p= 2.5 num clusters= 1
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 100]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
empirical probabilities from test set: {2: 0.275, 3: 0.247, 4: 0.252, 59: 0.059, 40: 0.072, 84: 0.06, 0: 0.035}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.3356477723353257), 3: np.float64(0.32736059930887246), 4: np.float64(0.3192780373134786), 59: np.float64(0.004428397760581248), 40: np.float64(0.004428397760581248), 84: np.float64(0.004428397760581248), 0: np.float64(0.004428397760581248)}
err dic= {2: np.float64(0.0606477723353257), 3: np.float64(0.08036059930887246), 4: np.float64(0.06727803731347859), 59: np.float64(0.054571602239418746), 40: np.float64(0.06757160223941874), 84: np.float64(0.055571602239418746), 0: np.float64(0.030571602239418755)} 

err list= [np.float64(0.0606477723353257), np.float64(0.08036059930887246), np.float64(0.06727803731347859), np.float64(0.054571602239418746), np.float64(0.06757160223941874), np.float64(0.055571602239418746), np.float64(0.030571602239418755)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.3500925985616544), 3: np.float64(0.33301838105176196), 4: np.float64(0.31677688295602713), 59: np.float64(2.80343576391357e-05), 40: np.float64(2.80343576391357e-05), 84: np.float64(2.80343576391357e-05), 0: np.float64(2.80343576391357e-05)}
err dic= {2: np.float64(0.0750925985616544), 3: np.float64(0.08601838105176196), 4: np.float64(0.06477688295602713), 59: np.float64(0.05897196564236086), 40: np.float64(0.07197196564236086), 84: np.float64(0.05997196564236086), 0: np.float64(0.03497196564236087)} 

err list= [np.float64(0.0750925985616544), np.float64(0.08601838105176196), np.float64(0.06477688295602713), np.float64(0.05897196564236086), np.float64(0.07197196564236086), np.float64(0.05997196564236086), np.float64(0.03497196564236087)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.3671654007190072), 3: np.float64(0.33222499317872495), 4: np.float64(0.30060960503485185), 59: np.float64(2.6685410608024463e-10), 40: np.float64(2.6685410608024463e-10), 84: np.float64(2.6685410608024463e-10), 0: np.float64(2.6685410608024463e-10)}
err dic= {2: np.float64(0.0921654007190072), 3: np.float64(0.08522499317872495), 4: np.float64(0.048609605034851844), 59: np.float64(0.05899999973314589), 40: np.float64(0.07199999973314589), 84: np.float64(0.05999999973314589), 0: np.float64(0.034999999733145895)} 

err list= [np.float64(0.0921654007190072), np.float64(0.08522499317872495), np.float64(0.048609605034851844), np.float64(0.05899999973314589), np.float64(0.07199999973314589), np.float64(0.05999999973314589), np.float64(0.034999999733145895)]
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(2.230428613486859e-25), 40: np.float64(2.230428613486859e-25), 84: np.float64(2.230428613486859e-25), 0: np.float64(2.230428613486859e-25)}
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(1.7467994661268601e-50), 40: np.float64(1.7467994661268601e-50), 84: np.float64(1.7467994661268601e-50), 0: np.float64(1.7467994661268601e-50)}
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(1.542443811411837e-75), 40: np.float64(1.542443811411837e-75), 84: np.float64(1.542443811411837e-75), 0: np.float64(1.542443811411837e-75)}
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(1.4807887376531207e-100), 40: np.float64(1.4807887376531207e-100), 84: np.float64(1.4807887376531207e-100), 0: np.float64(1.4807887376531207e-100)}
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(1.4882438087563197e-125), 40: np.float64(1.4882438087563197e-125), 84: np.float64(1.4882438087563197e-125), 0: np.float64(1.4882438087563197e-125)}
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(1.5336616898211198e-150), 40: np.float64(1.5336616898211198e-150), 84: np.float64(1.5336616898211198e-150), 0: np.float64(1.5336616898211198e-150)}
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(1.603005843943864e-175), 40: np.float64(1.603005843943864e-175), 84: np.float64(1.603005843943864e-175), 0: np.float64(1.603005843943864e-175)}
err dic= {2: np.float64(0.5555845643329679), 3: np.float64(0.10266604488679029), 4: np.float64(0.226918519446178), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

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

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973345), 3: np.float64(0.11731042782619833), 4: np.float64(0.015876239976466765), 59: np.float64(1.6893278496264323e-200), 40: np.float64(1.6893278496264323e-200), 84: np.float64(1.6893278496264323e-200), 0: np.float64(1.6893278496264323e-200)}
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(0.3415530918645319), 4: np.float64(0.3331201159794015), 8: np.float64(0.30696949771409154), 74: np.float64(0.0045893236104942395), 40: np.float64(0.0045893236104942395), 87: np.float64(0.0045893236104942395), 0: np.float64(0.0045893236104942395)}
err dic= {3: np.float64(0.08255309186453191), 4: np.float64(0.0871201159794015), 8: np.float64(0.05096949771409154), 74: np.float64(0.061410676389505765), 40: np.float64(0.07241067638950575), 87: np.float64(0.04241067638950576), 0: np.float64(0.044410676389505764)} 

