p= 0.25 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(0.15008218499896023), 3: np.float64(0.14637664264835556), 4: np.float64(0.14276259046437026), 59: np.float64(0.14019464547207838), 40: np.float64(0.14019464547207838), 84: np.float64(0.14019464547207838), 0: np.float64(0.14019464547207838)}
err dic= {2: np.float64(0.1249178150010398), 3: np.float64(0.10062335735164443), 4: np.float64(0.10923740953562974), 59: np.float64(0.08119464547207839), 40: np.float64(0.06819464547207839), 84: np.float64(0.08019464547207839), 0: np.float64(0.10519464547207838)} 

err list= [np.float64(0.1249178150010398), np.float64(0.10062335735164443), np.float64(0.10923740953562974), np.float64(0.08119464547207839), np.float64(0.06819464547207839), np.float64(0.08019464547207839), np.float64(0.10519464547207838)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.22825370267096573), 3: np.float64(0.21712163823185995), 4: np.float64(0.20653249098194465), 59: np.float64(0.0870230420288106), 40: np.float64(0.0870230420288106), 84: np.float64(0.0870230420288106), 0: np.float64(0.0870230420288106)}
err dic= {2: np.float64(0.04674629732903429), 3: np.float64(0.029878361768140044), 4: np.float64(0.04546750901805535), 59: np.float64(0.028023042028810605), 40: np.float64(0.015023042028810607), 84: np.float64(0.027023042028810604), 0: np.float64(0.0520230420288106)} 

err list= [np.float64(0.04674629732903429), np.float64(0.029878361768140044), np.float64(0.04546750901805535), np.float64(0.028023042028810605), np.float64(0.015023042028810607), np.float64(0.027023042028810604), np.float64(0.0520230420288106)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.3343544784311051), 3: np.float64(0.3025364429723604), 4: np.float64(0.2737462939208937), 59: np.float64(0.022340696168910372), 40: np.float64(0.022340696168910372), 84: np.float64(0.022340696168910372), 0: np.float64(0.022340696168910372)}
err dic= {2: np.float64(0.059354478431105084), 3: np.float64(0.05553644297236038), 4: np.float64(0.021746293920893722), 59: np.float64(0.036659303831089625), 40: np.float64(0.04965930383108962), 84: np.float64(0.037659303831089626), 0: np.float64(0.012659303831089631)} 

err list= [np.float64(0.059354478431105084), np.float64(0.05553644297236038), np.float64(0.021746293920893722), np.float64(0.036659303831089625), np.float64(0.04965930383108962), np.float64(0.037659303831089626), np.float64(0.012659303831089631)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.41847113269968106), 3: np.float64(0.3259056458392895), 4: np.float64(0.2538155721870306), 59: np.float64(0.00045191231849988825), 40: np.float64(0.00045191231849988825), 84: np.float64(0.00045191231849988825), 0: np.float64(0.00045191231849988825)}
err dic= {2: np.float64(0.14347113269968104), 3: np.float64(0.0789056458392895), 4: np.float64(0.0018155721870306007), 59: np.float64(0.05854808768150011), 40: np.float64(0.0715480876815001), 84: np.float64(0.05954808768150011), 0: np.float64(0.03454808768150012)} 

err list= [np.float64(0.14347113269968104), np.float64(0.0789056458392895), np.float64(0.0018155721870306007), np.float64(0.05854808768150011), np.float64(0.0715480876815001), np.float64(0.05954808768150011), np.float64(0.03454808768150012)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5064800415926693), 3: np.float64(0.3071956737584837), 4: np.float64(0.18632359466560008), 59: np.float64(1.724958118227097e-07), 40: np.float64(1.724958118227097e-07), 84: np.float64(1.724958118227097e-07), 0: np.float64(1.724958118227097e-07)}
err dic= {2: np.float64(0.23148004159266933), 3: np.float64(0.060195673758483725), 4: np.float64(0.06567640533439992), 59: np.float64(0.058999827504188175), 40: np.float64(0.07199982750418817), 84: np.float64(0.059999827504188176), 0: np.float64(0.03499982750418818)} 

err list= [np.float64(0.23148004159266933), np.float64(0.060195673758483725), np.float64(0.06567640533439992), np.float64(0.058999827504188175), np.float64(0.07199982750418817), np.float64(0.059999827504188176), np.float64(0.03499982750418818)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5897976635436505), 3: np.float64(0.27860068914281905), 4: np.float64(0.13160164712166447), 59: np.float64(4.7966530204919266e-11), 40: np.float64(4.7966530204919266e-11), 84: np.float64(4.7966530204919266e-11), 0: np.float64(4.7966530204919266e-11)}
err dic= {2: np.float64(0.31479766354365046), 3: np.float64(0.03160068914281905), 4: np.float64(0.12039835287833553), 59: np.float64(0.05899999995203346), 40: np.float64(0.07199999995203346), 84: np.float64(0.059999999952033464), 0: np.float64(0.03499999995203347)} 

err list= [np.float64(0.31479766354365046), np.float64(0.03160068914281905), np.float64(0.12039835287833553), np.float64(0.05899999995203346), np.float64(0.07199999995203346), np.float64(0.059999999952033464), np.float64(0.03499999995203347)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652409557747835), 3: np.float64(0.24472847105478351), 4: np.float64(0.09003057317037526), 59: np.float64(1.4481065399527967e-14), 40: np.float64(1.4481065399527967e-14), 84: np.float64(1.4481065399527967e-14), 0: np.float64(1.4481065399527967e-14)}
err dic= {2: np.float64(0.39024095577478346), 3: np.float64(0.0022715289452164833), 4: np.float64(0.16196942682962473), 59: np.float64(0.058999999999985515), 40: np.float64(0.07199999999998552), 84: np.float64(0.059999999999985516), 0: np.float64(0.03499999999998552)} 

err list= [np.float64(0.39024095577478346), np.float64(0.0022715289452164833), np.float64(0.16196942682962473), np.float64(0.058999999999985515), np.float64(0.07199999999998552), np.float64(0.059999999999985516), np.float64(0.03499999999998552)]
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(4.576762280882798e-18), 40: np.float64(4.576762280882798e-18), 84: np.float64(4.576762280882798e-18), 0: np.float64(4.576762280882798e-18)}
err dic= {2: np.float64(0.4556791292026885), 3: np.float64(0.03765692451780317), 4: np.float64(0.19202220468488576), 59: np.float64(0.05899999999999999), 40: np.float64(0.072), 84: np.float64(0.05999999999999999), 0: np.float64(0.034999999999999996)} 

err list= [np.float64(0.4556791292026885), np.float64(0.03765692451780317), np.float64(0.19202220468488576), np.float64(0.05899999999999999), np.float64(0.072), np.float64(0.05999999999999999), np.float64(0.034999999999999996)]
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(1.483169187396448e-21), 40: np.float64(1.483169187396448e-21), 84: np.float64(1.483169187396448e-21), 0: np.float64(1.483169187396448e-21)}
err dic= {2: np.float64(0.5105970345892754), 3: np.float64(0.07170960785996347), 4: np.float64(0.2128874267293126), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

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

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845643329679), 3: np.float64(0.1443339551132097), 4: np.float64(0.025081480553821995), 59: np.float64(4.874982770286099e-25), 40: np.float64(4.874982770286099e-25), 84: np.float64(4.874982770286099e-25), 0: np.float64(4.874982770286099e-25)}
err dic= {2: np.float64(0.5555845643329679), 3: np.float64(0.10266604488679029), 4: np.float64(0.226918519446178), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

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

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973345), 3: np.float64(0.11731042782619833), 4: np.float64(0.015876239976466765), 59: np.float64(1.6155811428673194e-28), 40: np.float64(1.6155811428673194e-28), 84: np.float64(1.6155811428673194e-28), 0: np.float64(1.6155811428673194e-28)}
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(0.14856258377661594), 4: np.float64(0.14489456051387298), 8: np.float64(0.13192544627869496), 74: np.float64(0.14365435235770366), 40: np.float64(0.14365435235770366), 87: np.float64(0.14365435235770366), 0: np.float64(0.14365435235770366)}
err dic= {3: np.float64(0.11043741622338407), 4: np.float64(0.10110543948612702), 8: np.float64(0.12407455372130505), 74: np.float64(0.07765435235770365), 40: np.float64(0.06665435235770366), 87: np.float64(0.09665435235770366), 0: np.float64(0.09465435235770366)} 

err list= [np.float64(0.11043741622338407), np.float64(0.10110543948612702), np.float64(0.12407455372130505), np.float64(0.07765435235770365), np.float64(0.06665435235770366), np.float64(0.09665435235770366), np.float64(0.09465435235770366)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.2273333588048572), 4: np.float64(0.21624618006575896), 8: np.float64(0.180463085587464), 74: np.float64(0.09398934388548272), 40: np.float64(0.09398934388548272), 87: np.float64(0.09398934388548272), 0: np.float64(0.09398934388548272)}
err dic= {3: np.float64(0.031666641195142814), 4: np.float64(0.029753819934241033), 8: np.float64(0.07553691441253602), 74: np.float64(0.027989343885482715), 40: np.float64(0.01698934388548272), 87: np.float64(0.04698934388548272), 0: np.float64(0.044989343885482716)} 

