679), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
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(0.22001307711622542), 9: np.float64(0.003251848726695263), 100: np.float64(0.00034523286490644345), 22: np.float64(6.448676966155327e-61), 58: np.float64(6.448676966155327e-61), 0: np.float64(6.448676966155327e-61)}
err dic= {1: np.float64(0.5583898412921731), 3: np.float64(0.039013077116225425), 9: np.float64(0.19374815127330475), 100: np.float64(0.22165476713509355), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.5583898412921731), np.float64(0.039013077116225425), np.float64(0.19374815127330475), np.float64(0.22165476713509355), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
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(3.781322519873882e-81), 58: np.float64(3.781322519873882e-81), 0: np.float64(3.781322519873882e-81)}
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(2.2865993830247372e-101), 58: np.float64(2.2865993830247372e-101), 0: np.float64(2.2865993830247372e-101)}
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(1.412501768820957e-121), 58: np.float64(1.412501768820957e-121), 0: np.float64(1.412501768820957e-121)}
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(8.842005861801717e-142), 58: np.float64(8.842005861801717e-142), 0: np.float64(8.842005861801717e-142)}
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(5.57950522458187e-162), 58: np.float64(5.57950522458187e-162), 0: np.float64(5.57950522458187e-162)}
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(0.3196485674757058), 6: np.float64(0.32774050948681427), 8: np.float64(0.3117564162247129), 16: np.float64(0.010213626703191874), 83: np.float64(0.010213626703191874), 70: np.float64(0.010213626703191874), 0: np.float64(0.010213626703191874)}
err dic= {7: np.float64(0.11264856747570581), 6: np.float64(0.08174050948681427), 8: np.float64(0.0627564162247129), 16: np.float64(0.13778637329680812), 83: np.float64(0.037786373296808125), 70: np.float64(0.04778637329680813), 0: np.float64(0.03378637329680812)} 

err list= [np.float64(0.11264856747570581), np.float64(0.08174050948681427), np.float64(0.0627564162247129), np.float64(0.13778637329680812), np.float64(0.037786373296808125), np.float64(0.04778637329680813), np.float64(0.03378637329680812)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.3327321268541798), 6: np.float64(0.34979166779751986), 8: np.float64(0.31650458954039995), 16: np.float64(0.00024290395197516974), 83: np.float64(0.00024290395197516974), 70: np.float64(0.00024290395197516974), 0: np.float64(0.00024290395197516974)}
err dic= {7: np.float64(0.1257321268541798), 6: np.float64(0.10379166779751986), 8: np.float64(0.06750458954039995), 16: np.float64(0.1477570960480248), 83: np.float64(0.04775709604802483), 70: np.float64(0.057757096048024835), 0: np.float64(0.04375709604802483)} 

err list= [np.float64(0.1257321268541798), np.float64(0.10379166779751986), np.float64(0.06750458954039995), np.float64(0.1477570960480248), np.float64(0.04775709604802483), np.float64(0.057757096048024835), np.float64(0.04375709604802483)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.3322249613831249), 6: np.float64(0.3671653655794347), 8: np.float64(0.3006095762650032), 16: np.float64(2.4193109413156935e-08), 83: np.float64(2.4193109413156935e-08), 70: np.float64(2.4193109413156935e-08), 0: np.float64(2.4193109413156935e-08)}
err dic= {7: np.float64(0.12522496138312492), 6: np.float64(0.12116536557943469), 8: np.float64(0.051609576265003176), 16: np.float64(0.1479999758068906), 83: np.float64(0.04799997580689059), 70: np.float64(0.05799997580689059), 0: np.float64(0.043999975806890586)} 

err list= [np.float64(0.12522496138312492), np.float64(0.12116536557943469), np.float64(0.051609576265003176), np.float64(0.1479999758068906), np.float64(0.04799997580689059), np.float64(0.05799997580689059), np.float64(0.043999975806890586)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.3264958357998365), 6: np.float64(0.4192289516096974), 8: np.float64(0.2542752125904655), 16: np.float64(2.2647089063808753e-20), 83: np.float64(2.2647089063808753e-20), 70: np.float64(2.2647089063808753e-20), 0: np.float64(2.2647089063808753e-20)}
err dic= {7: np.float64(0.1194958357998365), 6: np.float64(0.17322895160969742), 8: np.float64(0.005275212590465483), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.1194958357998365), np.float64(0.17322895160969742), np.float64(0.005275212590465483), 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  0.5 

learned probs for this beta: {7: np.float64(0.30719588571849854), 6: np.float64(0.5064803910556542), 8: np.float64(0.1863237232258477), 16: np.float64(2.4557138459729578e-40), 83: np.float64(2.4557138459729578e-40), 70: np.float64(2.4557138459729578e-40), 0: np.float64(2.4557138459729578e-40)}
err dic= {7: np.float64(0.10019588571849855), 6: np.float64(0.26048039105565424), 8: np.float64(0.0626762767741523), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.10019588571849855), np.float64(0.26048039105565424), np.float64(0.0626762767741523), 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  0.75 

learned probs for this beta: {7: np.float64(0.27860068919627307), 6: np.float64(0.5897976636568125), 8: np.float64(0.13160164714691433), 16: np.float64(2.9650107843055287e-60), 83: np.float64(2.9650107843055287e-60), 70: np.float64(2.9650107843055287e-60), 0: np.float64(2.9650107843055287e-60)}
err dic= {7: np.float64(0.07160068919627308), 6: np.float64(0.3437976636568125), 8: np.float64(0.11739835285308567), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.07160068919627308), np.float64(0.3437976636568125), np.float64(0.11739835285308567), 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 

learned probs for this beta: {7: np.float64(0.24472847105479775), 6: np.float64(0.6652409557748219), 8: np.float64(0.09003057317038048), 16: np.float64(3.738707695043347e-80), 83: np.float64(3.738707695043347e-80), 70: np.float64(3.738707695043347e-80), 0: np.float64(3.738707695043347e-80)}
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(4.830359968454387e-100), 83: np.float64(4.830359968454387e-100), 70: np.float64(4.830359968454387e-100), 0: np.float64(4.830359968454387e-100)}
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(6.342569099787716e-120), 83: np.float64(6.342569099787716e-120), 70: np.float64(6.342569099787716e-120), 0: np.float64(6.342569099787716e-120)}
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(8.418826798133179e-140), 83: np.float64(8.418826798133179e-140), 70: np.float64(8.418826798133179e-140), 0: np.float64(8.418826798133179e-140)}
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(1.1253421561833064e-159), 83: np.float64(1.1253421561833064e-159), 70: np.float64(1.1253421561833064e-159), 0: np.float64(1.1253421561833064e-159)}
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= [0.07347014 0.0791677  0.08115941 0.08215527 0.08633429 0.09172611
 0.0972742  0.10250857 0.1082488  0.11412633 0.11987623]
mean_std= [0.         0.00569756 0.00543831 0.00501564 0.00948589 0.01484399
 0.01932754 0.02277389 0.02691884 0.03103337 0.03472941]
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
