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

beta is  0.025 

learned probs for this beta: {2: np.float64(0.2695985664783523), 3: np.float64(0.26294215415496563), 4: np.float64(0.2564500892374193), 59: np.float64(0.052752297532317124), 40: np.float64(0.052752297532317124), 84: np.float64(0.052752297532317124), 0: np.float64(0.052752297532317124)}
err dic= {2: np.float64(0.005401433521647736), 3: np.float64(0.015942154154965638), 4: np.float64(0.004450089237419297), 59: np.float64(0.006247702467682872), 40: np.float64(0.01924770246768287), 84: np.float64(0.007247702467682873), 0: np.float64(0.01775229753231712)} 

err list= [np.float64(0.005401433521647736), np.float64(0.015942154154965638), np.float64(0.004450089237419297), np.float64(0.006247702467682872), np.float64(0.01924770246768287), np.float64(0.007247702467682873), np.float64(0.01775229753231712)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.33983705635218264), 3: np.float64(0.3232630075379036), 4: np.float64(0.30749728462264997), 59: np.float64(0.007350662871816055), 40: np.float64(0.007350662871816055), 84: np.float64(0.007350662871816055), 0: np.float64(0.007350662871816055)}
err dic= {2: np.float64(0.06483705635218262), 3: np.float64(0.0762630075379036), 4: np.float64(0.05549728462264997), 59: np.float64(0.05164933712818394), 40: np.float64(0.06464933712818394), 84: np.float64(0.05264933712818394), 0: np.float64(0.02764933712818395)} 

err list= [np.float64(0.06483705635218262), np.float64(0.0762630075379036), np.float64(0.05549728462264997), np.float64(0.05164933712818394), np.float64(0.06464933712818394), np.float64(0.05264933712818394), np.float64(0.02764933712818395)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.36696253983656674), 3: np.float64(0.33204143706163697), 4: np.float64(0.3004435165918013), 59: np.float64(0.00013812662749883707), 40: np.float64(0.00013812662749883707), 84: np.float64(0.00013812662749883707), 0: np.float64(0.00013812662749883707)}
err dic= {2: np.float64(0.09196253983656671), 3: np.float64(0.08504143706163697), 4: np.float64(0.048443516591801294), 59: np.float64(0.05886187337250116), 40: np.float64(0.07186187337250116), 84: np.float64(0.05986187337250116), 0: np.float64(0.03486187337250116)} 

err list= [np.float64(0.09196253983656671), np.float64(0.08504143706163697), np.float64(0.048443516591801294), np.float64(0.05886187337250116), np.float64(0.07186187337250116), np.float64(0.05986187337250116), np.float64(0.03486187337250116)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.41922895152941575), 3: np.float64(0.326495835737313), 4: np.float64(0.2542752125417721), 59: np.float64(4.7874716010693255e-11), 40: np.float64(4.7874716010693255e-11), 84: np.float64(4.7874716010693255e-11), 0: np.float64(4.7874716010693255e-11)}
err dic= {2: np.float64(0.14422895152941573), 3: np.float64(0.079495835737313), 4: np.float64(0.002275212541772098), 59: np.float64(0.05899999995212528), 40: np.float64(0.07199999995212528), 84: np.float64(0.05999999995212528), 0: np.float64(0.034999999952125285)} 

err list= [np.float64(0.14422895152941573), np.float64(0.079495835737313), np.float64(0.002275212541772098), np.float64(0.05899999995212528), np.float64(0.07199999995212528), np.float64(0.05999999995212528), np.float64(0.034999999952125285)]
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(8.047831153196705e-22), 40: np.float64(8.047831153196705e-22), 84: np.float64(8.047831153196705e-22), 0: np.float64(8.047831153196705e-22)}
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(1.5253273616940724e-32), 40: np.float64(1.5253273616940724e-32), 84: np.float64(1.5253273616940724e-32), 0: np.float64(1.5253273616940724e-32)}
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(3.1431471530142335e-43), 40: np.float64(3.1431471530142335e-43), 84: np.float64(3.1431471530142335e-43), 0: np.float64(3.1431471530142335e-43)}
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(6.780529324617289e-54), 40: np.float64(6.780529324617289e-54), 84: np.float64(6.780529324617289e-54), 0: np.float64(6.780529324617289e-54)}
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(1.4998125594730086e-64), 40: np.float64(1.4998125594730086e-64), 84: np.float64(1.4998125594730086e-64), 0: np.float64(1.4998125594730086e-64)}
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(3.364809064377156e-75), 40: np.float64(3.364809064377156e-75), 84: np.float64(3.364809064377156e-75), 0: np.float64(3.364809064377156e-75)}
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(7.611270629911392e-86), 40: np.float64(7.611270629911392e-86), 84: np.float64(7.611270629911392e-86), 0: np.float64(7.611270629911392e-86)}
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(0.2712408791933575), 4: np.float64(0.2645439180245611), 8: np.float64(0.24255100222700177), 74: np.float64(0.055416050138770795), 40: np.float64(0.055416050138770795), 87: np.float64(0.055416050138770795), 0: np.float64(0.055416050138770795)}
err dic= {3: np.float64(0.012240879193357479), 4: np.float64(0.018543918024561123), 8: np.float64(0.013448997772998239), 74: np.float64(0.010583949861229208), 40: np.float64(0.021583949861229204), 87: np.float64(0.008416050138770795), 0: np.float64(0.006416050138770793)} 

err list= [np.float64(0.012240879193357479), np.float64(0.018543918024561123), np.float64(0.013448997772998239), np.float64(0.010583949861229208), np.float64(0.021583949861229204), np.float64(0.008416050138770795), np.float64(0.006416050138770793)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.3509332580271786), 4: np.float64(0.3338180410713531), 8: np.float64(0.28313689974707096), 74: np.float64(0.008027950288599593), 40: np.float64(0.008027950288599593), 87: np.float64(0.008027950288599593), 0: np.float64(0.008027950288599593)}
err dic= {3: np.float64(0.09193325802717861), 4: np.float64(0.0878180410713531), 8: np.float64(0.027136899747070953), 74: np.float64(0.05797204971140041), 40: np.float64(0.0689720497114004), 87: np.float64(0.038972049711400406), 0: np.float64(0.04097204971140041)} 