err list= [np.float64(0.031666641195142814), np.float64(0.029753819934241033), np.float64(0.07553691441253602), np.float64(0.027989343885482715), np.float64(0.01698934388548272), np.float64(0.04698934388548272), np.float64(0.044989343885482716)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.3483321013878513), 4: np.float64(0.31518391923882316), 8: np.float64(0.224168849736107), 74: np.float64(0.0280787824093047), 40: np.float64(0.0280787824093047), 87: np.float64(0.0280787824093047), 0: np.float64(0.0280787824093047)}
err dic= {3: np.float64(0.0893321013878513), 4: np.float64(0.06918391923882317), 8: np.float64(0.03183115026389299), 74: np.float64(0.037921217590695305), 40: np.float64(0.0489212175906953), 87: np.float64(0.0189212175906953), 0: np.float64(0.0209212175906953)} 

err list= [np.float64(0.0893321013878513), np.float64(0.06918391923882317), np.float64(0.03183115026389299), np.float64(0.037921217590695305), np.float64(0.0489212175906953), np.float64(0.0189212175906953), np.float64(0.0209212175906953)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.47169642091516417), 4: np.float64(0.3673575419807088), 8: np.float64(0.15829113093205754), 74: np.float64(0.0006637265430174823), 40: np.float64(0.0006637265430174823), 87: np.float64(0.0006637265430174823), 0: np.float64(0.0006637265430174823)}
err dic= {3: np.float64(0.21269642091516416), 4: np.float64(0.1213575419807088), 8: np.float64(0.09770886906794246), 74: np.float64(0.06533627345698252), 40: np.float64(0.07633627345698252), 87: np.float64(0.04633627345698252), 0: np.float64(0.04833627345698252)} 

err list= [np.float64(0.21269642091516416), np.float64(0.1213575419807088), np.float64(0.09770886906794246), np.float64(0.06533627345698252), np.float64(0.07633627345698252), np.float64(0.04633627345698252), np.float64(0.04833627345698252)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5841449497948266), 4: np.float64(0.3543018217668592), 8: np.float64(0.06155176229114151), 74: np.float64(3.665367932672087e-07), 40: np.float64(3.665367932672087e-07), 87: np.float64(3.665367932672087e-07), 0: np.float64(3.665367932672087e-07)}
err dic= {3: np.float64(0.32514494979482655), 4: np.float64(0.10830182176685921), 8: np.float64(0.1944482377088585), 74: np.float64(0.06599963346320674), 40: np.float64(0.07699963346320673), 87: np.float64(0.046999633463206736), 0: np.float64(0.04899963346320674)} 

err list= [np.float64(0.32514494979482655), np.float64(0.10830182176685921), np.float64(0.1944482377088585), np.float64(0.06599963346320674), np.float64(0.07699963346320673), np.float64(0.046999633463206736), np.float64(0.04899963346320674)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.6651469582331643), 4: np.float64(0.31419317572677147), 8: np.float64(0.020659865498076406), 74: np.float64(1.3549699522109362e-10), 40: np.float64(1.3549699522109362e-10), 87: np.float64(1.3549699522109362e-10), 0: np.float64(1.3549699522109362e-10)}
err dic= {3: np.float64(0.40614695823316427), 4: np.float64(0.06819317572677147), 8: np.float64(0.2353401345019236), 74: np.float64(0.06599999986450301), 40: np.float64(0.07699999986450301), 87: np.float64(0.046999999864503005), 0: np.float64(0.048999999864503006)} 

err list= [np.float64(0.40614695823316427), np.float64(0.06819317572677147), np.float64(0.2353401345019236), np.float64(0.06599999986450301), np.float64(0.07699999986450301), np.float64(0.046999999864503005), np.float64(0.048999999864503006)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.7263954957319392), 4: np.float64(0.26722596903931856), 8: np.float64(0.006378535228536034), 74: np.float64(5.160760964842436e-14), 40: np.float64(5.160760964842436e-14), 87: np.float64(5.160760964842436e-14), 0: np.float64(5.160760964842436e-14)}
err dic= {3: np.float64(0.46739549573193917), 4: np.float64(0.02122596903931856), 8: np.float64(0.24962146477146396), 74: np.float64(0.06599999999994839), 40: np.float64(0.07699999999994839), 87: np.float64(0.046999999999948396), 0: np.float64(0.0489999999999484)} 

err list= [np.float64(0.46739549573193917), np.float64(0.02122596903931856), np.float64(0.24962146477146396), np.float64(0.06599999999994839), np.float64(0.07699999999994839), np.float64(0.046999999999948396), np.float64(0.0489999999999484)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.7758322205460949), 4: np.float64(0.22227965274514916), 8: np.float64(0.0018881267087552528), 74: np.float64(2.018958315675773e-17), 40: np.float64(2.018958315675773e-17), 87: np.float64(2.018958315675773e-17), 0: np.float64(2.018958315675773e-17)}
err dic= {3: np.float64(0.5168322205460949), 4: np.float64(0.023720347254850838), 8: np.float64(0.25411187329124474), 74: np.float64(0.06599999999999999), 40: np.float64(0.07699999999999999), 87: np.float64(0.04699999999999998), 0: np.float64(0.04899999999999998)} 

err list= [np.float64(0.5168322205460949), np.float64(0.023720347254850838), np.float64(0.25411187329124474), np.float64(0.06599999999999999), np.float64(0.07699999999999999), np.float64(0.04699999999999998), np.float64(0.04899999999999998)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.8171262003129651), 4: np.float64(0.18232549993730982), 8: np.float64(0.0005482997497247672), 74: np.float64(8.071793583466605e-21), 40: np.float64(8.071793583466605e-21), 87: np.float64(8.071793583466605e-21), 0: np.float64(8.071793583466605e-21)}
err dic= {3: np.float64(0.5581262003129651), 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(0.5581262003129651), 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(3.2834352742513714e-24), 40: np.float64(3.2834352742513714e-24), 87: np.float64(3.2834352742513714e-24), 0: np.float64(3.2834352742513714e-24)}
err dic= {3: np.float64(0.592818249643065), 4: np.float64(0.0979761836564689), 8: np.float64(0.2558420659865968), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

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

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402411473), 4: np.float64(0.11919751703720469), 8: np.float64(4.534272164780921e-05), 74: np.float64(1.3538079558127684e-27), 40: np.float64(1.3538079558127684e-27), 87: np.float64(1.3538079558127684e-27), 0: np.float64(1.3538079558127684e-27)}
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(0.1448464418597949), 3: np.float64(0.13806669002204497), 9: np.float64(0.12277811562766935), 83: np.float64(0.14857718812262366), 79: np.float64(0.14857718812262366), 70: np.float64(0.14857718812262366), 0: np.float64(0.14857718812262366)}
err dic= {1: np.float64(0.12015355814020512), 3: np.float64(0.11293330997795503), 9: np.float64(0.11222188437233063), 83: np.float64(0.09657718812262367), 79: np.float64(0.08057718812262366), 70: np.float64(0.06757718812262366), 0: np.float64(0.10057718812262366)} 

err list= [np.float64(0.12015355814020512), np.float64(0.11293330997795503), np.float64(0.11222188437233063), np.float64(0.09657718812262367), np.float64(0.08057718812262366), np.float64(0.06757718812262366), np.float64(0.10057718812262366)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.23078705599605204), 3: np.float64(0.210258874506244), 9: np.float64(0.16770230402593503), 83: np.float64(0.0978129413679415), 79: np.float64(0.0978129413679415), 70: np.float64(0.0978129413679415), 0: np.float64(0.0978129413679415)}
err dic= {1: np.float64(0.034212944003947976), 3: np.float64(0.040741125493756), 9: np.float64(0.06729769597406496), 83: np.float64(0.0458129413679415), 79: np.float64(0.029812941367941492), 70: np.float64(0.016812941367941495), 0: np.float64(0.049812941367941496)} 

err list= [np.float64(0.034212944003947976), np.float64(0.040741125493756), np.float64(0.06729769597406496), np.float64(0.0458129413679415), np.float64(0.029812941367941492), np.float64(0.016812941367941495), np.float64(0.049812941367941496)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3715782320782824), 3: np.float64(0.31141945935392007), 9: np.float64(0.20375606568915458), 83: np.float64(0.02831156071966116), 79: np.float64(0.02831156071966116), 70: np.float64(0.02831156071966116), 0: np.float64(0.02831156071966116)}
err dic= {1: np.float64(0.10657823207828238), 3: np.float64(0.06041945935392007), 9: np.float64(0.031243934310845406), 83: np.float64(0.023688439280338838), 79: np.float64(0.03968843928033884), 70: np.float64(0.05268843928033884), 0: np.float64(0.01968843928033884)} 

err list= [np.float64(0.10657823207828238), np.float64(0.06041945935392007), np.float64(0.031243934310845406), np.float64(0.023688439280338838), np.float64(0.03968843928033884), np.float64(0.05268843928033884), np.float64(0.01968843928033884)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5304684402048608), 3: np.float64(0.3465715230382026), 9: np.float64(0.12058630771338516), 83: np.float64(0.0005934322608876287), 79: np.float64(0.0005934322608876287), 70: np.float64(0.0005934322608876287), 0: np.float64(0.0005934322608876287)}
err dic= {1: np.float64(0.2654684402048608), 3: np.float64(0.0955715230382026), 9: np.float64(0.11441369228661483), 83: np.float64(0.05140656773911237), 79: np.float64(0.06740656773911238), 70: np.float64(0.08040656773911238), 0: np.float64(0.04740656773911237)} 

err list= [np.float64(0.2654684402048608), np.float64(0.0955715230382026), np.float64(0.11441369228661483), np.float64(0.05140656773911237), np.float64(0.06740656773911238), np.float64(0.08040656773911238), np.float64(0.04740656773911237)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6768070636565284), 3: np.float64(0.29176196494779977), 9: np.float64(0.03142991748392354), 83: np.float64(2.6347793718826716e-07), 79: np.float64(2.6347793718826716e-07), 70: np.float64(2.6347793718826716e-07), 0: np.float64(2.6347793718826716e-07)}
err dic= {1: np.float64(0.4118070636565284), 3: np.float64(0.04076196494779977), 9: np.float64(0.20357008251607644), 83: np.float64(0.05199973652206281), 79: np.float64(0.06799973652206281), 70: np.float64(0.08099973652206281), 0: np.float64(0.04799973652206281)} 