err list= [np.float64(0.08255309186453191), np.float64(0.0871201159794015), np.float64(0.05096949771409154), np.float64(0.061410676389505765), np.float64(0.07241067638950575), np.float64(0.04241067638950576), np.float64(0.044410676389505764)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.3624121220858227), 4: np.float64(0.3447370743237797), 8: np.float64(0.2927311895408105), 74: np.float64(2.990351239681596e-05), 40: np.float64(2.990351239681596e-05), 87: np.float64(2.990351239681596e-05), 0: np.float64(2.990351239681596e-05)}
err dic= {3: np.float64(0.10341212208582268), 4: np.float64(0.0987370743237797), 8: np.float64(0.036731189540810505), 74: np.float64(0.06597009648760319), 40: np.float64(0.07697009648760318), 87: np.float64(0.04697009648760318), 0: np.float64(0.048970096487603185)} 

err list= [np.float64(0.10341212208582268), np.float64(0.0987370743237797), np.float64(0.036731189540810505), np.float64(0.06597009648760319), np.float64(0.07697009648760318), np.float64(0.04697009648760318), np.float64(0.048970096487603185)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.3912614393664996), 4: np.float64(0.35402799057341666), 8: np.float64(0.2547105688359967), 74: np.float64(3.060219088944294e-10), 40: np.float64(3.060219088944294e-10), 87: np.float64(3.060219088944294e-10), 0: np.float64(3.060219088944294e-10)}
err dic= {3: np.float64(0.1322614393664996), 4: np.float64(0.10802799057341667), 8: np.float64(0.0012894311640033185), 74: np.float64(0.0659999996939781), 40: np.float64(0.0769999996939781), 87: np.float64(0.04699999969397809), 0: np.float64(0.04899999969397809)} 

err list= [np.float64(0.1322614393664996), np.float64(0.10802799057341667), np.float64(0.0012894311640033185), np.float64(0.0659999996939781), np.float64(0.0769999996939781), np.float64(0.04699999969397809), np.float64(0.04899999969397809)]
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(3.2580100057157044e-25), 40: np.float64(3.2580100057157044e-25), 87: np.float64(3.2580100057157044e-25), 0: np.float64(3.2580100057157044e-25)}
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(3.7117541204490405e-50), 40: np.float64(3.7117541204490405e-50), 87: np.float64(3.7117541204490405e-50), 0: np.float64(3.7117541204490405e-50)}
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(4.3571319334156787e-75), 40: np.float64(4.3571319334156787e-75), 87: np.float64(4.3571319334156787e-75), 0: np.float64(4.3571319334156787e-75)}
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(5.277233755658232e-100), 40: np.float64(5.277233755658232e-100), 87: np.float64(5.277233755658232e-100), 0: np.float64(5.277233755658232e-100)}
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(6.565126237804038e-125), 40: np.float64(6.565126237804038e-125), 87: np.float64(6.565126237804038e-125), 0: np.float64(6.565126237804038e-125)}
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(8.346586951983166e-150), 40: np.float64(8.346586951983166e-150), 87: np.float64(8.346586951983166e-150), 0: np.float64(8.346586951983166e-150)}
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(1.0796686226087891e-174), 40: np.float64(1.0796686226087891e-174), 87: np.float64(1.0796686226087891e-174), 0: np.float64(1.0796686226087891e-174)}
err dic= {3: np.float64(0.592818249643065), 4: np.float64(0.0979761836564689), 8: np.float64(0.2558420659865968), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

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

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402411473), 4: np.float64(0.11919751703720469), 8: np.float64(4.534272164780921e-05), 74: np.float64(1.4156054574525095e-199), 40: np.float64(1.4156054574525095e-199), 87: np.float64(1.4156054574525095e-199), 0: np.float64(1.4156054574525095e-199)}
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(0.34827564658002097), 3: np.float64(0.33339076905644993), 9: np.float64(0.3014252650843861), 83: np.float64(0.00422707981978584), 79: np.float64(0.00422707981978584), 70: np.float64(0.00422707981978584), 0: np.float64(0.00422707981978584)}
err dic= {1: np.float64(0.08327564658002096), 3: np.float64(0.08239076905644993), 9: np.float64(0.06642526508438612), 83: np.float64(0.04777292018021416), 79: np.float64(0.06377292018021416), 70: np.float64(0.07677292018021416), 0: np.float64(0.04377292018021416)} 

err list= [np.float64(0.08327564658002096), np.float64(0.08239076905644993), np.float64(0.06642526508438612), np.float64(0.04777292018021416), np.float64(0.06377292018021416), np.float64(0.07677292018021416), np.float64(0.04377292018021416)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3750761429809564), 3: np.float64(0.3438536299044834), 9: np.float64(0.2809713407115961), 83: np.float64(2.4721600741091844e-05), 79: np.float64(2.4721600741091844e-05), 70: np.float64(2.4721600741091844e-05), 0: np.float64(2.4721600741091844e-05)}
err dic= {1: np.float64(0.11007614298095636), 3: np.float64(0.09285362990448343), 9: np.float64(0.04597134071159609), 83: np.float64(0.051975278399258903), 79: np.float64(0.06797527839925892), 70: np.float64(0.08097527839925892), 0: np.float64(0.04797527839925891)} 

