p= 5 num clusters= 4
linkage completed in  10.679880857467651
silhouette_score of the clusters -0.00403947628527654
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 2, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 2, 14: 3, 24: 4, 100: 1} [3, 4, 8, 100, 1, 2, 5, 6, 9, 11, 7, 14, 24]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 11: 0, 12: 0} [5, 6, 11, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 100: 1} [1, 2, 5, 6, 9, 10, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 13: 6, 17: 6, 20: 4, 100: 2} [2, 6, 7, 8, 10, 11, 100, 1, 20, 13, 17]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 2, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 11, 7]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 11: 0, 12: 0, 13: 0} [5, 6, 11, 12, 13]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 6: 1, 9: 1, 100: 1} [1, 5, 6, 9, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 13: 5, 17: 4, 100: 2} [2, 6, 7, 8, 10, 11, 100, 1, 17, 5, 13]
empirical probabilities from test set: {2: 0.262, 3: 0.236, 4: 0.261, 59: 0.069, 40: 0.078, 84: 0.055, 0: 0.039}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.26795632718462803), 3: np.float64(0.17900731618932958), 4: np.float64(0.17690907701205713), 59: np.float64(0.09403181990349627), 40: np.float64(0.09403181990349627), 84: np.float64(0.09403181990349627), 0: np.float64(0.09403181990349627)}
err dic= {2: np.float64(0.005956327184628019), 3: np.float64(0.05699268381067041), 4: np.float64(0.08409092298794288), 59: np.float64(0.02503181990349626), 40: np.float64(0.016031819903496267), 84: np.float64(0.039031819903496266), 0: np.float64(0.05503181990349627)} 

err list= [np.float64(0.005956327184628019), np.float64(0.05699268381067041), np.float64(0.08409092298794288), np.float64(0.02503181990349626), np.float64(0.016031819903496267), np.float64(0.039031819903496266), np.float64(0.05503181990349627)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.2641432119698989), 3: np.float64(0.18207615560497903), 4: np.float64(0.1777806308236727), 59: np.float64(0.09400000040036235), 40: np.float64(0.09400000040036235), 84: np.float64(0.09400000040036235), 0: np.float64(0.09400000040036235)}
err dic= {2: np.float64(0.0021432119698988616), 3: np.float64(0.05392384439502096), 4: np.float64(0.0832193691763273), 59: np.float64(0.02500000040036235), 40: np.float64(0.016000000400362355), 84: np.float64(0.039000000400362354), 0: np.float64(0.055000000400362355)} 

err list= [np.float64(0.0021432119698988616), np.float64(0.05392384439502096), np.float64(0.0832193691763273), np.float64(0.02500000040036235), np.float64(0.016000000400362355), np.float64(0.039000000400362354), np.float64(0.055000000400362355)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.2564975712139765), 3: np.float64(0.18823503921458296), 4: np.float64(0.17926738957144064), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.005502428786023528), 3: np.float64(0.04776496078541703), 4: np.float64(0.08173261042855937), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.005502428786023528), np.float64(0.04776496078541703), np.float64(0.08173261042855937), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.23630128663970373), 3: np.float64(0.20626592390828727), 4: np.float64(0.18143278945200889), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.025698713360296277), 3: np.float64(0.02973407609171272), 4: np.float64(0.07956721054799112), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.025698713360296277), np.float64(0.02973407609171272), np.float64(0.07956721054799112), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.21276989910604077), 3: np.float64(0.23295165930657644), 4: np.float64(0.17827844158738285), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.04923010089395924), 3: np.float64(0.0030483406934235513), 4: np.float64(0.08272155841261716), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.04923010089395924), np.float64(0.0030483406934235513), np.float64(0.08272155841261716), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.20012568653213375), 3: np.float64(0.25420080938999434), 4: np.float64(0.169673504077872), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.06187431346786626), 3: np.float64(0.018200809389994355), 4: np.float64(0.09132649592212802), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.06187431346786626), np.float64(0.018200809389994355), np.float64(0.09132649592212802), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.19426985308438272), 3: np.float64(0.2707188976161534), 4: np.float64(0.15901124929946384), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.0677301469156173), 3: np.float64(0.03471889761615343), 4: np.float64(0.10198875070053617), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.0677301469156173), np.float64(0.03471889761615343), np.float64(0.10198875070053617), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.19181275460570674), 3: np.float64(0.2838067119456144), 4: np.float64(0.14838053344867885), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.07018724539429327), 3: np.float64(0.04780671194561442), 4: np.float64(0.11261946655132116), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.07018724539429327), np.float64(0.04780671194561442), np.float64(0.11261946655132116), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.1908417764053821), 3: np.float64(0.2944351062399339), 4: np.float64(0.13872311735468396), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.0711582235946179), 3: np.float64(0.05843510623993392), 4: np.float64(0.12227688264531605), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.0711582235946179), np.float64(0.05843510623993392), np.float64(0.12227688264531605), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.19047092759521717), 3: np.float64(0.30317918119993487), 4: np.float64(0.13034989120484788), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.07152907240478285), 3: np.float64(0.06717918119993488), 4: np.float64(0.13065010879515213), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.07152907240478285), np.float64(0.06717918119993488), np.float64(0.13065010879515213), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.1903318715524307), 3: np.float64(0.31038376968891407), 4: np.float64(0.12328435875865515), 59: np.float64(0.094), 40: np.float64(0.094), 84: np.float64(0.094), 0: np.float64(0.094)}
err dic= {2: np.float64(0.07166812844756931), 3: np.float64(0.07438376968891408), 4: np.float64(0.13771564124134486), 59: np.float64(0.024999999999999994), 40: np.float64(0.016), 84: np.float64(0.039), 0: np.float64(0.055)} 