err list= [np.float64(0.4118070636565284), np.float64(0.04076196494779977), np.float64(0.20357008251607644), np.float64(0.05199973652206281), np.float64(0.06799973652206281), np.float64(0.08099973652206281), np.float64(0.04799973652206281)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7741057019718852), 3: np.float64(0.21917863841330323), 9: np.float64(0.006715659311346114), 83: np.float64(7.586630896144562e-11), 79: np.float64(7.586630896144562e-11), 70: np.float64(7.586630896144562e-11), 0: np.float64(7.586630896144562e-11)}
err dic= {1: np.float64(0.5091057019718852), 3: np.float64(0.03182136158669677), 9: np.float64(0.2282843406886539), 83: np.float64(0.05199999992413369), 79: np.float64(0.06799999992413369), 70: np.float64(0.08099999992413369), 0: np.float64(0.047999999924133695)} 

err list= [np.float64(0.5091057019718852), np.float64(0.03182136158669677), np.float64(0.2282843406886539), np.float64(0.05199999992413369), np.float64(0.06799999992413369), np.float64(0.08099999992413369), np.float64(0.047999999924133695)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.843119712953552), 3: np.float64(0.1555712984978038), 9: np.float64(0.001308988548555622), 83: np.float64(2.2231120615599807e-14), 79: np.float64(2.2231120615599807e-14), 70: np.float64(2.2231120615599807e-14), 0: np.float64(2.2231120615599807e-14)}
err dic= {1: np.float64(0.578119712953552), 3: np.float64(0.0954287015021962), 9: np.float64(0.23369101145144436), 83: np.float64(0.051999999999977765), 79: np.float64(0.06799999999997777), 70: np.float64(0.08099999999997777), 0: np.float64(0.04799999999997777)} 

err list= [np.float64(0.578119712953552), np.float64(0.0954287015021962), np.float64(0.23369101145144436), np.float64(0.051999999999977765), np.float64(0.06799999999997777), np.float64(0.08099999999997777), np.float64(0.04799999999997777)]
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(6.6682699092242944e-18), 79: np.float64(6.6682699092242944e-18), 70: np.float64(6.6682699092242944e-18), 0: np.float64(6.6682699092242944e-18)}
err dic= {1: np.float64(0.6281967343909478), 3: np.float64(0.14444174658875236), 9: np.float64(0.2347549878021958), 83: np.float64(0.05199999999999999), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.047999999999999994)} 

err list= [np.float64(0.6281967343909478), np.float64(0.14444174658875236), np.float64(0.2347549878021958), np.float64(0.05199999999999999), np.float64(0.068), np.float64(0.081), np.float64(0.047999999999999994)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707240606472), 3: np.float64(0.07108431987050234), 9: np.float64(4.495606885052531e-05), 83: np.float64(2.0363278218645007e-21), 79: np.float64(2.0363278218645007e-21), 70: np.float64(2.0363278218645007e-21), 0: np.float64(2.0363278218645007e-21)}
err dic= {1: np.float64(0.6638707240606472), 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(0.6638707240606472), 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(0.046448925805603274), 9: np.float64(8.149779623627911e-06), 83: np.float64(6.293425458517491e-25), 79: np.float64(6.293425458517491e-25), 70: np.float64(6.293425458517491e-25), 0: np.float64(6.293425458517491e-25)}
err dic= {1: np.float64(0.6885429244147727), 3: np.float64(0.20455107419439672), 9: np.float64(0.23499185022037636), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

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

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386587635774), 3: np.float64(0.029859876603523985), 9: np.float64(1.4646328981753289e-06), 83: np.float64(1.959823627484453e-28), 79: np.float64(1.959823627484453e-28), 70: np.float64(1.959823627484453e-28), 0: np.float64(1.959823627484453e-28)}
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(0.14513242287599126), 4: np.float64(0.13519661365548488), 8: np.float64(0.12302676139402133), 32: np.float64(0.14916105051862613), 27: np.float64(0.14916105051862613), 82: np.float64(0.14916105051862613), 0: np.float64(0.14916105051862613)}
err dic= {1: np.float64(0.07686757712400874), 4: np.float64(0.09480338634451513), 8: np.float64(0.10897323860597868), 32: np.float64(0.04716105051862614), 27: np.float64(0.029161050518626136), 82: np.float64(0.09916105051862613), 0: np.float64(0.10516105051862613)} 

err list= [np.float64(0.07686757712400874), np.float64(0.09480338634451513), np.float64(0.10897323860597868), np.float64(0.04716105051862614), np.float64(0.029161050518626136), np.float64(0.09916105051862613), np.float64(0.10516105051862613)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.23224668253904954), 4: np.float64(0.20260573658856224), 8: np.float64(0.16882025670122386), 32: np.float64(0.09908183104279049), 27: np.float64(0.09908183104279049), 82: np.float64(0.09908183104279049), 0: np.float64(0.09908183104279049)}
err dic= {1: np.float64(0.010246682539049534), 4: np.float64(0.027394263411437775), 8: np.float64(0.06317974329877615), 32: np.float64(0.002918168957209505), 27: np.float64(0.020918168957209507), 82: np.float64(0.049081831042790486), 0: np.float64(0.05508183104279049)} 

err list= [np.float64(0.010246682539049534), np.float64(0.027394263411437775), np.float64(0.06317974329877615), np.float64(0.002918168957209505), np.float64(0.020918168957209507), np.float64(0.049081831042790486), np.float64(0.05508183104279049)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.379252058154081), 4: np.float64(0.2941831972864956), 8: np.float64(0.20849992794700525), 32: np.float64(0.029516204153104953), 27: np.float64(0.029516204153104953), 82: np.float64(0.029516204153104953), 0: np.float64(0.029516204153104953)}
err dic= {1: np.float64(0.15725205815408097), 4: np.float64(0.0641831972864956), 8: np.float64(0.023500072052994758), 32: np.float64(0.07248379584689504), 27: np.float64(0.09048379584689505), 82: np.float64(0.02048379584689505), 0: np.float64(0.014483795846895044)} 

err list= [np.float64(0.15725205815408097), np.float64(0.0641831972864956), np.float64(0.023500072052994758), np.float64(0.07248379584689504), np.float64(0.09048379584689505), np.float64(0.02048379584689505), np.float64(0.014483795846895044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5606472323864409), 4: np.float64(0.30663863018056176), 8: np.float64(0.1301532199028808), 32: np.float64(0.0006402293825288791), 27: np.float64(0.0006402293825288791), 82: np.float64(0.0006402293825288791), 0: np.float64(0.0006402293825288791)}
err dic= {1: np.float64(0.3386472323864409), 4: np.float64(0.07663863018056175), 8: np.float64(0.1018467800971192), 32: np.float64(0.10135977061747112), 27: np.float64(0.11935977061747112), 82: np.float64(0.04935977061747113), 0: np.float64(0.04335977061747112)} 

err list= [np.float64(0.3386472323864409), np.float64(0.07663863018056175), np.float64(0.1018467800971192), np.float64(0.10135977061747112), np.float64(0.11935977061747112), np.float64(0.04935977061747113), np.float64(0.04335977061747112)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.738300043823492), 4: np.float64(0.224656388024082), 8: np.float64(0.03704232220155934), 32: np.float64(3.114877167863767e-07), 27: np.float64(3.114877167863767e-07), 82: np.float64(3.114877167863767e-07), 0: np.float64(3.114877167863767e-07)}
err dic= {1: np.float64(0.516300043823492), 4: np.float64(0.005343611975918011), 8: np.float64(0.19495767779844067), 32: np.float64(0.10199968851228321), 27: np.float64(0.11999968851228321), 82: np.float64(0.049999688512283216), 0: np.float64(0.04399968851228321)} 

err list= [np.float64(0.516300043823492), np.float64(0.005343611975918011), np.float64(0.19495767779844067), np.float64(0.10199968851228321), np.float64(0.11999968851228321), np.float64(0.049999688512283216), np.float64(0.04399968851228321)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8494867466444627), 4: np.float64(0.1419625131558573), 8: np.float64(0.008550739811834877), 32: np.float64(9.69612204599512e-11), 27: np.float64(9.69612204599512e-11), 82: np.float64(9.69612204599512e-11), 0: np.float64(9.69612204599512e-11)}
err dic= {1: np.float64(0.6274867466444627), 4: np.float64(0.0880374868441427), 8: np.float64(0.22344926018816513), 32: np.float64(0.10199999990303878), 27: np.float64(0.11999999990303878), 82: np.float64(0.04999999990303878), 0: np.float64(0.043999999903038774)} 

err list= [np.float64(0.6274867466444627), np.float64(0.0880374868441427), np.float64(0.22344926018816513), np.float64(0.10199999990303878), np.float64(0.11999999990303878), np.float64(0.04999999990303878), np.float64(0.043999999903038774)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159711584828698), 4: np.float64(0.08226343877514228), 8: np.float64(0.001765402741867987), 32: np.float64(3.004999761778332e-14), 27: np.float64(3.004999761778332e-14), 82: np.float64(3.004999761778332e-14), 0: np.float64(3.004999761778332e-14)}
err dic= {1: np.float64(0.6939711584828698), 4: np.float64(0.14773656122485773), 8: np.float64(0.23023459725813203), 32: np.float64(0.10199999999996995), 27: np.float64(0.11999999999996995), 82: np.float64(0.04999999999996995), 0: np.float64(0.043999999999969945)} 