err list= [np.float64(0.09193325802717861), np.float64(0.0878180410713531), np.float64(0.027136899747070953), np.float64(0.05797204971140041), np.float64(0.0689720497114004), np.float64(0.038972049711400406), np.float64(0.04097204971140041)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.39101686325335944), 4: np.float64(0.35380668895468964), 8: np.float64(0.2545428065885417), 74: np.float64(0.00015841030085242977), 40: np.float64(0.00015841030085242977), 87: np.float64(0.00015841030085242977), 0: np.float64(0.00015841030085242977)}
err dic= {3: np.float64(0.13201686325335943), 4: np.float64(0.10780668895468964), 8: np.float64(0.0014571934114582796), 74: np.float64(0.06584158969914758), 40: np.float64(0.07684158969914757), 87: np.float64(0.04684158969914757), 0: np.float64(0.04884158969914757)} 

err list= [np.float64(0.13201686325335943), np.float64(0.10780668895468964), np.float64(0.0014571934114582796), np.float64(0.06584158969914758), np.float64(0.07684158969914757), np.float64(0.04684158969914757), np.float64(0.04884158969914757)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.47291907811402145), 4: np.float64(0.3683097483646068), 8: np.float64(0.15877117324164686), 74: np.float64(6.99310898695858e-11), 40: np.float64(6.99310898695858e-11), 87: np.float64(6.99310898695858e-11), 0: np.float64(6.99310898695858e-11)}
err dic= {3: np.float64(0.21391907811402144), 4: np.float64(0.12230974836460679), 8: np.float64(0.09722882675835315), 74: np.float64(0.06599999993006891), 40: np.float64(0.07699999993006891), 87: np.float64(0.04699999993006891), 0: np.float64(0.04899999993006891)} 

err list= [np.float64(0.21391907811402144), np.float64(0.12230974836460679), np.float64(0.09722882675835315), np.float64(0.06599999993006891), np.float64(0.07699999993006891), np.float64(0.04699999993006891), np.float64(0.04899999993006891)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5841457846018505), 4: np.float64(0.3543023281029142), 8: np.float64(0.06155188729523564), 74: np.float64(1.7100743973656916e-21), 40: np.float64(1.7100743973656916e-21), 87: np.float64(1.7100743973656916e-21), 0: np.float64(1.7100743973656916e-21)}
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(4.3087809794942437e-32), 40: np.float64(4.3087809794942437e-32), 87: np.float64(4.3087809794942437e-32), 0: np.float64(4.3087809794942437e-32)}
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(1.120154538801832e-42), 40: np.float64(1.120154538801832e-42), 87: np.float64(1.120154538801832e-42), 0: np.float64(1.120154538801832e-42)}
err dic= {3: np.float64(0.46739549573208805), 4: np.float64(0.02122596903937335), 8: np.float64(0.24962146477146127), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

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

beta is  1.25 

learned probs for this beta: {3: np.float64(0.775832220546095), 4: np.float64(0.22227965274514916), 8: np.float64(0.001888126708755253), 74: np.float64(2.9911114505118967e-53), 40: np.float64(2.9911114505118967e-53), 87: np.float64(2.9911114505118967e-53), 0: np.float64(2.9911114505118967e-53)}
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(8.162371155517336e-64), 40: np.float64(8.162371155517336e-64), 87: np.float64(8.162371155517336e-64), 0: np.float64(8.162371155517336e-64)}
err dic= {3: np.float64(0.558126200312965), 4: np.float64(0.06367450006269018), 8: np.float64(0.25545170025027525), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

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

beta is  1.75 

learned probs for this beta: {3: np.float64(0.851818249643065), 4: np.float64(0.1480238163435311), 8: np.float64(0.00015793401340318878), 74: np.float64(2.2662916555186763e-74), 40: np.float64(2.2662916555186763e-74), 87: np.float64(2.2662916555186763e-74), 0: np.float64(2.2662916555186763e-74)}
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(6.378013743296297e-85), 40: np.float64(6.378013743296297e-85), 87: np.float64(6.378013743296297e-85), 0: np.float64(6.378013743296297e-85)}
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(0.27473302731420807), 3: np.float64(0.26252493676221766), 9: np.float64(0.23567914621988803), 83: np.float64(0.056765722425922045), 79: np.float64(0.056765722425922045), 70: np.float64(0.056765722425922045), 0: np.float64(0.056765722425922045)}
err dic= {1: np.float64(0.009733027314208054), 3: np.float64(0.011524936762217663), 9: np.float64(0.0006791462198880438), 83: np.float64(0.004765722425922048), 79: np.float64(0.01123427757407796), 70: np.float64(0.024234277574077957), 0: np.float64(0.008765722425922044)} 

err list= [np.float64(0.009733027314208054), np.float64(0.011524936762217663), np.float64(0.0006791462198880438), np.float64(0.004765722425922048), np.float64(0.01123427757407796), np.float64(0.024234277574077957), np.float64(0.008765722425922044)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.36392241230255273), 3: np.float64(0.3335071937123231), 9: np.float64(0.2721139653569471), 83: np.float64(0.007614107157044179), 79: np.float64(0.007614107157044179), 70: np.float64(0.007614107157044179), 0: np.float64(0.007614107157044179)}
err dic= {1: np.float64(0.09892241230255272), 3: np.float64(0.08250719371232312), 9: np.float64(0.03711396535694711), 83: np.float64(0.04438589284295582), 79: np.float64(0.06038589284295583), 70: np.float64(0.07338589284295582), 0: np.float64(0.04038589284295582)} 

err list= [np.float64(0.09892241230255272), np.float64(0.08250719371232312), np.float64(0.03711396535694711), np.float64(0.04438589284295582), np.float64(0.06038589284295583), np.float64(0.07338589284295582), np.float64(0.04038589284295582)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.41631550021639097), 3: np.float64(0.3502639457240046), 9: np.float64(0.23287483388232427), 83: np.float64(0.00013643004432023538), 79: np.float64(0.00013643004432023538), 70: np.float64(0.00013643004432023538), 0: np.float64(0.00013643004432023538)}
err dic= {1: np.float64(0.15131550021639095), 3: np.float64(0.0992639457240046), 9: np.float64(0.002125166117675714), 83: np.float64(0.05186356995567976), 79: np.float64(0.06786356995567977), 70: np.float64(0.08086356995567977), 0: np.float64(0.047863569955679766)} 