err list= [np.float64(0.07166812844756931), np.float64(0.07438376968891408), np.float64(0.13771564124134486), np.float64(0.024999999999999994), np.float64(0.016), np.float64(0.039), np.float64(0.055)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: 0.262, 3: 0.236, 4: 0.261, 59: 0.069, 40: 0.078, 84: 0.055, 0: np.float64(0.503628870624823)} 

err MNL list= [0.262, 0.236, 0.261, 0.069, 0.078, 0.055, np.float64(0.503628870624823)]
sampled assortment [1, 4, 5, 35, 19, 15] number: 1
#  Learning probs for MM model, A = [1, 4, 5, 35, 19, 15]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 12: 3, 14: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 1, 12, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 8: 0, 10: 0, 12: 0} [5, 6, 8, 10, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 9: 1, 10: 1, 17: 3, 100: 1} [1, 5, 9, 10, 100, 17]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 6: 1, 7: 1, 8: 0, 10: 1, 11: 4, 14: 6, 17: 5, 18: 7, 20: 5, 100: 1} [2, 8, 6, 7, 10, 100, 1, 11, 17, 20, 14, 18]
#  Learning probs for MM model, A = [1, 4, 5, 35, 19, 15]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 11: 2, 12: 3, 19: 2, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 11, 19, 1, 12]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 10: 0, 11: 0, 12: 0, 21: 0, 100: 0} [5, 6, 10, 11, 12, 21, 100]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 13: 1, 14: 1, 15: 1, 100: 1} [1, 2, 5, 6, 9, 10, 13, 14, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 5, 6: 1, 7: 1, 8: 0, 10: 1, 11: 3, 17: 5, 23: 7, 100: 2} [2, 8, 6, 7, 10, 100, 1, 11, 5, 17, 23]
empirical probabilities from test set: {1: 0.198, 4: 0.202, 5: 0.186, 35: 0.068, 19: 0.163, 15: 0.159, 0: 0.024}
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.1686437061456097), 4: np.float64(0.0685993315173168), 5: np.float64(0.6509900448974931), 35: np.float64(9.569199036030547e-05), 19: np.float64(0.0579185647599517), 15: np.float64(0.05365696869890809), 0: np.float64(9.569199036030547e-05)}
err dic= {1: np.float64(0.029356293854390314), 4: np.float64(0.13340066848268323), 5: np.float64(0.4649900448974931), 35: np.float64(0.0679043080096397), 19: np.float64(0.10508143524004832), 15: np.float64(0.1053430313010919), 0: np.float64(0.023904308009639694)} 

err list= [np.float64(0.029356293854390314), np.float64(0.13340066848268323), np.float64(0.4649900448974931), np.float64(0.0679043080096397), np.float64(0.10508143524004832), np.float64(0.1053430313010919), np.float64(0.023904308009639694)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1687232503244343), 4: np.float64(0.07590585394076799), 5: np.float64(0.6528534186639938), 35: np.float64(9.239197037075164e-10), 19: np.float64(0.05413535173957824), 15: np.float64(0.048382123483386275), 0: np.float64(9.239197037075164e-10)}
err dic= {1: np.float64(0.029276749675565705), 4: np.float64(0.12609414605923203), 5: np.float64(0.4668534186639938), 35: np.float64(0.0679999990760803), 19: np.float64(0.10886464826042178), 15: np.float64(0.11061787651661373), 0: np.float64(0.023999999076080296)} 

err list= [np.float64(0.029276749675565705), np.float64(0.12609414605923203), np.float64(0.4668534186639938), np.float64(0.0679999990760803), np.float64(0.10886464826042178), np.float64(0.11061787651661373), np.float64(0.023999999076080296)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.16931351928263688), 4: np.float64(0.09131706489436758), 5: np.float64(0.6539507167320584), 35: np.float64(1.0000689150220595e-19), 19: np.float64(0.046592300706419905), 15: np.float64(0.03882639838451754), 0: np.float64(1.0000689150220595e-19)}
err dic= {1: np.float64(0.028686480717363128), 4: np.float64(0.11068293510563243), 5: np.float64(0.4679507167320584), 35: np.float64(0.068), 19: np.float64(0.11640769929358011), 15: np.float64(0.12017360161548246), 0: np.float64(0.024)} 