err list= [np.float64(0.11007614298095636), np.float64(0.09285362990448343), np.float64(0.04597134071159609), np.float64(0.051975278399258903), np.float64(0.06797527839925892), np.float64(0.08097527839925892), np.float64(0.04797527839925891)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.41653659878053), 3: np.float64(0.3504535280779416), 9: np.float64(0.2330098722391585), 83: np.float64(2.2559261862978403e-10), 79: np.float64(2.2559261862978403e-10), 70: np.float64(2.2559261862978403e-10), 0: np.float64(2.2559261862978403e-10)}
err dic= {1: np.float64(0.15153659878053), 3: np.float64(0.09945352807794161), 9: np.float64(0.0019901277608414814), 83: np.float64(0.05199999977440738), 79: np.float64(0.06799999977440739), 70: np.float64(0.08099999977440739), 0: np.float64(0.04799999977440738)} 

err list= [np.float64(0.15153659878053), np.float64(0.09945352807794161), np.float64(0.0019901277608414814), np.float64(0.05199999977440738), np.float64(0.06799999977440739), np.float64(0.08099999977440739), np.float64(0.04799999977440738)]
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(1.624955828314309e-25), 79: np.float64(1.624955828314309e-25), 70: np.float64(1.624955828314309e-25), 0: np.float64(1.624955828314309e-25)}
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(8.660783099957349e-51), 79: np.float64(8.660783099957349e-51), 70: np.float64(8.660783099957349e-51), 0: np.float64(8.660783099957349e-51)}
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(4.5128178334443866e-76), 79: np.float64(4.5128178334443866e-76), 70: np.float64(4.5128178334443866e-76), 0: np.float64(4.5128178334443866e-76)}
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(2.3960250679161565e-101), 79: np.float64(2.3960250679161565e-101), 70: np.float64(2.3960250679161565e-101), 0: np.float64(2.3960250679161565e-101)}
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(1.3021939368629912e-126), 79: np.float64(1.3021939368629912e-126), 70: np.float64(1.3021939368629912e-126), 0: np.float64(1.3021939368629912e-126)}
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(7.205144470339175e-152), 79: np.float64(7.205144470339175e-152), 70: np.float64(7.205144470339175e-152), 0: np.float64(7.205144470339175e-152)}
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(4.034731051401425e-177), 79: np.float64(4.034731051401425e-177), 70: np.float64(4.034731051401425e-177), 0: np.float64(4.034731051401425e-177)}
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(2.276548918839449e-202), 79: np.float64(2.276548918839449e-202), 70: np.float64(2.276548918839449e-202), 0: np.float64(2.276548918839449e-202)}
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(0.35041831686226493), 4: np.float64(0.32922624954313606), 8: np.float64(0.30334298614139055), 32: np.float64(0.004253111863302237), 27: np.float64(0.004253111863302237), 82: np.float64(0.004253111863302237), 0: np.float64(0.004253111863302237)}
err dic= {1: np.float64(0.12841831686226493), 4: np.float64(0.09922624954313605), 8: np.float64(0.07134298614139054), 32: np.float64(0.09774688813669775), 27: np.float64(0.11574688813669776), 82: np.float64(0.045746888136697764), 0: np.float64(0.03974688813669776)} 

err list= [np.float64(0.12841831686226493), np.float64(0.09922624954313605), np.float64(0.07134298614139054), np.float64(0.09774688813669775), np.float64(0.11574688813669776), np.float64(0.045746888136697764), np.float64(0.03974688813669776)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.37972915495085036), 4: np.float64(0.3354722137825904), 8: np.float64(0.28469863351640895), 32: np.float64(2.4999437537629675e-05), 27: np.float64(2.4999437537629675e-05), 82: np.float64(2.4999437537629675e-05), 0: np.float64(2.4999437537629675e-05)}
err dic= {1: np.float64(0.15772915495085035), 4: np.float64(0.10547221378259039), 8: np.float64(0.05269863351640894), 32: np.float64(0.10197500056246236), 27: np.float64(0.11997500056246237), 82: np.float64(0.049975000562462374), 0: np.float64(0.04397500056246237)} 

err list= [np.float64(0.15772915495085035), np.float64(0.10547221378259039), np.float64(0.05269863351640894), np.float64(0.10197500056246236), np.float64(0.11997500056246237), np.float64(0.049975000562462374), np.float64(0.04397500056246237)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.42674105759094805), 4: np.float64(0.3337256313854407), 8: np.float64(0.23953331009880446), 32: np.float64(2.3120181159877167e-10), 27: np.float64(2.3120181159877167e-10), 82: np.float64(2.3120181159877167e-10), 0: np.float64(2.3120181159877167e-10)}
err dic= {1: np.float64(0.20474105759094804), 4: np.float64(0.10372563138544069), 8: np.float64(0.007533310098804452), 32: np.float64(0.10199999976879819), 27: np.float64(0.11999999976879819), 82: np.float64(0.04999999976879819), 0: np.float64(0.04399999976879818)} 