err list= [np.float64(0.15131550021639095), np.float64(0.0992639457240046), np.float64(0.002125166117675714), np.float64(0.05186356995567976), np.float64(0.06786356995567977), np.float64(0.08086356995567977), np.float64(0.047863569955679766)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5316600099796782), 3: np.float64(0.34739957328829946), 9: np.float64(0.1209404165290293), 83: np.float64(5.0748110650822514e-11), 79: np.float64(5.0748110650822514e-11), 70: np.float64(5.0748110650822514e-11), 0: np.float64(5.0748110650822514e-11)}
err dic= {1: np.float64(0.2666600099796782), 3: np.float64(0.09639957328829946), 9: np.float64(0.11405958347097069), 83: np.float64(0.051999999949251884), 79: np.float64(0.06799999994925189), 70: np.float64(0.08099999994925189), 0: np.float64(0.04799999994925189)} 

err list= [np.float64(0.2666600099796782), np.float64(0.09639957328829946), np.float64(0.11405958347097069), np.float64(0.051999999949251884), np.float64(0.06799999994925189), np.float64(0.08099999994925189), np.float64(0.04799999994925189)]
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(8.447220470930103e-22), 79: np.float64(8.447220470930103e-22), 70: np.float64(8.447220470930103e-22), 0: np.float64(8.447220470930103e-22)}
err dic= {1: np.float64(0.41180772718138936), 3: np.float64(0.04076229833973133), 9: np.float64(0.20357002552112036), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.41180772718138936), np.float64(0.04076229833973133), np.float64(0.20357002552112036), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.774105702190221), 3: np.float64(0.2191786384934047), 9: np.float64(0.006715659316374057), 83: np.float64(1.3746204593406542e-32), 79: np.float64(1.3746204593406542e-32), 70: np.float64(1.3746204593406542e-32), 0: np.float64(1.3746204593406542e-32)}
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(2.2793168000147057e-43), 79: np.float64(2.2793168000147057e-43), 70: np.float64(2.2793168000147057e-43), 0: np.float64(2.2793168000147057e-43)}
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(3.868720337307535e-54), 79: np.float64(3.868720337307535e-54), 70: np.float64(3.868720337307535e-54), 0: np.float64(3.868720337307535e-54)}
err dic= {1: np.float64(0.6281967343909478), 3: np.float64(0.14444174658875236), 9: np.float64(0.2347549878021958), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

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

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707240606471), 3: np.float64(0.07108431987050234), 9: np.float64(4.495606885052531e-05), 83: np.float64(6.685173675981478e-65), 79: np.float64(6.685173675981478e-65), 70: np.float64(6.685173675981478e-65), 0: np.float64(6.685173675981478e-65)}
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(1.1691303246837086e-75), 79: np.float64(1.1691303246837086e-75), 70: np.float64(1.1691303246837086e-75), 0: np.float64(1.1691303246837086e-75)}
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(2.0601728290322915e-86), 79: np.float64(2.0601728290322915e-86), 70: np.float64(2.0601728290322915e-86), 0: np.float64(2.0601728290322915e-86)}
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(0.2759392113105598), 4: np.float64(0.2583245668320745), 8: np.float64(0.23674367792400353), 32: np.float64(0.057248135983340775), 27: np.float64(0.057248135983340775), 82: np.float64(0.057248135983340775), 0: np.float64(0.057248135983340775)}
err dic= {1: np.float64(0.053939211310559815), 4: np.float64(0.028324566832074488), 8: np.float64(0.004743677924003514), 32: np.float64(0.04475186401665922), 27: np.float64(0.06275186401665922), 82: np.float64(0.007248135983340773), 0: np.float64(0.013248135983340778)} 

err list= [np.float64(0.053939211310559815), np.float64(0.028324566832074488), np.float64(0.004743677924003514), np.float64(0.04475186401665922), np.float64(0.06275186401665922), np.float64(0.007248135983340773), np.float64(0.013248135983340778)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3683051912870214), 4: np.float64(0.3251379466507342), 8: np.float64(0.2756151058534395), 32: np.float64(0.007735439052201083), 27: np.float64(0.007735439052201083), 82: np.float64(0.007735439052201083), 0: np.float64(0.007735439052201083)}
err dic= {1: np.float64(0.14630519128702138), 4: np.float64(0.09513794665073419), 8: np.float64(0.0436151058534395), 32: np.float64(0.0942645609477989), 27: np.float64(0.11226456094779891), 82: np.float64(0.04226456094779892), 0: np.float64(0.03626456094779892)} 

err list= [np.float64(0.14630519128702138), np.float64(0.09513794665073419), np.float64(0.0436151058534395), np.float64(0.0942645609477989), np.float64(0.11226456094779891), np.float64(0.04226456094779892), np.float64(0.03626456094779892)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.4265104430561246), 4: np.float64(0.3335383865119005), 8: np.float64(0.23939187533866146), 32: np.float64(0.00013982377332850444), 27: np.float64(0.00013982377332850444), 82: np.float64(0.00013982377332850444), 0: np.float64(0.00013982377332850444)}
err dic= {1: np.float64(0.20451044305612462), 4: np.float64(0.10353838651190048), 8: np.float64(0.007391875338661452), 32: np.float64(0.10186017622667148), 27: np.float64(0.11986017622667149), 82: np.float64(0.0498601762266715), 0: np.float64(0.043860176226671495)} 

err list= [np.float64(0.20451044305612462), np.float64(0.10353838651190048), np.float64(0.007391875338661452), np.float64(0.10186017622667148), np.float64(0.11986017622667149), np.float64(0.0498601762266715), np.float64(0.043860176226671495)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5619787292976779), 4: np.float64(0.30746143024828915), 8: np.float64(0.13055984023532194), 32: np.float64(5.467755624877417e-11), 27: np.float64(5.467755624877417e-11), 82: np.float64(5.467755624877417e-11), 0: np.float64(5.467755624877417e-11)}
err dic= {1: np.float64(0.3399787292976779), 4: np.float64(0.07746143024828914), 8: np.float64(0.10144015976467807), 32: np.float64(0.10199999994532244), 27: np.float64(0.11999999994532244), 82: np.float64(0.04999999994532245), 0: np.float64(0.04399999994532244)} 