err list= [np.float64(0.028686480717363128), np.float64(0.11068293510563243), np.float64(0.4679507167320584), np.float64(0.068), np.float64(0.11640769929358011), np.float64(0.12017360161548246), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.17438785829304373), 4: np.float64(0.13760055343779265), 5: np.float64(0.6443947539844227), 35: np.float64(4.541145862596847e-49), 19: np.float64(0.02583813754913545), 15: np.float64(0.017778696735604945), 0: np.float64(4.541145862596847e-49)}
err dic= {1: np.float64(0.023612141706956274), 4: np.float64(0.06439944656220736), 5: np.float64(0.4583947539844227), 35: np.float64(0.068), 19: np.float64(0.13716186245086456), 15: np.float64(0.14122130326439505), 0: np.float64(0.024)} 

err list= [np.float64(0.023612141706956274), np.float64(0.06439944656220736), np.float64(0.4583947539844227), np.float64(0.068), np.float64(0.13716186245086456), np.float64(0.14122130326439505), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.19228581841435727), 4: np.float64(0.1939242624997467), 5: np.float64(0.6036474174884818), 35: np.float64(1.7918146824178247e-97), 19: np.float64(0.006589936727828237), 15: np.float64(0.003552564869586073), 0: np.float64(1.7918146824178247e-97)}
err dic= {1: np.float64(0.005714181585642741), 4: np.float64(0.00807573750025331), 5: np.float64(0.41764741748848183), 35: np.float64(0.068), 19: np.float64(0.15641006327217177), 15: np.float64(0.15544743513041392), 0: np.float64(0.024)} 

err list= [np.float64(0.005714181585642741), np.float64(0.00807573750025331), np.float64(0.41764741748848183), np.float64(0.068), np.float64(0.15641006327217177), np.float64(0.15544743513041392), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.21303804472076862), 4: np.float64(0.222336069756313), 5: np.float64(0.5627955896322765), 35: np.float64(7.428180695665791e-146), 19: np.float64(0.0012541339670663922), 15: np.float64(0.0005761619235753597), 0: np.float64(7.428180695665791e-146)}
err dic= {1: np.float64(0.015038044720768612), 4: np.float64(0.020336069756312997), 5: np.float64(0.3767955896322765), 35: np.float64(0.068), 19: np.float64(0.16174586603293362), 15: np.float64(0.15842383807642466), 0: np.float64(0.024)} 

err list= [np.float64(0.015038044720768612), np.float64(0.020336069756312997), np.float64(0.3767955896322765), np.float64(0.068), np.float64(0.16174586603293362), np.float64(0.15842383807642466), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  1 

learned probs for this beta: {1: np.float64(0.23067273405141728), 4: np.float64(0.2355002110374642), 5: np.float64(0.5335340620067656), 35: np.float64(3.057777939378115e-194), 19: np.float64(0.0002068830890981944), 15: np.float64(8.610981525487111e-05), 0: np.float64(3.057777939378115e-194)}
err dic= {1: np.float64(0.03267273405141727), 4: np.float64(0.0335002110374642), 5: np.float64(0.34753406200676557), 35: np.float64(0.068), 19: np.float64(0.16279311691090181), 15: np.float64(0.15891389018474514), 0: np.float64(0.024)} 

err list= [np.float64(0.03267273405141727), np.float64(0.0335002110374642), np.float64(0.34753406200676557), np.float64(0.068), np.float64(0.16279311691090181), np.float64(0.15891389018474514), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.24412063816630927), 4: np.float64(0.2414213899538333), 5: np.float64(0.514413730342685), 35: np.float64(1.265964548299573e-242), 19: np.float64(3.177250293893262e-05), 15: np.float64(1.2469034233343181e-05), 0: np.float64(1.265964548299573e-242)}
err dic= {1: np.float64(0.046120638166309263), 4: np.float64(0.03942138995383329), 5: np.float64(0.328413730342685), 35: np.float64(0.068), 19: np.float64(0.16296822749706108), 15: np.float64(0.15898753096576665), 0: np.float64(0.024)} 

err list= [np.float64(0.046120638166309263), np.float64(0.03942138995383329), np.float64(0.328413730342685), np.float64(0.068), np.float64(0.16296822749706108), np.float64(0.15898753096576665), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.25382414749189613), 4: np.float64(0.24398198091567597), 5: np.float64(0.5021874048749491), 35: np.float64(5.3060235209007555e-291), 19: np.float64(4.68919638784215e-06), 15: np.float64(1.777521090598619e-06), 0: np.float64(5.3060235209007555e-291)}
err dic= {1: np.float64(0.055824147491896126), 4: np.float64(0.041981980915675954), 5: np.float64(0.31618740487494906), 35: np.float64(0.068), 19: np.float64(0.16299531080361215), 15: np.float64(0.1589982224789094), 0: np.float64(0.024)} 