err list= [np.float64(0.20474105759094804), np.float64(0.10372563138544069), np.float64(0.007533310098804452), np.float64(0.10199999976879819), np.float64(0.11999999976879819), np.float64(0.04999999976879819), np.float64(0.04399999976879818)]
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(1.7507767789140443e-25), 27: np.float64(1.7507767789140443e-25), 82: np.float64(1.7507767789140443e-25), 0: np.float64(1.7507767789140443e-25)}
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(1.0238893835384157e-50), 27: np.float64(1.0238893835384157e-50), 82: np.float64(1.0238893835384157e-50), 0: np.float64(1.0238893835384157e-50)}
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(5.767623729236815e-76), 27: np.float64(5.767623729236815e-76), 82: np.float64(5.767623729236815e-76), 0: np.float64(5.767623729236815e-76)}
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(3.23872776491314e-101), 27: np.float64(3.23872776491314e-101), 82: np.float64(3.23872776491314e-101), 0: np.float64(3.23872776491314e-101)}
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(1.8277928473779416e-126), 27: np.float64(1.8277928473779416e-126), 82: np.float64(1.8277928473779416e-126), 0: np.float64(1.8277928473779416e-126)}
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(1.0364324030508814e-151), 27: np.float64(1.0364324030508814e-151), 82: np.float64(1.0364324030508814e-151), 0: np.float64(1.0364324030508814e-151)}
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(5.895393732885234e-177), 27: np.float64(5.895393732885234e-177), 82: np.float64(5.895393732885234e-177), 0: np.float64(5.895393732885234e-177)}
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(3.3594800730690545e-202), 27: np.float64(3.3594800730690545e-202), 82: np.float64(3.3594800730690545e-202), 0: np.float64(3.3594800730690545e-202)}
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(0.007449277826899224), 4: np.float64(0.49147672993435704), 6: np.float64(0.4712768809311465), 51: np.float64(0.007449277826899224), 82: np.float64(0.007449277826899224), 41: np.float64(0.007449277826899224), 0: np.float64(0.007449277826899224)}
err dic= {9: np.float64(0.21355072217310078), 4: np.float64(0.24647672993435704), 6: np.float64(0.2152768809311465), 51: np.float64(0.07855072217310077), 82: np.float64(0.032550722173100774), 41: np.float64(0.08555072217310078), 0: np.float64(0.05155072217310077)} 

err list= [np.float64(0.21355072217310078), np.float64(0.24647672993435704), np.float64(0.2152768809311465), np.float64(0.07855072217310077), np.float64(0.032550722173100774), np.float64(0.08555072217310078), np.float64(0.05155072217310077)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(2.991702855012438e-05), 4: np.float64(0.5207444873411244), 6: np.float64(0.4791059275161252), 51: np.float64(2.991702855012438e-05), 82: np.float64(2.991702855012438e-05), 41: np.float64(2.991702855012438e-05), 0: np.float64(2.991702855012438e-05)}
err dic= {9: np.float64(0.22097008297144988), 4: np.float64(0.27574448734112444), 6: np.float64(0.22310592751612518), 51: np.float64(0.08597008297144987), 82: np.float64(0.039970082971449876), 41: np.float64(0.09297008297144987), 0: np.float64(0.05897008297144987)} 

err list= [np.float64(0.22097008297144988), np.float64(0.27574448734112444), np.float64(0.22310592751612518), np.float64(0.08597008297144987), np.float64(0.039970082971449876), np.float64(0.09297008297144987), np.float64(0.05897008297144987)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(2.747430349251946e-10), 4: np.float64(0.5415766075389157), 6: np.float64(0.4584233910873693), 51: np.float64(2.747430349251946e-10), 82: np.float64(2.747430349251946e-10), 41: np.float64(2.747430349251946e-10), 0: np.float64(2.747430349251946e-10)}
err dic= {9: np.float64(0.22099999972525697), 4: np.float64(0.2965766075389157), 6: np.float64(0.2024233910873693), 51: np.float64(0.08599999972525696), 82: np.float64(0.03999999972525697), 41: np.float64(0.09299999972525697), 0: np.float64(0.05899999972525696)} 

err list= [np.float64(0.22099999972525697), np.float64(0.2965766075389157), np.float64(0.2024233910873693), np.float64(0.08599999972525696), np.float64(0.03999999972525697), np.float64(0.09299999972525697), np.float64(0.05899999972525696)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(2.208623608178907e-25), 4: np.float64(0.6027772381334338), 6: np.float64(0.3972227618665658), 51: np.float64(2.208623608178907e-25), 82: np.float64(2.208623608178907e-25), 41: np.float64(2.208623608178907e-25), 0: np.float64(2.208623608178907e-25)}
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(1.674673073389341e-50), 4: np.float64(0.6976973366279521), 6: np.float64(0.3023026633720482), 51: np.float64(1.674673073389341e-50), 82: np.float64(1.674673073389341e-50), 41: np.float64(1.674673073389341e-50), 0: np.float64(1.674673073389341e-50)}
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(1.317318932706417e-75), 4: np.float64(0.7790173173345053), 6: np.float64(0.22098268266549476), 51: np.float64(1.317318932706417e-75), 82: np.float64(1.317318932706417e-75), 41: np.float64(1.317318932706417e-75), 0: np.float64(1.317318932706417e-75)}
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(1.0471563459718944e-100), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(1.0471563459718944e-100), 82: np.float64(1.0471563459718944e-100), 41: np.float64(1.0471563459718944e-100), 0: np.float64(1.0471563459718944e-100)}
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(8.402286691527065e-126), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(8.402286691527065e-126), 82: np.float64(8.402286691527065e-126), 41: np.float64(8.402286691527065e-126), 0: np.float64(8.402286691527065e-126)}
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(6.807804147719108e-151), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(6.807804147719108e-151), 82: np.float64(6.807804147719108e-151), 41: np.float64(6.807804147719108e-151), 0: np.float64(6.807804147719108e-151)}
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(5.561264697349003e-176), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(5.561264697349003e-176), 82: np.float64(5.561264697349003e-176), 41: np.float64(5.561264697349003e-176), 0: np.float64(5.561264697349003e-176)}
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(4.570256841590897e-201), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(4.570256841590897e-201), 82: np.float64(4.570256841590897e-201), 41: np.float64(4.570256841590897e-201), 0: np.float64(4.570256841590897e-201)}
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(0.3389310941276566), 9: np.float64(0.31043351107225525), 6: np.float64(0.3305628555973113), 39: np.float64(0.005018134800693949), 80: np.float64(0.005018134800693949), 68: np.float64(0.005018134800693949), 0: np.float64(0.005018134800693949)}
err dic= {5: np.float64(0.0939310941276566), 9: np.float64(0.08243351107225524), 6: np.float64(0.0725628555973113), 39: np.float64(0.09498186519930606), 80: np.float64(0.05798186519930605), 68: np.float64(0.05098186519930605), 0: np.float64(0.044981865199306054)} 