err list= [np.float64(0.6939711584828698), np.float64(0.14773656122485773), np.float64(0.23023459725813203), np.float64(0.10199999999996995), np.float64(0.11999999999996995), np.float64(0.04999999999996995), np.float64(0.043999999999969945)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545811653267547), 4: np.float64(0.04507527208962381), 8: np.float64(0.0003435625836213035), 32: np.float64(9.359754871710872e-18), 27: np.float64(9.359754871710872e-18), 82: np.float64(9.359754871710872e-18), 0: np.float64(9.359754871710872e-18)}
err dic= {1: np.float64(0.7325811653267548), 4: np.float64(0.1849247279103762), 8: np.float64(0.2316564374163787), 32: np.float64(0.10199999999999998), 27: np.float64(0.11999999999999998), 82: np.float64(0.049999999999999996), 0: np.float64(0.04399999999999999)} 

err list= [np.float64(0.7325811653267548), np.float64(0.1849247279103762), np.float64(0.2316564374163787), np.float64(0.10199999999999998), np.float64(0.11999999999999998), np.float64(0.049999999999999996), np.float64(0.04399999999999999)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9761795795657281), 4: np.float64(0.02375577729882298), 8: np.float64(6.464313544905663e-05), 32: np.float64(2.9291794862720376e-21), 27: np.float64(2.9291794862720376e-21), 82: np.float64(2.9291794862720376e-21), 0: np.float64(2.9291794862720376e-21)}
err dic= {1: np.float64(0.7541795795657281), 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(0.7541795795657281), 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(0.9878141691253703), 4: np.float64(0.012173924284659169), 8: np.float64(1.1906589970439097e-05), 32: np.float64(9.195711073142601e-25), 27: np.float64(9.195711073142601e-25), 82: np.float64(9.195711073142601e-25), 0: np.float64(9.195711073142601e-25)}
err dic= {1: np.float64(0.7658141691253704), 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(0.7658141691253704), 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(2.892091783654862e-28), 27: np.float64(2.892091783654862e-28), 82: np.float64(2.892091783654862e-28), 0: np.float64(2.892091783654862e-28)}
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(0.14878757675443288), 4: np.float64(0.13111866895501875), 6: np.float64(0.12494344727282002), 51: np.float64(0.14878757675443288), 82: np.float64(0.14878757675443288), 41: np.float64(0.14878757675443288), 0: np.float64(0.14878757675443288)}
err dic= {9: np.float64(0.07221242324556712), 4: np.float64(0.11388133104498124), 6: np.float64(0.13105655272717998), 51: np.float64(0.06278757675443289), 82: np.float64(0.10878757675443287), 41: np.float64(0.05578757675443288), 0: np.float64(0.08978757675443289)} 

err list= [np.float64(0.07221242324556712), np.float64(0.11388133104498124), np.float64(0.13105655272717998), np.float64(0.06278757675443289), np.float64(0.10878757675443287), np.float64(0.05578757675443288), np.float64(0.08978757675443289)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.118382351002577), 4: np.float64(0.21365127932439654), 6: np.float64(0.19443696566271562), 51: np.float64(0.118382351002577), 82: np.float64(0.118382351002577), 41: np.float64(0.118382351002577), 0: np.float64(0.118382351002577)}
err dic= {9: np.float64(0.102617648997423), 4: np.float64(0.03134872067560346), 6: np.float64(0.061563034337284384), 51: np.float64(0.03238235100257701), 82: np.float64(0.07838235100257701), 41: np.float64(0.025382351002577005), 0: np.float64(0.05938235100257701)} 

err list= [np.float64(0.102617648997423), np.float64(0.03134872067560346), np.float64(0.061563034337284384), np.float64(0.03238235100257701), np.float64(0.07838235100257701), np.float64(0.025382351002577005), np.float64(0.05938235100257701)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.057758899629979946), 4: np.float64(0.38723192064816087), 6: np.float64(0.32397358120193986), 51: np.float64(0.057758899629979946), 82: np.float64(0.057758899629979946), 41: np.float64(0.057758899629979946), 0: np.float64(0.057758899629979946)}
err dic= {9: np.float64(0.16324110037002004), 4: np.float64(0.14223192064816087), 6: np.float64(0.06797358120193986), 51: np.float64(0.028241100370020047), 82: np.float64(0.017758899629979945), 41: np.float64(0.035241100370020054), 0: np.float64(0.0012411003700200512)} 

err list= [np.float64(0.16324110037002004), np.float64(0.14223192064816087), np.float64(0.06797358120193986), np.float64(0.028241100370020047), np.float64(0.017758899629979945), np.float64(0.035241100370020054), np.float64(0.0012411003700200512)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.0018220514404302282), 4: np.float64(0.5974625282717161), 6: np.float64(0.3934272145261327), 51: np.float64(0.0018220514404302282), 82: np.float64(0.0018220514404302282), 41: np.float64(0.0018220514404302282), 0: np.float64(0.0018220514404302282)}
err dic= {9: np.float64(0.21917794855956976), 4: np.float64(0.3524625282717161), 6: np.float64(0.1374272145261327), 51: np.float64(0.08417794855956977), 82: np.float64(0.038177948559569776), 41: np.float64(0.09117794855956977), 0: np.float64(0.05717794855956977)} 

err list= [np.float64(0.21917794855956976), np.float64(0.3524625282717161), np.float64(0.1374272145261327), np.float64(0.08417794855956977), np.float64(0.038177948559569776), np.float64(0.09117794855956977), np.float64(0.05717794855956977)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(1.5701779872046649e-06), 4: np.float64(0.6976921071650287), 6: np.float64(0.3023000419450355), 51: np.float64(1.5701779872046649e-06), 82: np.float64(1.5701779872046649e-06), 41: np.float64(1.5701779872046649e-06), 0: np.float64(1.5701779872046649e-06)}
err dic= {9: np.float64(0.2209984298220128), 4: np.float64(0.4526921071650287), 6: np.float64(0.04630004194503551), 51: np.float64(0.08599842982201279), 82: np.float64(0.03999842982201279), 41: np.float64(0.0929984298220128), 0: np.float64(0.05899842982201279)} 

err list= [np.float64(0.2209984298220128), np.float64(0.4526921071650287), np.float64(0.04630004194503551), np.float64(0.08599842982201279), np.float64(0.03999842982201279), np.float64(0.0929984298220128), np.float64(0.05899842982201279)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(1.1971938538551756e-09), 4: np.float64(0.7790173129478278), 6: np.float64(0.22098268106620306), 51: np.float64(1.1971938538551756e-09), 82: np.float64(1.1971938538551756e-09), 41: np.float64(1.1971938538551756e-09), 0: np.float64(1.1971938538551756e-09)}
err dic= {9: np.float64(0.22099999880280616), 4: np.float64(0.5340173129478278), 6: np.float64(0.03501731893379695), 51: np.float64(0.08599999880280614), 82: np.float64(0.03999999880280615), 41: np.float64(0.09299999880280614), 0: np.float64(0.058999998802806146)} 

err list= [np.float64(0.22099999880280616), np.float64(0.5340173129478278), np.float64(0.03501731893379695), np.float64(0.08599999880280614), np.float64(0.03999999880280615), np.float64(0.09299999880280614), np.float64(0.058999998802806146)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(9.2181572383986e-13), 4: np.float64(0.8441518039707983), 6: np.float64(0.15584819602459285), 51: np.float64(9.2181572383986e-13), 82: np.float64(9.2181572383986e-13), 41: np.float64(9.2181572383986e-13), 0: np.float64(9.2181572383986e-13)}
err dic= {9: np.float64(0.22099999999907818), 4: np.float64(0.5991518039707983), 6: np.float64(0.10015180397540716), 51: np.float64(0.08599999999907817), 82: np.float64(0.03999999999907818), 41: np.float64(0.09299999999907818), 0: np.float64(0.05899999999907818)} 

err list= [np.float64(0.22099999999907818), np.float64(0.5991518039707983), np.float64(0.10015180397540716), np.float64(0.08599999999907817), np.float64(0.03999999999907818), np.float64(0.09299999999907818), np.float64(0.05899999999907818)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(7.164538612806617e-16), 4: np.float64(0.8934014727128801), 6: np.float64(0.10659852728711604), 51: np.float64(7.164538612806617e-16), 82: np.float64(7.164538612806617e-16), 41: np.float64(7.164538612806617e-16), 0: np.float64(7.164538612806617e-16)}
err dic= {9: np.float64(0.22099999999999928), 4: np.float64(0.6484014727128801), 6: np.float64(0.14940147271288395), 51: np.float64(0.08599999999999927), 82: np.float64(0.039999999999999286), 41: np.float64(0.09299999999999928), 0: np.float64(0.05899999999999928)} 