err list= [np.float64(0.3399787292976779), np.float64(0.07746143024828914), np.float64(0.10144015976467807), np.float64(0.10199999994532244), np.float64(0.11999999994532244), np.float64(0.04999999994532245), np.float64(0.04399999994532244)]
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(9.986417233605934e-22), 27: np.float64(9.986417233605934e-22), 82: np.float64(9.986417233605934e-22), 0: np.float64(9.986417233605934e-22)}
err dic= {1: np.float64(0.5163008689607047), 4: np.float64(0.00534327038621174), 8: np.float64(0.19495759857449255), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.5163008689607047), np.float64(0.00534327038621174), np.float64(0.19495759857449255), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8494867469393008), 4: np.float64(0.14196251324014011), 8: np.float64(0.008550739820558834), 32: np.float64(1.7568388250088835e-32), 27: np.float64(1.7568388250088835e-32), 82: np.float64(1.7568388250088835e-32), 0: np.float64(1.7568388250088835e-32)}
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(3.080972191856432e-43), 27: np.float64(3.080972191856432e-43), 82: np.float64(3.080972191856432e-43), 0: np.float64(3.080972191856432e-43)}
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(5.430235206033127e-54), 27: np.float64(5.430235206033127e-54), 82: np.float64(5.430235206033127e-54), 0: np.float64(5.430235206033127e-54)}
err dic= {1: np.float64(0.7325811653267549), 4: np.float64(0.1849247279103762), 8: np.float64(0.2316564374163787), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

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

beta is  1.5 

learned probs for this beta: {1: np.float64(0.976179579565728), 4: np.float64(0.023755777298822976), 8: np.float64(6.464313544905663e-05), 32: np.float64(9.616365981741119e-65), 27: np.float64(9.616365981741119e-65), 82: np.float64(9.616365981741119e-65), 0: np.float64(9.616365981741119e-65)}
err dic= {1: np.float64(0.754179579565728), 4: np.float64(0.20624422270117704), 8: np.float64(0.23193535686455097), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

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

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141691253702), 4: np.float64(0.012173924284659167), 8: np.float64(1.1906589970439095e-05), 32: np.float64(1.7082882356365177e-75), 27: np.float64(1.7082882356365177e-75), 82: np.float64(1.7082882356365177e-75), 0: np.float64(1.7082882356365177e-75)}
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(3.040176079212285e-86), 27: np.float64(3.040176079212285e-86), 82: np.float64(3.040176079212285e-86), 0: np.float64(3.040176079212285e-86)}
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(0.08009230669073472), 4: np.float64(0.3065857532604964), 6: np.float64(0.29295271328582834), 51: np.float64(0.08009230669073472), 82: np.float64(0.08009230669073472), 41: np.float64(0.08009230669073472), 0: np.float64(0.08009230669073472)}
err dic= {9: np.float64(0.14090769330926528), 4: np.float64(0.06158575326049642), 6: np.float64(0.03695271328582833), 51: np.float64(0.005907693309265272), 82: np.float64(0.04009230669073472), 41: np.float64(0.012907693309265278), 0: np.float64(0.021092306690734725)} 

err list= [np.float64(0.14090769330926528), np.float64(0.06158575326049642), np.float64(0.03695271328582833), np.float64(0.005907693309265272), np.float64(0.04009230669073472), np.float64(0.012907693309265278), np.float64(0.021092306690734725)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.01603973562942816), 4: np.float64(0.4794027899917431), 6: np.float64(0.4403985318611161), 51: np.float64(0.01603973562942816), 82: np.float64(0.01603973562942816), 41: np.float64(0.01603973562942816), 0: np.float64(0.01603973562942816)}
err dic= {9: np.float64(0.20496026437057185), 4: np.float64(0.23440278999174308), 6: np.float64(0.1843985318611161), 51: np.float64(0.06996026437057183), 82: np.float64(0.023960264370571843), 41: np.float64(0.07696026437057184), 0: np.float64(0.042960264370571835)} 

err list= [np.float64(0.20496026437057185), np.float64(0.23440278999174308), np.float64(0.1843985318611161), np.float64(0.06996026437057183), np.float64(0.023960264370571843), np.float64(0.07696026437057184), np.float64(0.042960264370571835)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.00019775925140650986), 4: np.float64(0.5410460903265744), 6: np.float64(0.4579651134163934), 51: np.float64(0.00019775925140650986), 82: np.float64(0.00019775925140650986), 41: np.float64(0.00019775925140650986), 0: np.float64(0.00019775925140650986)}
err dic= {9: np.float64(0.2208022407485935), 4: np.float64(0.29604609032657436), 6: np.float64(0.2019651134163934), 51: np.float64(0.08580224074859348), 82: np.float64(0.03980224074859349), 41: np.float64(0.09280224074859349), 0: np.float64(0.058802240748593484)} 

err list= [np.float64(0.2208022407485935), np.float64(0.29604609032657436), np.float64(0.2019651134163934), np.float64(0.08580224074859348), np.float64(0.03980224074859349), np.float64(0.09280224074859349), np.float64(0.058802240748593484)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(1.0035995762962e-10), 4: np.float64(0.6027772378380363), 6: np.float64(0.39722276166016357), 51: np.float64(1.0035995762962e-10), 82: np.float64(1.0035995762962e-10), 41: np.float64(1.0035995762962e-10), 0: np.float64(1.0035995762962e-10)}
err dic= {9: np.float64(0.22099999989964003), 4: np.float64(0.3577772378380363), 6: np.float64(0.14122276166016356), 51: np.float64(0.08599999989964004), 82: np.float64(0.039999999899640044), 41: np.float64(0.09299999989964004), 0: np.float64(0.05899999989964004)} 