err list= [np.float64(0.0939310941276566), np.float64(0.08243351107225524), np.float64(0.0725628555973113), np.float64(0.09498186519930606), np.float64(0.05798186519930605), np.float64(0.05098186519930605), np.float64(0.044981865199306054)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.3583450576166906), 9: np.float64(0.30063988340897363), 6: np.float64(0.3408683629293998), 39: np.float64(3.667401123399472e-05), 80: np.float64(3.667401123399472e-05), 68: np.float64(3.667401123399472e-05), 0: np.float64(3.667401123399472e-05)}
err dic= {5: np.float64(0.11334505761669061), 9: np.float64(0.07263988340897362), 6: np.float64(0.08286836292939981), 39: np.float64(0.099963325988766), 80: np.float64(0.062963325988766), 68: np.float64(0.05596332598876601), 0: np.float64(0.04996332598876601)} 

err list= [np.float64(0.11334505761669061), np.float64(0.07263988340897362), np.float64(0.08286836292939981), np.float64(0.099963325988766), np.float64(0.062963325988766), np.float64(0.05596332598876601), np.float64(0.04996332598876601)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.38345895851001893), 9: np.float64(0.269573025827093), 6: np.float64(0.3469680139409636), 39: np.float64(4.304812816231224e-10), 80: np.float64(4.304812816231224e-10), 68: np.float64(4.304812816231224e-10), 0: np.float64(4.304812816231224e-10)}
err dic= {5: np.float64(0.13845895851001894), 9: np.float64(0.04157302582709302), 6: np.float64(0.0889680139409636), 39: np.float64(0.09999999956951873), 80: np.float64(0.06299999956951872), 68: np.float64(0.05599999956951872), 0: np.float64(0.04999999956951872)} 

err list= [np.float64(0.13845895851001894), np.float64(0.04157302582709302), np.float64(0.0889680139409636), np.float64(0.09999999956951873), np.float64(0.06299999956951872), np.float64(0.05599999956951872), np.float64(0.04999999956951872)]
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(7.264295202617563e-25), 80: np.float64(7.264295202617563e-25), 68: np.float64(7.264295202617563e-25), 0: np.float64(7.264295202617563e-25)}
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(1.9610520026277316e-49), 80: np.float64(1.9610520026277316e-49), 68: np.float64(1.9610520026277316e-49), 0: np.float64(1.9610520026277316e-49)}
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(5.626992164330583e-74), 80: np.float64(5.626992164330583e-74), 68: np.float64(5.626992164330583e-74), 0: np.float64(5.626992164330583e-74)}
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(1.6692195355964853e-98), 80: np.float64(1.6692195355964853e-98), 68: np.float64(1.6692195355964853e-98), 0: np.float64(1.6692195355964853e-98)}
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(5.066618546612073e-123), 80: np.float64(5.066618546612073e-123), 68: np.float64(5.066618546612073e-123), 0: np.float64(5.066618546612073e-123)}
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(1.563722898279209e-147), 80: np.float64(1.563722898279209e-147), 68: np.float64(1.563722898279209e-147), 0: np.float64(1.563722898279209e-147)}
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(4.8888674402237464e-172), 80: np.float64(4.8888674402237464e-172), 68: np.float64(4.8888674402237464e-172), 0: np.float64(4.8888674402237464e-172)}
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(1.5444356934535026e-196), 80: np.float64(1.5444356934535026e-196), 68: np.float64(1.5444356934535026e-196), 0: np.float64(1.5444356934535026e-196)}
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(0.32519072044729824), 3: np.float64(0.34615631873051367), 8: np.float64(0.3112118406223033), 15: np.float64(0.004360280049971409), 78: np.float64(0.004360280049971409), 97: np.float64(0.004360280049971409), 0: np.float64(0.004360280049971409)}
err dic= {6: np.float64(0.10419072044729824), 3: np.float64(0.11115631873051368), 8: np.float64(0.07321184062230329), 15: np.float64(0.16863971995002858), 78: np.float64(0.05163971995002859), 97: np.float64(0.03463971995002859), 0: np.float64(0.03363971995002859)} 