err list= [np.float64(0.22099999999999928), np.float64(0.6484014727128801), np.float64(0.14940147271288395), np.float64(0.08599999999999927), np.float64(0.039999999999999286), np.float64(0.09299999999999928), np.float64(0.05899999999999928)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(5.622842661505782e-19), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(5.622842661505782e-19), 82: np.float64(5.622842661505782e-19), 41: np.float64(5.622842661505782e-19), 0: np.float64(5.622842661505782e-19)}
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(4.449186297062545e-22), 4: np.float64(0.9535502818108355), 6: np.float64(0.046449718189164366), 51: np.float64(4.449186297062545e-22), 82: np.float64(4.449186297062545e-22), 41: np.float64(4.449186297062545e-22), 0: np.float64(4.449186297062545e-22)}
err dic= {9: np.float64(0.221), 4: np.float64(0.7085502818108355), 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(0.7085502818108355), 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(3.5416511254901574e-25), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(3.5416511254901574e-25), 82: np.float64(3.5416511254901574e-25), 41: np.float64(3.5416511254901574e-25), 0: np.float64(3.5416511254901574e-25)}
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(0.1519899731825775), 9: np.float64(0.13813031186107683), 6: np.float64(0.14823732737388826), 39: np.float64(0.14041059689561466), 80: np.float64(0.14041059689561466), 68: np.float64(0.14041059689561466), 0: np.float64(0.14041059689561466)}
err dic= {5: np.float64(0.09301002681742249), 9: np.float64(0.08986968813892318), 6: np.float64(0.10976267262611175), 39: np.float64(0.04041059689561466), 80: np.float64(0.07741059689561466), 68: np.float64(0.08441059689561467), 0: np.float64(0.09041059689561466)} 

err list= [np.float64(0.09301002681742249), np.float64(0.08986968813892318), np.float64(0.10976267262611175), np.float64(0.04041059689561466), np.float64(0.07741059689561466), np.float64(0.08441059689561467), np.float64(0.09041059689561466)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.22576229145687526), 9: np.float64(0.18726868189282642), 6: np.float64(0.2147517345764861), 39: np.float64(0.09305432301845032), 80: np.float64(0.09305432301845032), 68: np.float64(0.09305432301845032), 0: np.float64(0.09305432301845032)}
err dic= {5: np.float64(0.019237708543124732), 9: np.float64(0.04073131810717359), 6: np.float64(0.0432482654235139), 39: np.float64(0.006945676981549687), 80: np.float64(0.03005432301845032), 68: np.float64(0.03705432301845032), 0: np.float64(0.043054323018450316)} 

err list= [np.float64(0.019237708543124732), np.float64(0.04073131810717359), np.float64(0.0432482654235139), np.float64(0.006945676981549687), np.float64(0.03005432301845032), np.float64(0.03705432301845032), np.float64(0.043054323018450316)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.33801027403787204), 9: np.float64(0.23570874930556923), 6: np.float64(0.30584434363005547), 39: np.float64(0.030109158256627657), 80: np.float64(0.030109158256627657), 68: np.float64(0.030109158256627657), 0: np.float64(0.030109158256627657)}
err dic= {5: np.float64(0.09301027403787204), 9: np.float64(0.0077087493055692236), 6: np.float64(0.047844343630055464), 39: np.float64(0.06989084174337235), 80: np.float64(0.03289084174337234), 68: np.float64(0.025890841743372344), 0: np.float64(0.019890841743372346)} 

err list= [np.float64(0.09301027403787204), np.float64(0.0077087493055692236), np.float64(0.047844343630055464), np.float64(0.06989084174337235), np.float64(0.03289084174337234), np.float64(0.025890841743372344), np.float64(0.019890841743372346)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.45534558522749946), 9: np.float64(0.18671578573223618), 6: np.float64(0.35462349834328366), 39: np.float64(0.0008287826742450379), 80: np.float64(0.0008287826742450379), 68: np.float64(0.0008287826742450379), 0: np.float64(0.0008287826742450379)}
err dic= {5: np.float64(0.21034558522749947), 9: np.float64(0.041284214267763825), 6: np.float64(0.09662349834328365), 39: np.float64(0.09917121732575497), 80: np.float64(0.062171217325754966), 68: np.float64(0.055171217325754966), 0: np.float64(0.04917121732575497)} 

err list= [np.float64(0.21034558522749947), np.float64(0.041284214267763825), np.float64(0.09662349834328365), np.float64(0.09917121732575497), np.float64(0.062171217325754966), np.float64(0.055171217325754966), np.float64(0.04917121732575497)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5654173673737399), 9: np.float64(0.09163714938775556), 6: np.float64(0.3429429688461749), 39: np.float64(6.285980824705831e-07), 80: np.float64(6.285980824705831e-07), 68: np.float64(6.285980824705831e-07), 0: np.float64(6.285980824705831e-07)}
err dic= {5: np.float64(0.32041736737373994), 9: np.float64(0.13636285061224446), 6: np.float64(0.08494296884617492), 39: np.float64(0.09999937140191753), 80: np.float64(0.06299937140191753), 68: np.float64(0.05599937140191753), 0: np.float64(0.049999371401917535)} 

err list= [np.float64(0.32041736737373994), np.float64(0.13636285061224446), np.float64(0.08494296884617492), np.float64(0.09999937140191753), np.float64(0.06299937140191753), np.float64(0.05599937140191753), np.float64(0.049999371401917535)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6518852866171935), 9: np.float64(0.04018590646608363), 6: np.float64(0.307928805621952), 39: np.float64(3.2369278450607e-10), 80: np.float64(3.2369278450607e-10), 68: np.float64(3.2369278450607e-10), 0: np.float64(3.2369278450607e-10)}
err dic= {5: np.float64(0.4068852866171935), 9: np.float64(0.18781409353391637), 6: np.float64(0.04992880562195201), 39: np.float64(0.09999999967630722), 80: np.float64(0.06299999967630722), 68: np.float64(0.05599999967630721), 0: np.float64(0.049999999676307215)} 

err list= [np.float64(0.4068852866171935), np.float64(0.18781409353391637), np.float64(0.04992880562195201), np.float64(0.09999999967630722), np.float64(0.06299999967630722), np.float64(0.05599999967630721), np.float64(0.049999999676307215)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7191002954874188), 9: np.float64(0.016357489661762956), 6: np.float64(0.2645422148501306), 39: np.float64(1.72051429574958e-13), 80: np.float64(1.72051429574958e-13), 68: np.float64(1.72051429574958e-13), 0: np.float64(1.72051429574958e-13)}
err dic= {5: np.float64(0.47410029548741883), 9: np.float64(0.21164251033823706), 6: np.float64(0.006542214850130568), 39: np.float64(0.09999999999982795), 80: np.float64(0.06299999999982794), 68: np.float64(0.05599999999982795), 0: np.float64(0.04999999999982795)} 

err list= [np.float64(0.47410029548741883), np.float64(0.21164251033823706), np.float64(0.006542214850130568), np.float64(0.09999999999982795), np.float64(0.06299999999982794), np.float64(0.05599999999982795), np.float64(0.04999999999982795)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723569153432929), 9: np.float64(0.006359123522713143), 6: np.float64(0.22128396113399318), 39: np.float64(9.357271900164296e-17), 80: np.float64(9.357271900164296e-17), 68: np.float64(9.357271900164296e-17), 0: np.float64(9.357271900164296e-17)}
err dic= {5: np.float64(0.5273569153432929), 9: np.float64(0.22164087647728686), 6: np.float64(0.03671603886600683), 39: np.float64(0.09999999999999991), 80: np.float64(0.0629999999999999), 68: np.float64(0.05599999999999991), 0: np.float64(0.04999999999999991)} 

err list= [np.float64(0.5273569153432929), np.float64(0.22164087647728686), np.float64(0.03671603886600683), np.float64(0.09999999999999991), np.float64(0.0629999999999999), np.float64(0.05599999999999991), np.float64(0.04999999999999991)]
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(5.1746031031593e-20), 80: np.float64(5.1746031031593e-20), 68: np.float64(5.1746031031593e-20), 0: np.float64(5.1746031031593e-20)}
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(2.898756387823114e-23), 80: np.float64(2.898756387823114e-23), 68: np.float64(2.898756387823114e-23), 0: np.float64(2.898756387823114e-23)}
err dic= {5: np.float64(0.6061869021360521), 9: np.float64(0.2271010067336025), 6: np.float64(0.11008589540245015), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

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

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036406466493), 9: np.float64(0.00033314975556754796), 6: np.float64(0.11916320959778291), 39: np.float64(1.640814537406912e-26), 80: np.float64(1.640814537406912e-26), 68: np.float64(1.640814537406912e-26), 0: np.float64(1.640814537406912e-26)}
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(0.13014607988823046), 3: np.float64(0.13973369918054576), 8: np.float64(0.12402849048679454), 15: np.float64(0.15152293261110825), 78: np.float64(0.15152293261110825), 97: np.float64(0.15152293261110825), 0: np.float64(0.15152293261110825)}
err dic= {6: np.float64(0.09085392011176954), 3: np.float64(0.09526630081945422), 8: np.float64(0.11397150951320545), 15: np.float64(0.02147706738889174), 78: np.float64(0.09552293261110825), 97: np.float64(0.11252293261110824), 0: np.float64(0.11352293261110824)} 

err list= [np.float64(0.09085392011176954), np.float64(0.09526630081945422), np.float64(0.11397150951320545), np.float64(0.02147706738889174), np.float64(0.09552293261110825), np.float64(0.11252293261110824), np.float64(0.11352293261110824)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.1905537069196371), 3: np.float64(0.21862544363898703), 8: np.float64(0.1734021317396734), 15: np.float64(0.10435467942542447), 78: np.float64(0.10435467942542447), 97: np.float64(0.10435467942542447), 0: np.float64(0.10435467942542447)}
err dic= {6: np.float64(0.030446293080362896), 3: np.float64(0.016374556361012954), 8: np.float64(0.0645978682603266), 15: np.float64(0.06864532057457552), 78: np.float64(0.048354679425424464), 97: np.float64(0.06535467942542447), 0: np.float64(0.06635467942542447)} 