err list= [np.float64(0.055824147491896126), np.float64(0.041981980915675954), np.float64(0.31618740487494906), np.float64(0.068), np.float64(0.16299531080361215), np.float64(0.1589982224789094), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.26055750546886125), 4: np.float64(0.24504679097038054), 5: np.float64(0.4943947775693027), 35: np.float64(0.0), 19: np.float64(6.752328505806517e-07), 15: np.float64(2.50758604438187e-07), 0: np.float64(0.0)}
err dic= {1: np.float64(0.06255750546886124), 4: np.float64(0.04304679097038053), 5: np.float64(0.3083947775693027), 35: np.float64(0.068), 19: np.float64(0.16299932476714943), 15: np.float64(0.15899974924139557), 0: np.float64(0.024)} 

err list= [np.float64(0.06255750546886124), np.float64(0.04304679097038053), np.float64(0.3083947775693027), np.float64(0.068), np.float64(0.16299932476714943), np.float64(0.15899974924139557), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

beta is  2 

learned probs for this beta: {1: np.float64(0.2650907393633445), 4: np.float64(0.24547581292317103), 5: np.float64(0.4894333169792045), 35: np.float64(0.0), 19: np.float64(9.564628261473468e-08), 15: np.float64(3.508799704425239e-08), 0: np.float64(0.0)}
err dic= {1: np.float64(0.06709073936334448), 4: np.float64(0.043475812923171014), 5: np.float64(0.3034333169792045), 35: np.float64(0.068), 19: np.float64(0.1629999043537174), 15: np.float64(0.15899996491200297), 0: np.float64(0.024)} 

err list= [np.float64(0.06709073936334448), np.float64(0.043475812923171014), np.float64(0.3034333169792045), np.float64(0.068), np.float64(0.1629999043537174), np.float64(0.15899996491200297), np.float64(0.024)]
results for assortment [1, 4, 5, 35, 19, 15] :

err MNL dic= {1: 0.198, 4: 0.202, 5: 0.186, 35: 0.068, 19: 0.163, 15: 0.159, 0: np.float64(0.5071412409125975)} 

err MNL list= [0.198, 0.202, 0.186, 0.068, 0.163, 0.159, np.float64(0.5071412409125975)]
sampled assortment [2, 4, 8, 36, 65, 43] number: 2
#  Learning probs for MM model, A = [2, 4, 8, 36, 65, 43]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 15: 3, 100: 0} [3, 4, 8, 100, 5, 6, 1, 7, 15]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 7: 0, 8: 0, 12: 0} [5, 7, 8, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 15: 1, 100: 1} [1, 2, 5, 6, 9, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 3, 17: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 5, 17]
#  Learning probs for MM model, A = [2, 4, 8, 36, 65, 43]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 3, 14: 3, 100: 0} [3, 4, 8, 100, 5, 6, 9, 1, 7, 11, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 11: 0, 12: 0, 21: 0} [5, 11, 12, 21]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 13: 1, 100: 1} [1, 2, 5, 6, 9, 10, 13, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 14: 6, 18: 6, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 5, 14, 18]
empirical probabilities from test set: {2: 0.237, 4: 0.242, 8: 0.249, 36: 0.08, 65: 0.057, 43: 0.094, 0: 0.041}
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.2950504473440631), 4: np.float64(0.19313059455792042), 8: np.float64(0.23676466059324763), 36: np.float64(0.0687635743761922), 65: np.float64(0.0687635743761922), 43: np.float64(0.0687635743761922), 0: np.float64(0.0687635743761922)}
err dic= {2: np.float64(0.058050447344063116), 4: np.float64(0.04886940544207957), 8: np.float64(0.012235339406752366), 36: np.float64(0.011236425623807805), 65: np.float64(0.011763574376192194), 43: np.float64(0.025236425623807804), 0: np.float64(0.027763574376192195)} 

err list= [np.float64(0.058050447344063116), np.float64(0.04886940544207957), np.float64(0.012235339406752366), np.float64(0.011236425623807805), np.float64(0.011763574376192194), np.float64(0.025236425623807804), np.float64(0.027763574376192195)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.29664365459518943), 4: np.float64(0.19466052086417482), 8: np.float64(0.2338386795510939), 36: np.float64(0.06871428624738544), 65: np.float64(0.06871428624738544), 43: np.float64(0.06871428624738544), 0: np.float64(0.06871428624738544)}
err dic= {2: np.float64(0.059643654595189444), 4: np.float64(0.047339479135825174), 8: np.float64(0.015161320448906113), 36: np.float64(0.011285713752614557), 65: np.float64(0.011714286247385443), 43: np.float64(0.025285713752614555), 0: np.float64(0.027714286247385443)} 