err list= [np.float64(0.10419072044729824), np.float64(0.11115631873051368), np.float64(0.07321184062230329), np.float64(0.16863971995002858), np.float64(0.05163971995002859), np.float64(0.03463971995002859), np.float64(0.03363971995002859)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.32803340112417784), 3: np.float64(0.37144179906287955), 8: np.float64(0.3004201452791165), 15: np.float64(2.6163633456661298e-05), 78: np.float64(2.6163633456661298e-05), 97: np.float64(2.6163633456661298e-05), 0: np.float64(2.6163633456661298e-05)}
err dic= {6: np.float64(0.10703340112417783), 3: np.float64(0.13644179906287957), 8: np.float64(0.06242014527911649), 15: np.float64(0.17297383636654332), 78: np.float64(0.05597383636654334), 97: np.float64(0.03897383636654334), 0: np.float64(0.03797383636654334)} 

err list= [np.float64(0.10703340112417783), np.float64(0.13644179906287957), np.float64(0.06242014527911649), np.float64(0.17297383636654332), np.float64(0.05597383636654334), np.float64(0.03897383636654334), np.float64(0.03797383636654334)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.32067553292096296), 3: np.float64(0.4106068098483138), 8: np.float64(0.2687176562065452), 15: np.float64(2.5604461929368524e-10), 78: np.float64(2.5604461929368524e-10), 97: np.float64(2.5604461929368524e-10), 0: np.float64(2.5604461929368524e-10)}
err dic= {6: np.float64(0.09967553292096296), 3: np.float64(0.17560680984831384), 8: np.float64(0.030717656206545207), 15: np.float64(0.17299999974395536), 78: np.float64(0.055999999743955385), 97: np.float64(0.038999999743955384), 0: np.float64(0.03799999974395538)} 

err list= [np.float64(0.09967553292096296), np.float64(0.17560680984831384), np.float64(0.030717656206545207), np.float64(0.17299999974395536), np.float64(0.055999999743955385), np.float64(0.038999999743955384), np.float64(0.03799999974395538)]
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(2.438008598507549e-25), 78: np.float64(2.438008598507549e-25), 97: np.float64(2.438008598507549e-25), 0: np.float64(2.438008598507549e-25)}
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(2.358390666720802e-50), 78: np.float64(2.358390666720802e-50), 97: np.float64(2.358390666720802e-50), 0: np.float64(2.358390666720802e-50)}
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(2.2921686970307835e-75), 78: np.float64(2.2921686970307835e-75), 97: np.float64(2.2921686970307835e-75), 0: np.float64(2.2921686970307835e-75)}
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(2.2099160497851368e-100), 78: np.float64(2.2099160497851368e-100), 97: np.float64(2.2099160497851368e-100), 0: np.float64(2.2099160497851368e-100)}
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(2.1163706666973495e-125), 78: np.float64(2.1163706666973495e-125), 97: np.float64(2.1163706666973495e-125), 0: np.float64(2.1163706666973495e-125)}
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(2.016628248430249e-150), 78: np.float64(2.016628248430249e-150), 97: np.float64(2.016628248430249e-150), 0: np.float64(2.016628248430249e-150)}
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(1.9143534789583893e-175), 78: np.float64(1.9143534789583893e-175), 97: np.float64(1.9143534789583893e-175), 0: np.float64(1.9143534789583893e-175)}
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(1.812284420993627e-200), 78: np.float64(1.812284420993627e-200), 97: np.float64(1.812284420993627e-200), 0: np.float64(1.812284420993627e-200)}
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(0.23633043529111758), 2: np.float64(0.26912991111697493), 4: np.float64(0.2573319793977868), 95: np.float64(0.003778252900890362), 11: np.float64(0.2258729154914486), 22: np.float64(0.003778252900890362), 0: np.float64(0.003778252900890362)}
err dic= {8: np.float64(0.0013304352911175932), 2: np.float64(0.06712991111697492), 4: np.float64(0.060331979397786784), 95: np.float64(0.03822174709910964), 11: np.float64(0.0598729154914486), 22: np.float64(0.13322174709910964), 0: np.float64(0.01722174709910964)} 

err list= [np.float64(0.0013304352911175932), np.float64(0.06712991111697492), np.float64(0.060331979397786784), np.float64(0.03822174709910964), np.float64(0.0598729154914486), np.float64(0.13322174709910964), np.float64(0.01722174709910964)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.2275360633243021), 2: np.float64(0.29488148069847325), 4: np.float64(0.2697295992480827), 95: np.float64(2.7868440580286916e-05), 11: np.float64(0.2077692514074011), 22: np.float64(2.7868440580286916e-05), 0: np.float64(2.7868440580286916e-05)}
err dic= {8: np.float64(0.007463936675697891), 2: np.float64(0.09288148069847324), 4: np.float64(0.0727295992480827), 95: np.float64(0.041972131559419715), 11: np.float64(0.04176925140740109), 22: np.float64(0.13697213155941973), 0: np.float64(0.020972131559419713)} 