err list= [np.float64(0.030446293080362896), np.float64(0.016374556361012954), np.float64(0.0645978682603266), np.float64(0.06864532057457552), np.float64(0.048354679425424464), np.float64(0.06535467942542447), np.float64(0.06635467942542447)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.27494339372632887), 3: np.float64(0.35554282277296), 8: np.float64(0.2292519362301032), 15: np.float64(0.035065461817652264), 78: np.float64(0.035065461817652264), 97: np.float64(0.035065461817652264), 0: np.float64(0.035065461817652264)}
err dic= {6: np.float64(0.053943393726328864), 3: np.float64(0.12054282277296002), 8: np.float64(0.008748063769896786), 15: np.float64(0.13793453818234772), 78: np.float64(0.020934538182347737), 97: np.float64(0.0039345381823477354), 0: np.float64(0.0029345381823477346)} 

err list= [np.float64(0.053943393726328864), np.float64(0.12054282277296002), np.float64(0.008748063769896786), np.float64(0.13793453818234772), np.float64(0.020934538182347737), np.float64(0.0039345381823477354), np.float64(0.0029345381823477346)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2864297564135497), 3: np.float64(0.5272084465400095), 8: np.float64(0.18277055784934604), 15: np.float64(0.0008978097992733856), 78: np.float64(0.0008978097992733856), 97: np.float64(0.0008978097992733856), 0: np.float64(0.0008978097992733856)}
err dic= {6: np.float64(0.06542975641354967), 3: np.float64(0.29220844654000955), 8: np.float64(0.05522944215065395), 15: np.float64(0.1721021902007266), 78: np.float64(0.05510219020072662), 97: np.float64(0.03810219020072662), 0: np.float64(0.037102190200726616)} 

err list= [np.float64(0.06542975641354967), np.float64(0.29220844654000955), np.float64(0.05522944215065395), np.float64(0.1721021902007266), np.float64(0.05510219020072662), np.float64(0.03810219020072662), np.float64(0.037102190200726616)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.21136650438352955), 3: np.float64(0.7045751307309608), 8: np.float64(0.08405549497900901), 15: np.float64(7.174766252960577e-07), 78: np.float64(7.174766252960577e-07), 97: np.float64(7.174766252960577e-07), 0: np.float64(7.174766252960577e-07)}
err dic= {6: np.float64(0.00963349561647045), 3: np.float64(0.4695751307309608), 8: np.float64(0.153944505020991), 15: np.float64(0.17299928252337468), 78: np.float64(0.0559992825233747), 97: np.float64(0.0389992825233747), 0: np.float64(0.0379992825233747)} 

err list= [np.float64(0.00963349561647045), np.float64(0.4695751307309608), np.float64(0.153944505020991), np.float64(0.17299928252337468), np.float64(0.0559992825233747), np.float64(0.0389992825233747), np.float64(0.0379992825233747)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13673323297138326), 3: np.float64(0.830037871555994), 8: np.float64(0.033228893931249705), 15: np.float64(3.8534323339496353e-10), 78: np.float64(3.8534323339496353e-10), 97: np.float64(3.8534323339496353e-10), 0: np.float64(3.8534323339496353e-10)}
err dic= {6: np.float64(0.08426676702861674), 3: np.float64(0.595037871555994), 8: np.float64(0.2047711060687503), 15: np.float64(0.17299999961465676), 78: np.float64(0.055999999614656765), 97: np.float64(0.03899999961465676), 0: np.float64(0.03799999961465676)} 

err list= [np.float64(0.08426676702861674), np.float64(0.595037871555994), np.float64(0.2047711060687503), np.float64(0.17299999961465676), np.float64(0.055999999614656765), np.float64(0.03899999961465676), np.float64(0.03799999961465676)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.08066515382262558), 3: np.float64(0.9074958368078069), 8: np.float64(0.011839009368747613), 15: np.float64(2.0504339003773626e-13), 78: np.float64(2.0504339003773626e-13), 97: np.float64(2.0504339003773626e-13), 0: np.float64(2.0504339003773626e-13)}
err dic= {6: np.float64(0.1403348461773744), 3: np.float64(0.6724958368078069), 8: np.float64(0.2261609906312524), 15: np.float64(0.17299999999979496), 78: np.float64(0.05599999999979496), 97: np.float64(0.038999999999794956), 0: np.float64(0.037999999999794955)} 

err list= [np.float64(0.1403348461773744), np.float64(0.6724958368078069), np.float64(0.2261609906312524), np.float64(0.17299999999979496), np.float64(0.05599999999979496), np.float64(0.038999999999794956), np.float64(0.037999999999794955)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.04464840069712352), 3: np.float64(0.9514153882278128), 8: np.float64(0.003936211075063265), 15: np.float64(1.0837503104568679e-16), 78: np.float64(1.0837503104568679e-16), 97: np.float64(1.0837503104568679e-16), 0: np.float64(1.0837503104568679e-16)}
err dic= {6: np.float64(0.17635159930287647), 3: np.float64(0.7164153882278128), 8: np.float64(0.23406378892493673), 15: np.float64(0.17299999999999988), 78: np.float64(0.05599999999999989), 97: np.float64(0.03899999999999989), 0: np.float64(0.03799999999999989)} 

err list= [np.float64(0.17635159930287647), np.float64(0.7164153882278128), np.float64(0.23406378892493673), np.float64(0.17299999999999988), np.float64(0.05599999999999989), np.float64(0.03899999999999989), np.float64(0.03799999999999989)]
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(0.9750994307929841), 8: np.float64(0.0012505556826808662), 15: np.float64(5.699422441203433e-20), 78: np.float64(5.699422441203433e-20), 97: np.float64(5.699422441203433e-20), 0: np.float64(5.699422441203433e-20)}
err dic= {6: np.float64(0.19734998647566443), 3: np.float64(0.7400994307929841), 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(0.7400994307929841), 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(0.01214882045989001), 3: np.float64(0.9874656934961611), 8: np.float64(0.00038548604394830424), 15: np.float64(2.986033212026252e-23), 78: np.float64(2.986033212026252e-23), 97: np.float64(2.986033212026252e-23), 0: np.float64(2.986033212026252e-23)}
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(1.5601500141696597e-26), 78: np.float64(1.5601500141696597e-26), 97: np.float64(1.5601500141696597e-26), 0: np.float64(1.5601500141696597e-26)}
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(0.1333829488777747), 2: np.float64(0.1535783936844405), 4: np.float64(0.14643387070002217), 95: np.float64(0.14648769495267483), 11: np.float64(0.12714170187973806), 22: np.float64(0.14648769495267483), 0: np.float64(0.14648769495267483)}
err dic= {8: np.float64(0.1016170511222253), 2: np.float64(0.0484216063155595), 4: np.float64(0.050566129299977836), 95: np.float64(0.10448769495267482), 11: np.float64(0.03885829812026195), 22: np.float64(0.009487694952674819), 0: np.float64(0.12548769495267484)} 

err list= [np.float64(0.1016170511222253), np.float64(0.0484216063155595), np.float64(0.050566129299977836), np.float64(0.10448769495267482), np.float64(0.03885829812026195), np.float64(0.009487694952674819), np.float64(0.12548769495267484)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.17108745296608863), 2: np.float64(0.22481824311323317), 4: np.float64(0.2049161467408679), 95: np.float64(0.081157128043853), 11: np.float64(0.15570677304824218), 22: np.float64(0.081157128043853), 0: np.float64(0.081157128043853)}
err dic= {8: np.float64(0.06391254703391136), 2: np.float64(0.02281824311323316), 4: np.float64(0.00791614674086788), 95: np.float64(0.039157128043853), 11: np.float64(0.010293226951757828), 22: np.float64(0.05584287195614701), 0: np.float64(0.060157128043852995)} 

err list= [np.float64(0.06391254703391136), np.float64(0.02281824311323316), np.float64(0.00791614674086788), np.float64(0.039157128043853), np.float64(0.010293226951757828), np.float64(0.05584287195614701), np.float64(0.060157128043852995)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.1917232406251303), 2: np.float64(0.3236879904256409), 4: np.float64(0.27084514075538146), 95: np.float64(0.018138334001343525), 11: np.float64(0.15932862618982593), 22: np.float64(0.018138334001343525), 0: np.float64(0.018138334001343525)}
err dic= {8: np.float64(0.04327675937486969), 2: np.float64(0.12168799042564088), 4: np.float64(0.07384514075538146), 95: np.float64(0.023861665998656478), 11: np.float64(0.006671373810174075), 22: np.float64(0.11886166599865648), 0: np.float64(0.0028616659986564763)} 

err list= [np.float64(0.04327675937486969), np.float64(0.12168799042564088), np.float64(0.07384514075538146), np.float64(0.023861665998656478), np.float64(0.006671373810174075), np.float64(0.11886166599865648), np.float64(0.0028616659986564763)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.13062503562781314), 2: np.float64(0.4769189587925679), 4: np.float64(0.30961612282812395), 95: np.float64(0.0004484277817794589), 11: np.float64(0.08149459940615672), 22: np.float64(0.0004484277817794589), 0: np.float64(0.0004484277817794589)}
err dic= {8: np.float64(0.10437496437218685), 2: np.float64(0.2749189587925679), 4: np.float64(0.11261612282812394), 95: np.float64(0.04155157221822054), 11: np.float64(0.08450540059384329), 22: np.float64(0.13655157221822056), 0: np.float64(0.020551572218220543)} 