err list= [np.float64(0.22099999989964003), np.float64(0.3577772378380363), np.float64(0.14122276166016356), np.float64(0.08599999989964004), np.float64(0.039999999899640044), np.float64(0.09299999989964004), np.float64(0.05899999989964004)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(3.457861274989172e-21), 4: np.float64(0.6976973366279521), 6: np.float64(0.3023026633720482), 51: np.float64(3.457861274989172e-21), 82: np.float64(3.457861274989172e-21), 41: np.float64(3.457861274989172e-21), 0: np.float64(3.457861274989172e-21)}
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(1.2359679988098285e-31), 4: np.float64(0.7790173173345053), 6: np.float64(0.22098268266549476), 51: np.float64(1.2359679988098285e-31), 82: np.float64(1.2359679988098285e-31), 41: np.float64(1.2359679988098285e-31), 0: np.float64(1.2359679988098285e-31)}
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(4.464435839730548e-42), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(4.464435839730548e-42), 82: np.float64(4.464435839730548e-42), 41: np.float64(4.464435839730548e-42), 0: np.float64(4.464435839730548e-42)}
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(1.6277635417811058e-52), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(1.6277635417811058e-52), 82: np.float64(1.6277635417811058e-52), 41: np.float64(1.6277635417811058e-52), 0: np.float64(1.6277635417811058e-52)}
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(5.992935982779385e-63), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(5.992935982779385e-63), 82: np.float64(5.992935982779385e-63), 41: np.float64(5.992935982779385e-63), 0: np.float64(5.992935982779385e-63)}
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(2.22456405828698e-73), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(2.22456405828698e-73), 82: np.float64(2.22456405828698e-73), 41: np.float64(2.22456405828698e-73), 0: np.float64(2.22456405828698e-73)}
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(8.307124538045458e-84), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(8.307124538045458e-84), 82: np.float64(8.307124538045458e-84), 41: np.float64(8.307124538045458e-84), 0: np.float64(8.307124538045458e-84)}
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(0.26964546938650097), 9: np.float64(0.24616840111665778), 6: np.float64(0.2629878990261868), 39: np.float64(0.05529955761766303), 80: np.float64(0.05529955761766303), 68: np.float64(0.05529955761766303), 0: np.float64(0.05529955761766303)}
err dic= {5: np.float64(0.024645469386500973), 9: np.float64(0.018168401116657767), 6: np.float64(0.004987899026186793), 39: np.float64(0.044700442382336975), 80: np.float64(0.007700442382336969), 68: np.float64(0.0007004423823369701), 0: np.float64(0.005299557617663028)} 

err list= [np.float64(0.024645469386500973), np.float64(0.018168401116657767), np.float64(0.004987899026186793), np.float64(0.044700442382336975), np.float64(0.007700442382336969), np.float64(0.0007004423823369701), np.float64(0.005299557617663028)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.3460121653030371), 9: np.float64(0.29005660606612765), 6: np.float64(0.32913695287145384), 39: np.float64(0.008698568939845237), 80: np.float64(0.008698568939845237), 68: np.float64(0.008698568939845237), 0: np.float64(0.008698568939845237)}
err dic= {5: np.float64(0.10101216530303708), 9: np.float64(0.062056606066127645), 6: np.float64(0.07113695287145383), 39: np.float64(0.09130143106015477), 80: np.float64(0.05430143106015477), 68: np.float64(0.04730143106015476), 0: np.float64(0.04130143106015477)} 

err list= [np.float64(0.10101216530303708), np.float64(0.062056606066127645), np.float64(0.07113695287145383), np.float64(0.09130143106015477), np.float64(0.05430143106015477), np.float64(0.04730143106015476), np.float64(0.04130143106015477)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.3831692606409547), 9: np.float64(0.2693622196504359), 6: np.float64(0.34670588446910905), 39: np.float64(0.00019065880987520213), 80: np.float64(0.00019065880987520213), 68: np.float64(0.00019065880987520213), 0: np.float64(0.00019065880987520213)}
err dic= {5: np.float64(0.1381692606409547), 9: np.float64(0.04136221965043588), 6: np.float64(0.08870588446910904), 39: np.float64(0.0998093411901248), 80: np.float64(0.0628093411901248), 68: np.float64(0.055809341190124796), 0: np.float64(0.0498093411901248)} 

err list= [np.float64(0.1381692606409547), np.float64(0.04136221965043588), np.float64(0.08870588446910904), np.float64(0.0998093411901248), np.float64(0.0628093411901248), np.float64(0.055809341190124796), np.float64(0.0498093411901248)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.4568298020797436), 9: np.float64(0.18739078990153837), 6: np.float64(0.3557794075900593), 39: np.float64(1.0716449731068563e-10), 80: np.float64(1.0716449731068563e-10), 68: np.float64(1.0716449731068563e-10), 0: np.float64(1.0716449731068563e-10)}
err dic= {5: np.float64(0.2118298020797436), 9: np.float64(0.040609210098461634), 6: np.float64(0.09777940759005932), 39: np.float64(0.0999999998928355), 80: np.float64(0.0629999998928355), 68: np.float64(0.0559999998928355), 0: np.float64(0.0499999998928355)} 

err list= [np.float64(0.2118298020797436), np.float64(0.040609210098461634), np.float64(0.09777940759005932), np.float64(0.0999999998928355), np.float64(0.0629999998928355), np.float64(0.0559999998928355), np.float64(0.0499999998928355)]
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(4.267799955047485e-21), 80: np.float64(4.267799955047485e-21), 68: np.float64(4.267799955047485e-21), 0: np.float64(4.267799955047485e-21)}
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(1.8065447612670218e-31), 80: np.float64(1.8065447612670218e-31), 68: np.float64(1.8065447612670218e-31), 0: np.float64(1.8065447612670218e-31)}
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(7.905754923286889e-42), 80: np.float64(7.905754923286889e-42), 68: np.float64(7.905754923286889e-42), 0: np.float64(7.905754923286889e-42)}
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(3.540018804660563e-52), 80: np.float64(3.540018804660563e-52), 68: np.float64(3.540018804660563e-52), 0: np.float64(3.540018804660563e-52)}
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(1.6117757909624476e-62), 80: np.float64(1.6117757909624476e-62), 68: np.float64(1.6117757909624476e-62), 0: np.float64(1.6117757909624476e-62)}
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(7.433794757972374e-73), 80: np.float64(7.433794757972374e-73), 68: np.float64(7.433794757972374e-73), 0: np.float64(7.433794757972374e-73)}
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(3.464412578820005e-83), 80: np.float64(3.464412578820005e-83), 68: np.float64(3.464412578820005e-83), 0: np.float64(3.464412578820005e-83)}
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(0.252366999134126), 3: np.float64(0.2696360116537524), 8: np.float64(0.2410730802291606), 15: np.float64(0.05923097724574047), 78: np.float64(0.05923097724574047), 97: np.float64(0.05923097724574047), 0: np.float64(0.05923097724574047)}
err dic= {6: np.float64(0.03136699913412602), 3: np.float64(0.03463601165375241), 8: np.float64(0.003073080229160613), 15: np.float64(0.11376902275425951), 78: np.float64(0.0032309772457404656), 97: np.float64(0.020230977245740467), 0: np.float64(0.021230977245740468)} 