err list= [np.float64(0.059643654595189444), np.float64(0.047339479135825174), np.float64(0.015161320448906113), np.float64(0.011285713752614557), np.float64(0.011714286247385443), np.float64(0.025285713752614555), np.float64(0.027714286247385443)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.29943058165034786), 4: np.float64(0.19772792103723524), 8: np.float64(0.22798435445527415), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.06243058165034787), 4: np.float64(0.04427207896276475), 8: np.float64(0.021015645544725847), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.06243058165034787), np.float64(0.04427207896276475), np.float64(0.021015645544725847), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.30752039780029966), 4: np.float64(0.20686916080697054), 8: np.float64(0.2107532985355868), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.07052039780029967), 4: np.float64(0.03513083919302945), 8: np.float64(0.038246701464413196), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.07052039780029967), np.float64(0.03513083919302945), np.float64(0.038246701464413196), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.3192896934501213), 4: np.float64(0.22168366635714148), 8: np.float64(0.1841694973355944), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.08228969345012133), 4: np.float64(0.02031633364285851), 8: np.float64(0.0648305026644056), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.08228969345012133), np.float64(0.02031633364285851), np.float64(0.0648305026644056), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.32811695558811593), 4: np.float64(0.23562245103663854), 8: np.float64(0.16140345051810262), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.09111695558811594), 4: np.float64(0.006377548963361457), 8: np.float64(0.08759654948189738), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.09111695558811594), np.float64(0.006377548963361457), np.float64(0.08759654948189738), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  1 

learned probs for this beta: {2: np.float64(0.33401811209248855), 4: np.float64(0.24837193141260944), 8: np.float64(0.14275281363775918), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.09701811209248856), 4: np.float64(0.006371931412609444), 8: np.float64(0.10624718636224081), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.09701811209248856), np.float64(0.006371931412609444), np.float64(0.10624718636224081), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.3376216943115813), 4: np.float64(0.259735726597966), 8: np.float64(0.12778543623330973), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.1006216943115813), 4: np.float64(0.017735726597966017), 8: np.float64(0.12121456376669026), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.1006216943115813), np.float64(0.017735726597966017), np.float64(0.12121456376669026), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.33967721905932813), 4: np.float64(0.2696332132388735), 8: np.float64(0.11583242484465528), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.10267721905932814), 4: np.float64(0.027633213238873522), 8: np.float64(0.13316757515534472), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.10267721905932814), np.float64(0.027633213238873522), np.float64(0.13316757515534472), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.34079246667035656), 4: np.float64(0.27808168679799794), 8: np.float64(0.10626870367450239), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.10379246667035658), 4: np.float64(0.03608168679799795), 8: np.float64(0.1427312963254976), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.10379246667035658), np.float64(0.03608168679799795), np.float64(0.1427312963254976), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

beta is  2 

learned probs for this beta: {2: np.float64(0.34137596392569564), 4: np.float64(0.28517016762735026), 8: np.float64(0.09859672558981109), 36: np.float64(0.06871428571428571), 65: np.float64(0.06871428571428571), 43: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.10437596392569565), 4: np.float64(0.043170167627350264), 8: np.float64(0.15040327441018891), 36: np.float64(0.011285714285714288), 65: np.float64(0.011714285714285712), 43: np.float64(0.025285714285714286), 0: np.float64(0.027714285714285712)} 

err list= [np.float64(0.10437596392569565), np.float64(0.043170167627350264), np.float64(0.15040327441018891), np.float64(0.011285714285714288), np.float64(0.011714285714285712), np.float64(0.025285714285714286), np.float64(0.027714285714285712)]
results for assortment [2, 4, 8, 36, 65, 43] :

err MNL dic= {2: 0.237, 4: 0.242, 8: 0.249, 36: 0.08, 65: 0.057, 43: 0.094, 0: np.float64(0.5024698198774357)} 

err MNL list= [0.237, 0.242, 0.249, 0.08, 0.057, 0.094, np.float64(0.5024698198774357)]
sampled assortment [2, 7, 4, 47, 36, 90] number: 3
#  Learning probs for MM model, A = [2, 7, 4, 47, 36, 90]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 14: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 7, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {2: 0, 5: 0, 6: 0, 8: 0, 11: 0, 13: 0} [2, 5, 6, 8, 11, 13]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 13: 1, 14: 1, 100: 1} [1, 2, 5, 6, 9, 10, 13, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 17: 5, 19: 5, 20: 4, 25: 6, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 20, 5, 17, 19, 25]
#  Learning probs for MM model, A = [2, 7, 4, 47, 36, 90]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 2, 12: 3, 14: 3, 19: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 11, 1, 7, 12, 14, 19]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 8: 0, 12: 0} [5, 8, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 7: 3, 9: 1, 10: 1, 14: 1, 17: 3, 100: 1} [1, 2, 5, 6, 9, 10, 14, 100, 7, 17]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 6, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 17: 5, 100: 2} [2, 6, 7, 8, 10, 11, 100, 1, 17, 5]
empirical probabilities from test set: {2: 0.253, 7: 0.216, 4: 0.255, 47: 0.09, 36: 0.095, 90: 0.047, 0: 0.044}
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.295085079774263), 7: np.float64(0.2726534656981962), 4: np.float64(0.15731179912782736), 47: np.float64(0.06873741384992835), 36: np.float64(0.06873741384992835), 90: np.float64(0.06873741384992835), 0: np.float64(0.06873741384992835)}
err dic= {2: np.float64(0.04208507977426301), 7: np.float64(0.05665346569819621), 4: np.float64(0.09768820087217264), 47: np.float64(0.02126258615007165), 36: np.float64(0.026262586150071654), 90: np.float64(0.021737413849928347), 0: np.float64(0.02473741384992835)} 