err list= [np.float64(0.10437496437218685), np.float64(0.2749189587925679), np.float64(0.11261612282812394), np.float64(0.04155157221822054), np.float64(0.08450540059384329), np.float64(0.13655157221822056), np.float64(0.020551572218220543)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.047093219932573024), 2: np.float64(0.6544663648226382), 4: np.float64(0.28068024832817595), 95: np.float64(1.8990132917574507e-07), 11: np.float64(0.017759597212625614), 22: np.float64(1.8990132917574507e-07), 0: np.float64(1.8990132917574507e-07)}
err dic= {8: np.float64(0.18790678006742695), 2: np.float64(0.4524663648226382), 4: np.float64(0.08368024832817594), 95: np.float64(0.04199981009867083), 11: np.float64(0.14824040278737438), 22: np.float64(0.13699981009867082), 0: np.float64(0.020999810098670826)} 

err list= [np.float64(0.18790678006742695), np.float64(0.4524663648226382), np.float64(0.08368024832817594), np.float64(0.04199981009867083), np.float64(0.14824040278737438), np.float64(0.13699981009867082), np.float64(0.020999810098670826)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.0135365490125478), 2: np.float64(0.7668515970723313), 4: np.float64(0.21655036653091986), 95: np.float64(5.000066894461938e-11), 11: np.float64(0.0030614872341990064), 22: np.float64(5.000066894461938e-11), 0: np.float64(5.000066894461938e-11)}
err dic= {8: np.float64(0.22146345098745218), 2: np.float64(0.5648515970723313), 4: np.float64(0.01955036653091985), 95: np.float64(0.04199999994999933), 11: np.float64(0.162938512765801), 22: np.float64(0.13699999994999934), 0: np.float64(0.02099999994999933)} 

err list= [np.float64(0.22146345098745218), np.float64(0.5648515970723313), np.float64(0.01955036653091985), np.float64(0.04199999994999933), np.float64(0.162938512765801), np.float64(0.13699999994999934), np.float64(0.02099999994999933)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034775536988860857), 2: np.float64(0.8410328325211283), 4: np.float64(0.15501625097214627), 95: np.float64(1.3218546308132138e-14), 11: np.float64(0.0004733628077999375), 22: np.float64(1.3218546308132138e-14), 0: np.float64(1.3218546308132138e-14)}
err dic= {8: np.float64(0.2315224463011139), 2: np.float64(0.6390328325211283), 4: np.float64(0.041983749027853734), 95: np.float64(0.041999999999986784), 11: np.float64(0.16552663719220007), 22: np.float64(0.1369999999999868), 0: np.float64(0.020999999999986783)} 

err list= [np.float64(0.2315224463011139), np.float64(0.6390328325211283), np.float64(0.041983749027853734), np.float64(0.041999999999986784), np.float64(0.16552663719220007), np.float64(0.1369999999999868), np.float64(0.020999999999986783)]
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(3.538059045984987e-18), 11: np.float64(6.965386583462914e-05), 22: np.float64(3.538059045984987e-18), 0: np.float64(3.538059045984987e-18)}
err dic= {8: np.float64(0.23415326068897938), 2: np.float64(0.6906352815932923), 4: np.float64(0.09055167477014839), 95: np.float64(0.041999999999999996), 11: np.float64(0.16593034613416538), 22: np.float64(0.137), 0: np.float64(0.020999999999999998)} 

err list= [np.float64(0.23415326068897938), np.float64(0.6906352815932923), np.float64(0.09055167477014839), np.float64(0.041999999999999996), np.float64(0.16593034613416538), np.float64(0.137), np.float64(0.020999999999999998)]
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(0.0710633695791427), 95: np.float64(9.582626404986561e-22), 11: np.float64(9.99775588346969e-06), 22: np.float64(9.582626404986561e-22), 0: np.float64(9.582626404986561e-22)}
err dic= {8: np.float64(0.23479933625493712), 2: np.float64(0.7267259689199104), 4: np.float64(0.12593663042085732), 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(0.12593663042085732), 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(2.619127164843276e-25), 11: np.float64(1.414291028627564e-06), 22: np.float64(2.619127164843276e-25), 0: np.float64(2.619127164843276e-25)}
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(7.203996594252231e-29), 11: np.float64(1.9810924551184603e-07), 22: np.float64(7.203996594252231e-29), 0: np.float64(7.203996594252231e-29)}
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(0.1572768069854504), 3: np.float64(0.1499678641403835), 9: np.float64(0.13051819385184663), 100: np.float64(0.12157593185175292), 22: np.float64(0.14688706772352297), 58: np.float64(0.14688706772352297), 0: np.float64(0.14688706772352297)}
err dic= {1: np.float64(0.06072319301454959), 3: np.float64(0.031032135859616505), 9: np.float64(0.06648180614815338), 100: np.float64(0.10042406814824709), 22: np.float64(0.03388706772352297), 58: np.float64(0.10588706772352297), 0: np.float64(0.11888706772352298)} 

err list= [np.float64(0.06072319301454959), np.float64(0.031032135859616505), np.float64(0.06648180614815338), np.float64(0.10042406814824709), np.float64(0.03388706772352297), np.float64(0.10588706772352297), np.float64(0.11888706772352298)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.2348235065102177), 3: np.float64(0.2140940945300482), 9: np.float64(0.1638710910922236), 100: np.float64(0.1425976052229851), 22: np.float64(0.081537900881505), 58: np.float64(0.081537900881505), 0: np.float64(0.081537900881505)}
err dic= {1: np.float64(0.01682350651021769), 3: np.float64(0.03309409453004822), 9: np.float64(0.03312890890777642), 100: np.float64(0.07940239477701491), 22: np.float64(0.031462099118495), 58: np.float64(0.040537900881505), 0: np.float64(0.05353790088150501)} 

err list= [np.float64(0.01682350651021769), np.float64(0.03309409453004822), np.float64(0.03312890890777642), np.float64(0.07940239477701491), np.float64(0.031462099118495), np.float64(0.040537900881505), np.float64(0.05353790088150501)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3470399416162064), 3: np.float64(0.2907198575432173), 9: np.float64(0.17471849105957282), 100: np.float64(0.13297697821162907), 22: np.float64(0.018181577189794164), 58: np.float64(0.018181577189794164), 0: np.float64(0.018181577189794164)}
err dic= {1: np.float64(0.12903994161620638), 3: np.float64(0.10971985754321728), 9: np.float64(0.022281508940427186), 100: np.float64(0.08902302178837093), 22: np.float64(0.09481842281020583), 58: np.float64(0.022818422810205838), 0: np.float64(0.009818422810205837)} 

err list= [np.float64(0.12903994161620638), np.float64(0.10971985754321728), np.float64(0.022281508940427186), np.float64(0.08902302178837093), np.float64(0.09481842281020583), np.float64(0.022818422810205838), np.float64(0.009818422810205837)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5193369703666727), 3: np.float64(0.3387571197521242), 9: np.float64(0.09424125304918166), 100: np.float64(0.04644367747548594), 22: np.float64(0.0004069931188453428), 58: np.float64(0.0004069931188453428), 0: np.float64(0.0004069931188453428)}
err dic= {1: np.float64(0.30133697036667273), 3: np.float64(0.1577571197521242), 9: np.float64(0.10275874695081835), 100: np.float64(0.17555632252451406), 22: np.float64(0.11259300688115466), 58: np.float64(0.04059300688115466), 0: np.float64(0.02759300688115466)} 

err list= [np.float64(0.30133697036667273), np.float64(0.1577571197521242), np.float64(0.10275874695081835), np.float64(0.17555632252451406), np.float64(0.11259300688115466), np.float64(0.04059300688115466), np.float64(0.02759300688115466)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6814821384123474), 3: np.float64(0.2940819442155042), 9: np.float64(0.019892536445678285), 100: np.float64(0.004542991264876723), 22: np.float64(1.298871979141893e-07), 58: np.float64(1.298871979141893e-07), 0: np.float64(1.298871979141893e-07)}
err dic= {1: np.float64(0.4634821384123474), 3: np.float64(0.11308194421550422), 9: np.float64(0.17710746355432172), 100: np.float64(0.21745700873512328), 22: np.float64(0.11299987011280209), 58: np.float64(0.04099987011280209), 0: np.float64(0.027999870112802087)} 

err list= [np.float64(0.4634821384123474), np.float64(0.11308194421550422), np.float64(0.17710746355432172), np.float64(0.21745700873512328), np.float64(0.11299987011280209), np.float64(0.04099987011280209), np.float64(0.027999870112802087)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7763898412376402), 3: np.float64(0.22001307709612006), 9: np.float64(0.0032518487259784903), 100: np.float64(0.00034523286482339254), 22: np.float64(2.514605449875401e-11), 58: np.float64(2.514605449875401e-11), 0: np.float64(2.514605449875401e-11)}
err dic= {1: np.float64(0.5583898412376402), 3: np.float64(0.03901307709612006), 9: np.float64(0.1937481512740215), 100: np.float64(0.22165476713517662), 22: np.float64(0.11299999997485395), 58: np.float64(0.04099999997485395), 0: np.float64(0.027999999974853945)} 

err list= [np.float64(0.5583898412376402), np.float64(0.03901307709612006), np.float64(0.1937481512740215), np.float64(0.22165476713517662), np.float64(0.11299999997485395), np.float64(0.04099999997485395), np.float64(0.027999999974853945)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437493664948538), 3: np.float64(0.15573992576809997), 9: np.float64(0.0004864470221915299), 100: np.float64(2.4260714840119286e-05), 22: np.float64(5.0000987905574394e-15), 58: np.float64(5.0000987905574394e-15), 0: np.float64(5.0000987905574394e-15)}
err dic= {1: np.float64(0.6257493664948538), 3: np.float64(0.02526007423190002), 9: np.float64(0.19651355297780848), 100: np.float64(0.22197573928515987), 22: np.float64(0.11299999999999501), 58: np.float64(0.040999999999995), 0: np.float64(0.027999999999995)} 

err list= [np.float64(0.6257493664948538), np.float64(0.02526007423190002), np.float64(0.19651355297780848), np.float64(0.22197573928515987), np.float64(0.11299999999999501), np.float64(0.040999999999995), np.float64(0.027999999999995)]
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(1.6573248786188938e-06), 22: np.float64(1.0253182064762245e-18), 58: np.float64(1.0253182064762245e-18), 0: np.float64(1.0253182064762245e-18)}
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(0.9289011179586113), 3: np.float64(0.07108872798785827), 9: np.float64(1.0042483851945802e-05), 100: np.float64(1.1156967800869512e-07), 22: np.float64(2.14778747288061e-22), 58: np.float64(2.14778747288061e-22), 0: np.float64(2.14778747288061e-22)}
err dic= {1: np.float64(0.7109011179586113), 3: np.float64(0.10991127201214172), 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(0.7109011179586113), np.float64(0.10991127201214172), 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(4.559180858264662e-26), 58: np.float64(4.559180858264662e-26), 0: np.float64(4.559180858264662e-26)}
err dic= {1: np.float64(0.7355489961513725), 3: np.float64(0.13455042030088832), 9: np.float64(0.19699858328481948), 100: np.float64(0.22199999256566533), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