err list= [np.float64(0.03136699913412602), np.float64(0.03463601165375241), np.float64(0.003073080229160613), np.float64(0.11376902275425951), np.float64(0.0032309772457404656), np.float64(0.020230977245740467), np.float64(0.021230977245740468)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.3171752591711544), 3: np.float64(0.35943993730908447), 8: np.float64(0.2903563381874296), 15: np.float64(0.008257116333082796), 78: np.float64(0.008257116333082796), 97: np.float64(0.008257116333082796), 0: np.float64(0.008257116333082796)}
err dic= {6: np.float64(0.09617525917115441), 3: np.float64(0.12443993730908448), 8: np.float64(0.05235633818742963), 15: np.float64(0.1647428836669172), 78: np.float64(0.0477428836669172), 97: np.float64(0.030742883666917204), 0: np.float64(0.029742883666917203)} 

err list= [np.float64(0.09617525917115441), np.float64(0.12443993730908448), np.float64(0.05235633818742963), np.float64(0.1647428836669172), np.float64(0.0477428836669172), np.float64(0.030742883666917204), np.float64(0.029742883666917203)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.32047490631050096), 3: np.float64(0.41035895926993066), 8: np.float64(0.2685467135417698), 15: np.float64(0.00015485521944978988), 78: np.float64(0.00015485521944978988), 97: np.float64(0.00015485521944978988), 0: np.float64(0.00015485521944978988)}
err dic= {6: np.float64(0.09947490631050096), 3: np.float64(0.17535895926993067), 8: np.float64(0.0305467135417698), 15: np.float64(0.1728451447805502), 78: np.float64(0.055845144780550214), 97: np.float64(0.03884514478055021), 0: np.float64(0.03784514478055021)} 

err list= [np.float64(0.09947490631050096), np.float64(0.17535895926993067), np.float64(0.0305467135417698), np.float64(0.1728451447805502), np.float64(0.055845144780550214), np.float64(0.03884514478055021), np.float64(0.03784514478055021)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2875137925582489), 3: np.float64(0.528988846404597), 8: np.float64(0.18349736073259307), 15: np.float64(7.614011900720228e-11), 78: np.float64(7.614011900720228e-11), 97: np.float64(7.614011900720228e-11), 0: np.float64(7.614011900720228e-11)}
err dic= {6: np.float64(0.06651379255824888), 3: np.float64(0.293988846404597), 8: np.float64(0.05450263926740692), 15: np.float64(0.17299999992385987), 78: np.float64(0.05599999992385988), 97: np.float64(0.03899999992385988), 0: np.float64(0.03799999992385988)} 

err list= [np.float64(0.06651379255824888), np.float64(0.293988846404597), np.float64(0.05450263926740692), np.float64(0.17299999992385987), np.float64(0.05599999992385988), np.float64(0.03899999992385988), np.float64(0.03799999992385988)]
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(2.3002360974116248e-21), 78: np.float64(2.3002360974116248e-21), 97: np.float64(2.3002360974116248e-21), 0: np.float64(2.3002360974116248e-21)}
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(6.982027867040768e-32), 78: np.float64(6.982027867040768e-32), 97: np.float64(6.982027867040768e-32), 0: np.float64(6.982027867040768e-32)}
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(2.102272988019364e-42), 78: np.float64(2.102272988019364e-42), 97: np.float64(2.102272988019364e-42), 0: np.float64(2.102272988019364e-42)}
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(6.287578222992905e-53), 78: np.float64(6.287578222992905e-53), 97: np.float64(6.287578222992905e-53), 0: np.float64(6.287578222992905e-53)}
err dic= {6: np.float64(0.17635159930287642), 3: np.float64(0.7164153882278131), 8: np.float64(0.23406378892493673), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

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

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023650013524335572), 3: np.float64(0.975099430792984), 8: np.float64(0.0012505556826808662), 15: np.float64(1.8710950399599565e-63), 78: np.float64(1.8710950399599565e-63), 97: np.float64(1.8710950399599565e-63), 0: np.float64(1.8710950399599565e-63)}
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(5.547157111343559e-74), 78: np.float64(5.547157111343559e-74), 97: np.float64(5.547157111343559e-74), 0: np.float64(5.547157111343559e-74)}
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(1.6400346558390367e-84), 78: np.float64(1.6400346558390367e-84), 97: np.float64(1.6400346558390367e-84), 0: np.float64(1.6400346558390367e-84)}
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(0.20849390237919846), 2: np.float64(0.23822827822812304), 4: np.float64(0.227593317692785), 95: np.float64(0.04219411356161891), 11: np.float64(0.19910216101503136), 22: np.float64(0.04219411356161891), 0: np.float64(0.04219411356161891)}
err dic= {8: np.float64(0.026506097620801528), 2: np.float64(0.03622827822812302), 4: np.float64(0.030593317692785005), 95: np.float64(0.00019411356161890686), 11: np.float64(0.033102161015031356), 22: np.float64(0.0948058864383811), 0: np.float64(0.021194113561618908)} 

err list= [np.float64(0.026506097620801528), np.float64(0.03622827822812302), np.float64(0.030593317692785005), np.float64(0.00019411356161890686), np.float64(0.033102161015031356), np.float64(0.0948058864383811), np.float64(0.021194113561618908)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.22342474979825494), 2: np.float64(0.28972570055698305), 4: np.float64(0.2649733921948927), 95: np.float64(0.005963456782039109), 11: np.float64(0.20398578710375231), 22: np.float64(0.005963456782039109), 0: np.float64(0.005963456782039109)}
err dic= {8: np.float64(0.011575250201745046), 2: np.float64(0.08772570055698303), 4: np.float64(0.06797339219489268), 95: np.float64(0.0360365432179609), 11: np.float64(0.037985787103752305), 22: np.float64(0.1310365432179609), 0: np.float64(0.015036543217960892)} 

err list= [np.float64(0.011575250201745046), np.float64(0.08772570055698303), np.float64(0.06797339219489268), np.float64(0.0360365432179609), np.float64(0.037985787103752305), np.float64(0.1310365432179609), np.float64(0.015036543217960892)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.20331353358148369), 2: np.float64(0.3411613288670195), 4: np.float64(0.2858983809508925), 95: np.float64(0.00013581492509868244), 11: np.float64(0.16921931182530872), 22: np.float64(0.00013581492509868244), 0: np.float64(0.00013581492509868244)}
err dic= {8: np.float64(0.0316864664185163), 2: np.float64(0.13916132886701948), 4: np.float64(0.08889838095089247), 95: np.float64(0.04186418507490132), 11: np.float64(0.0032193118253087127), 22: np.float64(0.13686418507490133), 0: np.float64(0.020864185074901318)} 