err list= [np.float64(0.04208507977426301), np.float64(0.05665346569819621), np.float64(0.09768820087217264), np.float64(0.02126258615007165), np.float64(0.026262586150071654), np.float64(0.021737413849928347), np.float64(0.02473741384992835)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.3025842129274325), 7: np.float64(0.2585357275282018), 4: np.float64(0.1640229154589524), 47: np.float64(0.06871428602135335), 36: np.float64(0.06871428602135335), 90: np.float64(0.06871428602135335), 0: np.float64(0.06871428602135335)}
err dic= {2: np.float64(0.04958421292743248), 7: np.float64(0.04253572752820181), 4: np.float64(0.09097708454104761), 47: np.float64(0.021285713978646648), 36: np.float64(0.026285713978646652), 90: np.float64(0.02171428602135335), 0: np.float64(0.02471428602135335)} 

err list= [np.float64(0.04958421292743248), np.float64(0.04253572752820181), np.float64(0.09097708454104761), np.float64(0.021285713978646648), np.float64(0.026285713978646652), np.float64(0.02171428602135335), np.float64(0.02471428602135335)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.3160706825137319), 7: np.float64(0.23178870560028458), 4: np.float64(0.17728346902884096), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.06307068251373188), 7: np.float64(0.015788705600284586), 4: np.float64(0.07771653097115905), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.06307068251373188), np.float64(0.015788705600284586), np.float64(0.07771653097115905), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.34411984162232345), 7: np.float64(0.16803757924549595), 4: np.float64(0.21298543627503747), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.09111984162232345), 7: np.float64(0.04796242075450405), 4: np.float64(0.04201456372496254), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.09111984162232345), np.float64(0.04796242075450405), np.float64(0.04201456372496254), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.3574871188946768), 7: np.float64(0.11369030761845648), 4: np.float64(0.25396543062972404), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.10448711889467682), 7: np.float64(0.10230969238154351), 4: np.float64(0.0010345693702759617), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.10448711889467682), np.float64(0.10230969238154351), np.float64(0.0010345693702759617), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.35292072959620135), 7: np.float64(0.0934968218663685), 4: np.float64(0.2787253056802872), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.09992072959620135), 7: np.float64(0.1225031781336315), 4: np.float64(0.02372530568028719), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.09992072959620135), np.float64(0.1225031781336315), np.float64(0.02372530568028719), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  1 

learned probs for this beta: {2: np.float64(0.34658661904045485), 7: np.float64(0.08443050853380536), 4: np.float64(0.29412572956859706), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.09358661904045484), 7: np.float64(0.13156949146619462), 4: np.float64(0.039125729568597056), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.09358661904045484), np.float64(0.13156949146619462), np.float64(0.039125729568597056), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.34265893690037735), 7: np.float64(0.07911346690659296), 4: np.float64(0.3033704533358865), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.08965893690037735), 7: np.float64(0.13688653309340704), 4: np.float64(0.04837045333588652), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.08965893690037735), np.float64(0.13688653309340704), np.float64(0.04837045333588652), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.3409358256036525), 7: np.float64(0.0755829117884534), 4: np.float64(0.30862411975075094), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.08793582560365248), 7: np.float64(0.14041708821154658), 4: np.float64(0.05362411975075093), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.08793582560365248), np.float64(0.14041708821154658), np.float64(0.05362411975075093), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.3404806860698695), 7: np.float64(0.07318991091066511), 4: np.float64(0.31147226016232216), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.08748068606986947), 7: np.float64(0.1428100890893349), 4: np.float64(0.05647226016232215), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.08748068606986947), np.float64(0.1428100890893349), np.float64(0.05647226016232215), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

beta is  2 

learned probs for this beta: {2: np.float64(0.3405915213632238), 7: np.float64(0.07158918999122017), 4: np.float64(0.312962145788413), 47: np.float64(0.06871428571428571), 36: np.float64(0.06871428571428571), 90: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {2: np.float64(0.08759152136322379), 7: np.float64(0.1444108100087798), 4: np.float64(0.05796214578841302), 47: np.float64(0.021285714285714283), 36: np.float64(0.026285714285714287), 90: np.float64(0.021714285714285714), 0: np.float64(0.024714285714285716)} 

err list= [np.float64(0.08759152136322379), np.float64(0.1444108100087798), np.float64(0.05796214578841302), np.float64(0.021285714285714283), np.float64(0.026285714285714287), np.float64(0.021714285714285714), np.float64(0.024714285714285716)]
results for assortment [2, 7, 4, 47, 36, 90] :

err MNL dic= {2: 0.253, 7: 0.216, 4: 0.255, 47: 0.09, 36: 0.095, 90: 0.047, 0: np.float64(0.501064298315739)} 