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

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303256955), 3: np.float64(0.029859970945651217), 9: np.float64(1.9823727027203242e-07), 100: np.float64(4.913822077323317e-10), 22: np.float64(9.755857050909745e-30), 58: np.float64(9.755857050909745e-30), 0: np.float64(9.755857050909745e-30)}
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(0.12817153845281642), 6: np.float64(0.13141621639655107), 8: np.float64(0.1250069718929524), 16: np.float64(0.15385131831442025), 83: np.float64(0.15385131831442025), 70: np.float64(0.15385131831442025), 0: np.float64(0.15385131831442025)}
err dic= {7: np.float64(0.07882846154718356), 6: np.float64(0.11458378360344892), 8: np.float64(0.1239930281070476), 16: np.float64(0.005851318314420262), 83: np.float64(0.10585131831442025), 70: np.float64(0.09585131831442026), 0: np.float64(0.10985131831442026)} 

err list= [np.float64(0.07882846154718356), np.float64(0.11458378360344892), np.float64(0.1239930281070476), np.float64(0.005851318314420262), np.float64(0.10585131831442025), np.float64(0.09585131831442026), np.float64(0.10985131831442026)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.18697921482671884), 6: np.float64(0.19656584417041295), 8: np.float64(0.1778601309132151), 16: np.float64(0.10964870252241257), 83: np.float64(0.10964870252241257), 70: np.float64(0.10964870252241257), 0: np.float64(0.10964870252241257)}
err dic= {7: np.float64(0.020020785173281153), 6: np.float64(0.049434155829587045), 8: np.float64(0.07113986908678491), 16: np.float64(0.03835129747758742), 83: np.float64(0.06164870252241257), 70: np.float64(0.05164870252241257), 0: np.float64(0.06564870252241257)} 

err list= [np.float64(0.020020785173281153), np.float64(0.049434155829587045), np.float64(0.07113986908678491), np.float64(0.03835129747758742), np.float64(0.06164870252241257), np.float64(0.05164870252241257), np.float64(0.06564870252241257)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.27705129176374976), 6: np.float64(0.3061890304725878), 8: np.float64(0.2506863755030388), 16: np.float64(0.041518325565155875), 83: np.float64(0.041518325565155875), 70: np.float64(0.041518325565155875), 0: np.float64(0.041518325565155875)}
err dic= {7: np.float64(0.07005129176374977), 6: np.float64(0.06018903047258778), 8: np.float64(0.001686375503038795), 16: np.float64(0.10648167443484412), 83: np.float64(0.006481674434844126), 70: np.float64(0.016481674434844128), 0: np.float64(0.002481674434844122)} 

err list= [np.float64(0.07005129176374977), np.float64(0.06018903047258778), np.float64(0.001686375503038795), np.float64(0.10648167443484412), np.float64(0.006481674434844126), np.float64(0.016481674434844128), np.float64(0.002481674434844122)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.324871362897561), 6: np.float64(0.417143087114455), 8: np.float64(0.2530100718220951), 16: np.float64(0.0012438695414719186), 83: np.float64(0.0012438695414719186), 70: np.float64(0.0012438695414719186), 0: np.float64(0.0012438695414719186)}
err dic= {7: np.float64(0.11787136289756103), 6: np.float64(0.17114308711445503), 8: np.float64(0.004010071822095118), 16: np.float64(0.14675613045852806), 83: np.float64(0.046756130458528083), 70: np.float64(0.056756130458528085), 0: np.float64(0.04275613045852808)} 

err list= [np.float64(0.11787136289756103), np.float64(0.17114308711445503), np.float64(0.004010071822095118), np.float64(0.14675613045852806), np.float64(0.046756130458528083), np.float64(0.056756130458528085), np.float64(0.04275613045852808)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.3071938913769004), 6: np.float64(0.5064771029422404), 8: np.float64(0.18632251359652247), 16: np.float64(1.6230210843436993e-06), 83: np.float64(1.6230210843436993e-06), 70: np.float64(1.6230210843436993e-06), 0: np.float64(1.6230210843436993e-06)}
err dic= {7: np.float64(0.1001938913769004), 6: np.float64(0.26047710294224036), 8: np.float64(0.06267748640347753), 16: np.float64(0.14799837697891566), 83: np.float64(0.04799837697891566), 70: np.float64(0.05799837697891566), 0: np.float64(0.043998376978915656)} 

err list= [np.float64(0.1001938913769004), np.float64(0.26047710294224036), np.float64(0.06267748640347753), np.float64(0.14799837697891566), np.float64(0.04799837697891566), np.float64(0.05799837697891566), np.float64(0.043998376978915656)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.2786006874176198), 6: np.float64(0.5897976598914035), 8: np.float64(0.131601646306738), 16: np.float64(1.5960596502249146e-09), 83: np.float64(1.5960596502249146e-09), 70: np.float64(1.5960596502249146e-09), 0: np.float64(1.5960596502249146e-09)}
err dic= {7: np.float64(0.0716006874176198), 6: np.float64(0.34379765989140354), 8: np.float64(0.11739835369326199), 16: np.float64(0.14799999840394035), 83: np.float64(0.04799999840394035), 70: np.float64(0.05799999840394035), 0: np.float64(0.043999998403940345)} 

err list= [np.float64(0.0716006874176198), np.float64(0.34379765989140354), np.float64(0.11739835369326199), np.float64(0.14799999840394035), np.float64(0.04799999840394035), np.float64(0.05799999840394035), np.float64(0.043999998403940345)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24472847105319512), 6: np.float64(0.6652409557704656), 8: np.float64(0.0900305731697909), 16: np.float64(1.637144693249358e-12), 83: np.float64(1.637144693249358e-12), 70: np.float64(1.637144693249358e-12), 0: np.float64(1.637144693249358e-12)}
err dic= {7: np.float64(0.03772847105319513), 6: np.float64(0.4192409557704656), 8: np.float64(0.1589694268302091), 16: np.float64(0.14799999999836286), 83: np.float64(0.04799999999836286), 70: np.float64(0.05799999999836286), 0: np.float64(0.043999999998362856)} 

err list= [np.float64(0.03772847105319513), np.float64(0.4192409557704656), np.float64(0.1589694268302091), np.float64(0.14799999999836286), np.float64(0.04799999999836286), np.float64(0.05799999999836286), np.float64(0.043999999998362856)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20934307548219552), 6: np.float64(0.7306791292026836), 8: np.float64(0.05997779531511386), 16: np.float64(1.7206258449745757e-15), 83: np.float64(1.7206258449745757e-15), 70: np.float64(1.7206258449745757e-15), 0: np.float64(1.7206258449745757e-15)}
err dic= {7: np.float64(0.0023430754821955335), 6: np.float64(0.48467912920268363), 8: np.float64(0.18902220468488615), 16: np.float64(0.14799999999999827), 83: np.float64(0.04799999999999828), 70: np.float64(0.05799999999999828), 0: np.float64(0.04399999999999828)} 

err list= [np.float64(0.0023430754821955335), np.float64(0.48467912920268363), np.float64(0.18902220468488615), np.float64(0.14799999999999827), np.float64(0.04799999999999828), np.float64(0.05799999999999828), np.float64(0.04399999999999828)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.1752903921400367), 6: np.float64(0.7855970345892758), 8: np.float64(0.039112573270687456), 16: np.float64(1.8378647241896174e-18), 83: np.float64(1.8378647241896174e-18), 70: np.float64(1.8378647241896174e-18), 0: np.float64(1.8378647241896174e-18)}
err dic= {7: np.float64(0.031709607859963296), 6: np.float64(0.5395970345892758), 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(0.031709607859963296), np.float64(0.5395970345892758), 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(0.02508148055382201), 16: np.float64(1.9844551981860543e-21), 83: np.float64(1.9844551981860543e-21), 70: np.float64(1.9844551981860543e-21), 0: np.float64(1.9844551981860543e-21)}
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(2.1578224194726405e-24), 83: np.float64(2.1578224194726405e-24), 70: np.float64(2.1578224194726405e-24), 0: np.float64(2.1578224194726405e-24)}
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= [0.09068722 0.07090734 0.05983601 0.06580733 0.07325563 0.08082724
 0.0879323  0.09433441 0.10098288 0.107587   0.11393139]
mean_std= [0.         0.01977988 0.02249395 0.02205569 0.02471987 0.02821121
 0.03138579 0.0338946  0.03707844 0.04037153 0.04340741]
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