err list= [np.float64(0.007463936675697891), np.float64(0.09288148069847324), np.float64(0.0727295992480827), np.float64(0.041972131559419715), np.float64(0.04176925140740109), np.float64(0.13697213155941973), np.float64(0.020972131559419713)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.2033991444452379), 2: np.float64(0.34129604434923927), 4: np.float64(0.2860132474163723), 95: np.float64(3.0669144219134703e-10), 11: np.float64(0.169291562869077), 22: np.float64(3.0669144219134703e-10), 0: np.float64(3.0669144219134703e-10)}
err dic= {8: np.float64(0.03160085555476208), 2: np.float64(0.13929604434923926), 4: np.float64(0.08901324741637229), 95: np.float64(0.04199999969330856), 11: np.float64(0.0032915628690770027), 22: np.float64(0.13699999969330856), 0: np.float64(0.020999999693308558)} 

err list= [np.float64(0.03160085555476208), np.float64(0.13929604434923926), np.float64(0.08901324741637229), np.float64(0.04199999969330856), np.float64(0.0032915628690770027), np.float64(0.13699999969330856), np.float64(0.020999999693308558)]
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(3.971462217949508e-25), 11: np.float64(0.0816242751672552), 22: np.float64(3.971462217949508e-25), 0: np.float64(3.971462217949508e-25)}
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(5.924463255649898e-50), 11: np.float64(0.017759613108311294), 22: np.float64(5.924463255649898e-50), 0: np.float64(5.924463255649898e-50)}
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(8.691987879708063e-75), 11: np.float64(0.003061487235188769), 22: np.float64(8.691987879708063e-75), 0: np.float64(8.691987879708063e-75)}
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(1.2824453586043526e-99), 11: np.float64(0.00047336280779999217), 22: np.float64(1.2824453586043526e-99), 0: np.float64(1.2824453586043526e-99)}
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(1.9157288334307736e-124), 11: np.float64(6.965386583462914e-05), 22: np.float64(1.9157288334307736e-124), 0: np.float64(1.9157288334307736e-124)}
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(2.8957916262184007e-149), 11: np.float64(9.99775588346969e-06), 22: np.float64(2.8957916262184007e-149), 0: np.float64(2.8957916262184007e-149)}
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(4.417261682215284e-174), 11: np.float64(1.414291028627564e-06), 22: np.float64(4.417261682215284e-174), 0: np.float64(4.417261682215284e-174)}
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(6.780845258272723e-199), 11: np.float64(1.9810924551184603e-07), 22: np.float64(6.780845258272723e-199), 0: np.float64(6.780845258272723e-199)}
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(0.27537846141707684), 3: np.float64(0.2633279481631173), 9: np.float64(0.232348356676847), 100: np.float64(0.2175767953920038), 22: np.float64(0.003789479450317876), 58: np.float64(0.003789479450317876), 0: np.float64(0.003789479450317876)}
err dic= {1: np.float64(0.05737846141707684), 3: np.float64(0.08232794816311728), 9: np.float64(0.03534835667684699), 100: np.float64(0.004423204607996195), 22: np.float64(0.10921052054968212), 58: np.float64(0.03721052054968212), 0: np.float64(0.024210520549682125)} 

err list= [np.float64(0.05737846141707684), np.float64(0.08232794816311728), np.float64(0.03534835667684699), np.float64(0.004423204607996195), np.float64(0.10921052054968212), np.float64(0.03721052054968212), np.float64(0.024210520549682125)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3074965045253809), 3: np.float64(0.28135744444328076), 9: np.float64(0.21912192327169389), 100: np.float64(0.1919402694412047), 22: np.float64(2.7952772813268396e-05), 58: np.float64(2.7952772813268396e-05), 0: np.float64(2.7952772813268396e-05)}
err dic= {1: np.float64(0.08949650452538091), 3: np.float64(0.10035744444328076), 9: np.float64(0.022121923271693877), 100: np.float64(0.030059730558795295), 22: np.float64(0.11297204722718673), 58: np.float64(0.04097204722718673), 0: np.float64(0.02797204722718673)} 

err list= [np.float64(0.08949650452538091), np.float64(0.10035744444328076), np.float64(0.022121923271693877), np.float64(0.030059730558795295), np.float64(0.11297204722718673), np.float64(0.04097204722718673), np.float64(0.02797204722718673)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3655945240117551), 3: np.float64(0.30673146125613115), 9: np.float64(0.18580622892269136), 100: np.float64(0.1418677848942384), 22: np.float64(3.050614230364208e-10), 58: np.float64(3.050614230364208e-10), 0: np.float64(3.050614230364208e-10)}
err dic= {1: np.float64(0.14759452401175507), 3: np.float64(0.12573146125613116), 9: np.float64(0.01119377107730865), 100: np.float64(0.0801322151057616), 22: np.float64(0.11299999969493858), 58: np.float64(0.04099999969493858), 0: np.float64(0.027999999694938577)} 