err MNL list= [0.253, 0.216, 0.255, 0.09, 0.095, 0.047, np.float64(0.501064298315739)]
sampled assortment [2, 9, 4, 18, 85, 100] number: 4
#  Learning probs for MM model, A = [2, 9, 4, 18, 85, 100]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 12: 3, 20: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 1, 7, 12, 20]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 11: 0, 12: 0, 16: 0} [5, 6, 11, 12, 16]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1, 100: 1} [1, 2, 5, 6, 9, 10, 14, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 5: 6, 6: 1, 7: 1, 8: 1, 10: 1, 11: 3, 17: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 17, 5]
#  Learning probs for MM model, A = [2, 9, 4, 18, 85, 100]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 12: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 12]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 7: 0, 8: 0, 12: 0, 100: 0} [5, 6, 7, 8, 12, 100]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 100: 1} [1, 2, 5, 6, 9, 10, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 13: 6, 15: 5, 17: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 5, 15, 17, 13]
empirical probabilities from test set: {2: 0.22, 9: 0.183, 4: 0.212, 18: 0.136, 85: 0.019, 100: 0.206, 0: 0.024}
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.1740109127018395), 9: np.float64(0.11606813032749799), 4: np.float64(0.065400834399067), 18: np.float64(8.981121101440999e-05), 85: np.float64(8.981121101440999e-05), 100: np.float64(0.6442506889385523), 0: np.float64(8.981121101440999e-05)}
err dic= {2: np.float64(0.04598908729816051), 9: np.float64(0.066931869672502), 4: np.float64(0.146599165600933), 18: np.float64(0.1359101887889856), 85: np.float64(0.01891018878898559), 100: np.float64(0.43825068893855235), 0: np.float64(0.02391018878898559)} 

err list= [np.float64(0.04598908729816051), np.float64(0.066931869672502), np.float64(0.146599165600933), np.float64(0.1359101887889856), np.float64(0.01891018878898559), np.float64(0.43825068893855235), np.float64(0.02391018878898559)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.17927654564377815), 9: np.float64(0.11158798640448508), 4: np.float64(0.06928062696898507), 18: np.float64(8.25333686660766e-10), 85: np.float64(8.25333686660766e-10), 100: np.float64(0.6398548385067508), 0: np.float64(8.25333686660766e-10)}
err dic= {2: np.float64(0.04072345435622185), 9: np.float64(0.07141201359551491), 4: np.float64(0.14271937303101492), 18: np.float64(0.13599999917466632), 85: np.float64(0.018999999174666313), 100: np.float64(0.4338548385067509), 0: np.float64(0.023999999174666314)} 

err list= [np.float64(0.04072345435622185), np.float64(0.07141201359551491), np.float64(0.14271937303101492), np.float64(0.13599999917466632), np.float64(0.018999999174666313), np.float64(0.4338548385067509), np.float64(0.023999999174666314)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.18959358833810472), 9: np.float64(0.10292156020459124), 4: np.float64(0.07738565157090257), 18: np.float64(7.536805537165405e-20), 85: np.float64(7.536805537165405e-20), 100: np.float64(0.6300991998864016), 0: np.float64(7.536805537165405e-20)}
err dic= {2: np.float64(0.030406411661895283), 9: np.float64(0.08007843979540875), 4: np.float64(0.13461434842909742), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.42409919988640166), 0: np.float64(0.024)} 

err list= [np.float64(0.030406411661895283), np.float64(0.08007843979540875), np.float64(0.13461434842909742), np.float64(0.136), np.float64(0.019), np.float64(0.42409919988640166), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.21699198561411467), 9: np.float64(0.07883959584490041), 4: np.float64(0.10229791934413304), 18: np.float64(1.7310158517529354e-49), 85: np.float64(1.7310158517529354e-49), 100: np.float64(0.6018704991968512), 0: np.float64(1.7310158517529354e-49)}
err dic= {2: np.float64(0.003008014385885327), 9: np.float64(0.10416040415509958), 4: np.float64(0.10970208065586695), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.39587049919685124), 0: np.float64(0.024)} 

err list= [np.float64(0.003008014385885327), np.float64(0.10416040415509958), np.float64(0.10970208065586695), np.float64(0.136), np.float64(0.019), np.float64(0.39587049919685124), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.24783656286404032), 9: np.float64(0.04761872213289701), 4: np.float64(0.14119808982002935), 18: np.float64(4.233275335782077e-98), 85: np.float64(4.233275335782077e-98), 100: np.float64(0.5633466251830335), 0: np.float64(4.233275335782077e-98)}
err dic= {2: np.float64(0.02783656286404032), 9: np.float64(0.135381277867103), 4: np.float64(0.07080191017997065), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.3573466251830335), 0: np.float64(0.024)} 