err list= [np.float64(0.0316864664185163), np.float64(0.13916132886701948), np.float64(0.08889838095089247), np.float64(0.04186418507490132), np.float64(0.0032193118253087127), np.float64(0.13686418507490133), np.float64(0.020864185074901318)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.13082576067284035), 2: np.float64(0.4775204476292418), 4: np.float64(0.31002951637182136), 95: np.float64(5.858789326731119e-11), 11: np.float64(0.08162427515033202), 22: np.float64(5.858789326731119e-11), 0: np.float64(5.858789326731119e-11)}
err dic= {8: np.float64(0.10417423932715963), 2: np.float64(0.27552044762924177), 4: np.float64(0.11302951637182135), 95: np.float64(0.04199999994141211), 11: np.float64(0.08437572484966799), 22: np.float64(0.13699999994141213), 0: np.float64(0.020999999941412106)} 

err list= [np.float64(0.10417423932715963), np.float64(0.27552044762924177), np.float64(0.11302951637182135), np.float64(0.04199999994141211), np.float64(0.08437572484966799), np.float64(0.13699999994141213), np.float64(0.020999999941412106)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04709325965882175), 2: np.float64(0.6544667084443634), 4: np.float64(0.2806804187885039), 95: np.float64(1.2893296038178994e-21), 11: np.float64(0.017759613108311294), 22: np.float64(1.2893296038178994e-21), 0: np.float64(1.2893296038178994e-21)}
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(2.7905610511812576e-32), 11: np.float64(0.003061487235188769), 22: np.float64(2.7905610511812576e-32), 0: np.float64(2.7905610511812576e-32)}
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(6.073915678209323e-43), 11: np.float64(0.00047336280779999217), 22: np.float64(6.073915678209323e-43), 0: np.float64(6.073915678209323e-43)}
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(1.3385093100229854e-53), 11: np.float64(6.965386583462914e-05), 22: np.float64(1.3385093100229854e-53), 0: np.float64(1.3385093100229854e-53)}
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(2.984778725148027e-64), 11: np.float64(9.99775588346969e-06), 22: np.float64(2.984778725148027e-64), 0: np.float64(2.984778725148027e-64)}
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(6.716691982211195e-75), 11: np.float64(1.414291028627564e-06), 22: np.float64(6.716691982211195e-75), 0: np.float64(6.716691982211195e-75)}
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(1.5210504203812142e-85), 11: np.float64(1.9810924551184603e-07), 22: np.float64(1.5210504203812142e-85), 0: np.float64(1.5210504203812142e-85)}
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(0.2437968062760887), 3: np.float64(0.2329310068487228), 9: np.float64(0.20466156987589057), 100: np.float64(0.1913284282398761), 22: np.float64(0.04242739625313927), 58: np.float64(0.04242739625313927), 0: np.float64(0.04242739625313927)}
err dic= {1: np.float64(0.025796806276088713), 3: np.float64(0.051931006848722816), 9: np.float64(0.0076615698758905615), 100: np.float64(0.03067157176012389), 22: np.float64(0.07057260374686072), 58: np.float64(0.0014273962531392709), 0: np.float64(0.014427396253139272)} 

err list= [np.float64(0.025796806276088713), np.float64(0.051931006848722816), np.float64(0.0076615698758905615), np.float64(0.03067157176012389), np.float64(0.07057260374686072), np.float64(0.0014273962531392709), np.float64(0.014427396253139272)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3021395197709211), 3: np.float64(0.2764133071668627), 9: np.float64(0.21511053634485616), 100: np.float64(0.18837213031371408), 22: np.float64(0.005988168801215479), 58: np.float64(0.005988168801215479), 0: np.float64(0.005988168801215479)}
err dic= {1: np.float64(0.08413951977092107), 3: np.float64(0.0954133071668627), 9: np.float64(0.018110536344856154), 100: np.float64(0.03362786968628592), 22: np.float64(0.10701183119878452), 58: np.float64(0.035011831198784524), 0: np.float64(0.022011831198784523)} 

err list= [np.float64(0.08413951977092107), np.float64(0.0954133071668627), np.float64(0.018110536344856154), np.float64(0.03362786968628592), np.float64(0.10701183119878452), np.float64(0.035011831198784524), np.float64(0.022011831198784523)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3654524762780246), 3: np.float64(0.3066101216955032), 9: np.float64(0.18572669016533022), 100: np.float64(0.1418054320452656), 22: np.float64(0.00013509327195880923), 58: np.float64(0.00013509327195880923), 0: np.float64(0.00013509327195880923)}
err dic= {1: np.float64(0.14745247627802457), 3: np.float64(0.12561012169550323), 9: np.float64(0.011273309834669787), 100: np.float64(0.0801945679547344), 22: np.float64(0.1128649067280412), 58: np.float64(0.04086490672804119), 0: np.float64(0.02786490672804119)} 

err list= [np.float64(0.14745247627802457), np.float64(0.12561012169550323), np.float64(0.011273309834669787), np.float64(0.0801945679547344), np.float64(0.1128649067280412), np.float64(0.04086490672804119), np.float64(0.02786490672804119)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5199273619610574), 3: np.float64(0.33916654867845514), 9: np.float64(0.09438635238749335), 100: np.float64(0.0465197368134481), 22: np.float64(5.318179984127794e-11), 58: np.float64(5.318179984127794e-11), 0: np.float64(5.318179984127794e-11)}
err dic= {1: np.float64(0.3019273619610574), 3: np.float64(0.15816654867845514), 9: np.float64(0.10261364761250666), 100: np.float64(0.1754802631865519), 22: np.float64(0.1129999999468182), 58: np.float64(0.0409999999468182), 0: np.float64(0.0279999999468182)} 

err list= [np.float64(0.3019273619610574), np.float64(0.15816654867845514), np.float64(0.10261364761250666), np.float64(0.1754802631865519), np.float64(0.1129999999468182), np.float64(0.0409999999468182), np.float64(0.0279999999468182)]
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(8.818661424106765e-22), 58: np.float64(8.818661424106765e-22), 0: np.float64(8.818661424106765e-22)}
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(1.4034132307249132e-32), 58: np.float64(1.4034132307249132e-32), 0: np.float64(1.4034132307249132e-32)}
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(2.297542992144192e-43), 58: np.float64(2.297542992144192e-43), 0: np.float64(2.297542992144192e-43)}
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(3.8789572114741907e-54), 58: np.float64(3.8789572114741907e-54), 0: np.float64(3.8789572114741907e-54)}
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(6.689888642489012e-65), 58: np.float64(6.689888642489012e-65), 0: np.float64(6.689888642489012e-65)}
err dic= {1: np.float64(0.7109011179586114), 3: np.float64(0.10991127201214174), 9: np.float64(0.19698995751614806), 100: np.float64(0.221999888430322), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