err list= [np.float64(0.14759452401175507), np.float64(0.12573146125613116), np.float64(0.01119377107730865), np.float64(0.0801322151057616), np.float64(0.11299999969493858), np.float64(0.04099999969493858), np.float64(0.027999999694938577)]
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(3.605002620460541e-25), 58: np.float64(3.605002620460541e-25), 0: np.float64(3.605002620460541e-25)}
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(4.05217063320581e-50), 58: np.float64(4.05217063320581e-50), 0: np.float64(4.05217063320581e-50)}
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(4.3713255391847515e-75), 58: np.float64(4.3713255391847515e-75), 0: np.float64(4.3713255391847515e-75)}
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(4.851027743173971e-100), 58: np.float64(4.851027743173971e-100), 0: np.float64(4.851027743173971e-100)}
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(5.551720946593737e-125), 58: np.float64(5.551720946593737e-125), 0: np.float64(5.551720946593737e-125)}
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(6.49043875448171e-150), 58: np.float64(6.49043875448171e-150), 0: np.float64(6.49043875448171e-150)}
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(7.689239063238449e-175), 58: np.float64(7.689239063238449e-175), 0: np.float64(7.689239063238449e-175)}
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(9.182813478400112e-200), 58: np.float64(9.182813478400112e-200), 0: np.float64(9.182813478400112e-200)}
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(0.3273048087637322), 6: np.float64(0.3355905694458112), 8: np.float64(0.319223624241806), 16: np.float64(0.004470249387162786), 83: np.float64(0.004470249387162786), 70: np.float64(0.004470249387162786), 0: np.float64(0.004470249387162786)}
err dic= {7: np.float64(0.1203048087637322), 6: np.float64(0.08959056944581123), 8: np.float64(0.070223624241806), 16: np.float64(0.1435297506128372), 83: np.float64(0.04352975061283722), 70: np.float64(0.05352975061283722), 0: np.float64(0.039529750612837214)} 

err list= [np.float64(0.1203048087637322), np.float64(0.08959056944581123), np.float64(0.070223624241806), np.float64(0.1435297506128372), np.float64(0.04352975061283722), np.float64(0.05352975061283722), np.float64(0.039529750612837214)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.33301928389592045), 6: np.float64(0.3500935476956226), 8: np.float64(0.31677774176795626), 16: np.float64(2.7356660125234098e-05), 83: np.float64(2.7356660125234098e-05), 70: np.float64(2.7356660125234098e-05), 0: np.float64(2.7356660125234098e-05)}
err dic= {7: np.float64(0.12601928389592046), 6: np.float64(0.10409354769562262), 8: np.float64(0.06777774176795626), 16: np.float64(0.14797264333987475), 83: np.float64(0.04797264333987477), 70: np.float64(0.05797264333987477), 0: np.float64(0.043972643339874766)} 

err list= [np.float64(0.12601928389592046), np.float64(0.10409354769562262), np.float64(0.06777774176795626), np.float64(0.14797264333987475), np.float64(0.04797264333987477), np.float64(0.05797264333987477), np.float64(0.043972643339874766)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.33222499315787685), 6: np.float64(0.3671654006959666), 8: np.float64(0.30060960501598766), 16: np.float64(2.825423204349692e-10), 83: np.float64(2.825423204349692e-10), 70: np.float64(2.825423204349692e-10), 0: np.float64(2.825423204349692e-10)}
err dic= {7: np.float64(0.12522499315787686), 6: np.float64(0.1211654006959666), 8: np.float64(0.05160960501598766), 16: np.float64(0.14799999971745767), 83: np.float64(0.04799999971745768), 70: np.float64(0.05799999971745768), 0: np.float64(0.043999999717457675)} 

err list= [np.float64(0.12522499315787686), np.float64(0.1211654006959666), np.float64(0.05160960501598766), np.float64(0.14799999971745767), np.float64(0.04799999971745768), np.float64(0.05799999971745768), np.float64(0.043999999717457675)]
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(3.337999573578132e-25), 83: np.float64(3.337999573578132e-25), 70: np.float64(3.337999573578132e-25), 0: np.float64(3.337999573578132e-25)}
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(5.334890828118136e-50), 83: np.float64(5.334890828118136e-50), 70: np.float64(5.334890828118136e-50), 0: np.float64(5.334890828118136e-50)}
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(9.493971939833044e-75), 83: np.float64(9.493971939833044e-75), 70: np.float64(9.493971939833044e-75), 0: np.float64(9.493971939833044e-75)}
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(1.7644813288375407e-99), 83: np.float64(1.7644813288375407e-99), 70: np.float64(1.7644813288375407e-99), 0: np.float64(1.7644813288375407e-99)}
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(3.3600747621748224e-124), 83: np.float64(3.3600747621748224e-124), 70: np.float64(3.3600747621748224e-124), 0: np.float64(3.3600747621748224e-124)}
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(6.502921932580358e-149), 83: np.float64(6.502921932580358e-149), 70: np.float64(6.502921932580358e-149), 0: np.float64(6.502921932580358e-149)}
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(1.2722392695380162e-173), 83: np.float64(1.2722392695380162e-173), 70: np.float64(1.2722392695380162e-173), 0: np.float64(1.2722392695380162e-173)}
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(2.506546113235353e-198), 83: np.float64(2.506546113235353e-198), 70: np.float64(2.506546113235353e-198), 0: np.float64(2.506546113235353e-198)}
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= [0.080034   0.0825728  0.08342948 0.08385783 0.08769633 0.09286115
 0.09824709 0.10335985 0.10900549 0.11480736 0.12049534]
mean_std= [0.         0.0025388  0.002401   0.00220772 0.0079269  0.01362864
 0.01825528 0.02178488 0.02601606 0.03020111 0.03395173]
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