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

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489961513725), 3: np.float64(0.04644957969911168), 9: np.float64(1.416715180521834e-06), 100: np.float64(7.434334682403295e-09), 22: np.float64(1.169191550803888e-75), 58: np.float64(1.169191550803888e-75), 0: np.float64(1.169191550803888e-75)}
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(2.0598497340080428e-86), 58: np.float64(2.0598497340080428e-86), 0: np.float64(2.0598497340080428e-86)}
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(0.251605213681907), 6: np.float64(0.2579746299908391), 8: np.float64(0.24539305882197038), 16: np.float64(0.061256774376321245), 83: np.float64(0.061256774376321245), 70: np.float64(0.061256774376321245), 0: np.float64(0.061256774376321245)}
err dic= {7: np.float64(0.044605213681907036), 6: np.float64(0.011974629990839092), 8: np.float64(0.0036069411780296212), 16: np.float64(0.08674322562367875), 83: np.float64(0.013256774376321244), 70: np.float64(0.003256774376321242), 0: np.float64(0.017256774376321247)} 

err list= [np.float64(0.044605213681907036), np.float64(0.011974629990839092), np.float64(0.0036069411780296212), np.float64(0.08674322562367875), np.float64(0.013256774376321244), np.float64(0.003256774376321242), np.float64(0.017256774376321247)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.3212991025258194), 6: np.float64(0.3377724597769507), 8: np.float64(0.3056291603882311), 16: np.float64(0.00882481932724968), 83: np.float64(0.00882481932724968), 70: np.float64(0.00882481932724968), 0: np.float64(0.00882481932724968)}
err dic= {7: np.float64(0.1142991025258194), 6: np.float64(0.0917724597769507), 8: np.float64(0.056629160388231126), 16: np.float64(0.1391751806727503), 83: np.float64(0.03917518067275032), 70: np.float64(0.04917518067275033), 0: np.float64(0.035175180672750314)} 

err list= [np.float64(0.1142991025258194), np.float64(0.0917724597769507), np.float64(0.056629160388231126), np.float64(0.1391751806727503), np.float64(0.03917518067275032), np.float64(0.04917518067275033), np.float64(0.035175180672750314)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.33199789749383096), 6: np.float64(0.3669144211724419), 8: np.float64(0.30040412036168523), 16: np.float64(0.00017089024301060818), 83: np.float64(0.00017089024301060818), 70: np.float64(0.00017089024301060818), 0: np.float64(0.00017089024301060818)}
err dic= {7: np.float64(0.12499789749383097), 6: np.float64(0.12091442117244189), 8: np.float64(0.051404120361685235), 16: np.float64(0.14782910975698937), 83: np.float64(0.04782910975698939), 70: np.float64(0.05782910975698939), 0: np.float64(0.043829109756989386)} 

err list= [np.float64(0.12499789749383097), np.float64(0.12091442117244189), np.float64(0.051404120361685235), np.float64(0.14782910975698937), np.float64(0.04782910975698939), np.float64(0.05782910975698939), np.float64(0.043829109756989386)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.3264958356636913), 6: np.float64(0.4192289514348836), 8: np.float64(0.2542752124844356), 16: np.float64(1.0424724711058642e-10), 83: np.float64(1.0424724711058642e-10), 70: np.float64(1.0424724711058642e-10), 0: np.float64(1.0424724711058642e-10)}
err dic= {7: np.float64(0.11949583566369129), 6: np.float64(0.1732289514348836), 8: np.float64(0.005275212484435576), 16: np.float64(0.14799999989575274), 83: np.float64(0.04799999989575275), 70: np.float64(0.05799999989575275), 0: np.float64(0.04399999989575275)} 

err list= [np.float64(0.11949583566369129), np.float64(0.1732289514348836), np.float64(0.005275212484435576), np.float64(0.14799999989575274), np.float64(0.04799999989575275), np.float64(0.05799999989575275), np.float64(0.04399999989575275)]
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(5.20333998592791e-21), 83: np.float64(5.20333998592791e-21), 70: np.float64(5.20333998592791e-21), 0: np.float64(5.20333998592791e-21)}
err dic= {7: np.float64(0.10019588571849855), 6: np.float64(0.26048039105565424), 8: np.float64(0.0626762767741523), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.10019588571849855), np.float64(0.26048039105565424), np.float64(0.0626762767741523), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.27860068919627307), 6: np.float64(0.5897976636568125), 8: np.float64(0.13160164714691433), 16: np.float64(2.8918978231699992e-31), 83: np.float64(2.8918978231699992e-31), 70: np.float64(2.8918978231699992e-31), 0: np.float64(2.8918978231699992e-31)}
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(1.678534999481238e-41), 83: np.float64(1.678534999481238e-41), 70: np.float64(1.678534999481238e-41), 0: np.float64(1.678534999481238e-41)}
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(9.982529636572254e-52), 83: np.float64(9.982529636572254e-52), 70: np.float64(9.982529636572254e-52), 0: np.float64(9.982529636572254e-52)}
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(6.03362815271938e-62), 83: np.float64(6.03362815271938e-62), 70: np.float64(6.03362815271938e-62), 0: np.float64(6.03362815271938e-62)}
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(3.6865245572036473e-72), 83: np.float64(3.6865245572036473e-72), 70: np.float64(3.6865245572036473e-72), 0: np.float64(3.6865245572036473e-72)}
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(2.2683097887641518e-82), 83: np.float64(2.2683097887641518e-82), 70: np.float64(2.2683097887641518e-82), 0: np.float64(2.2683097887641518e-82)}
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= [0.02581433 0.05043584 0.06193975 0.06774052 0.07480249 0.08211628
 0.0890372  0.0953012  0.10184224 0.10836043 0.11463451]
mean_std= [0.         0.02462151 0.02586166 0.02454722 0.02610629 0.0289034
 0.03167739 0.03395127 0.03697153 0.04015702 0.0431234 ]
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