err list= [np.float64(0.02783656286404032), np.float64(0.135381277867103), np.float64(0.07080191017997065), np.float64(0.136), np.float64(0.019), np.float64(0.3573466251830335), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.26290479465451533), 9: np.float64(0.027377820674088667), 4: np.float64(0.17276780638289504), 18: np.float64(1.219808652100936e-146), 85: np.float64(1.219808652100936e-146), 100: np.float64(0.536949578288501), 0: np.float64(1.219808652100936e-146)}
err dic= {2: np.float64(0.04290479465451533), 9: np.float64(0.15562217932591133), 4: np.float64(0.03923219361710495), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.330949578288501), 0: np.float64(0.024)} 

err list= [np.float64(0.04290479465451533), np.float64(0.15562217932591133), np.float64(0.03923219361710495), np.float64(0.136), np.float64(0.019), np.float64(0.330949578288501), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  1 

learned probs for this beta: {2: np.float64(0.26919315011122574), 9: np.float64(0.01516775634678702), 4: np.float64(0.1964544129120442), 18: np.float64(3.548442731925969e-195), 85: np.float64(3.548442731925969e-195), 100: np.float64(0.5191846806299433), 0: np.float64(3.548442731925969e-195)}
err dic= {2: np.float64(0.04919315011122574), 9: np.float64(0.16783224365321298), 4: np.float64(0.015545587087955781), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.3131846806299433), 0: np.float64(0.024)} 

err list= [np.float64(0.04919315011122574), np.float64(0.16783224365321298), np.float64(0.015545587087955781), np.float64(0.136), np.float64(0.019), np.float64(0.3131846806299433), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.27164761405536475), 9: np.float64(0.008135849686647408), 4: np.float64(0.21334449692142665), 18: np.float64(1.0378611058887777e-243), 85: np.float64(1.0378611058887777e-243), 100: np.float64(0.5068720393365611), 0: np.float64(1.0378611058887777e-243)}
err dic= {2: np.float64(0.05164761405536475), 9: np.float64(0.1748641503133526), 4: np.float64(0.0013444969214266578), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.30087203933656115), 0: np.float64(0.024)} 

err list= [np.float64(0.05164761405536475), np.float64(0.1748641503133526), np.float64(0.0013444969214266578), np.float64(0.136), np.float64(0.019), np.float64(0.30087203933656115), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.27259829922142137), 9: np.float64(0.004244405581567148), 4: np.float64(0.224901986576494), 18: np.float64(3.042518863424089e-292), 85: np.float64(3.042518863424089e-292), 100: np.float64(0.49825530862051737), 0: np.float64(3.042518863424089e-292)}
err dic= {2: np.float64(0.05259829922142137), 9: np.float64(0.17875559441843286), 4: np.float64(0.012901986576493996), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.2922553086205174), 0: np.float64(0.024)} 

err list= [np.float64(0.05259829922142137), np.float64(0.17875559441843286), np.float64(0.012901986576493996), np.float64(0.136), np.float64(0.019), np.float64(0.2922553086205174), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.2729755285931868), 9: np.float64(0.002164505552651643), 4: np.float64(0.2325541288667428), 18: np.float64(0.0), 85: np.float64(0.0), 100: np.float64(0.49230583698741864), 0: np.float64(0.0)}
err dic= {2: np.float64(0.0529755285931868), 9: np.float64(0.18083549444734837), 4: np.float64(0.020554128866742793), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.2863058369874186), 0: np.float64(0.024)} 

err list= [np.float64(0.0529755285931868), np.float64(0.18083549444734837), np.float64(0.020554128866742793), np.float64(0.136), np.float64(0.019), np.float64(0.2863058369874186), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

beta is  2 

learned probs for this beta: {2: np.float64(0.2731307050147636), 9: np.float64(0.0010842165672637445), 4: np.float64(0.23749621398989132), 18: np.float64(0.0), 85: np.float64(0.0), 100: np.float64(0.48828886442808106), 0: np.float64(0.0)}
err dic= {2: np.float64(0.05313070501476361), 9: np.float64(0.18191578343273626), 4: np.float64(0.025496213989891325), 18: np.float64(0.136), 85: np.float64(0.019), 100: np.float64(0.2822888644280811), 0: np.float64(0.024)} 

err list= [np.float64(0.05313070501476361), np.float64(0.18191578343273626), np.float64(0.025496213989891325), np.float64(0.136), np.float64(0.019), np.float64(0.2822888644280811), np.float64(0.024)]
results for assortment [2, 9, 4, 18, 85, 100] :

err MNL dic= {2: 0.22, 9: 0.183, 4: 0.212, 18: 0.136, 85: 0.019, 100: 0.206, 0: np.float64(0.5092490676794582)} 

err MNL list= [0.22, 0.183, 0.212, 0.136, 0.019, 0.206, np.float64(0.5092490676794582)]
sampled assortment [9, 4, 7, 57, 70, 77] number: 5
#  Learning probs for MM model, A = [9, 4, 7, 57, 70, 77]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 12: 3, 14: 3, 15: 3, 19: 2, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 19, 1, 12, 14, 15]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 6: 0, 8: 0, 12: 0} [5, 6, 8, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 13: 1, 14: 1, 100: 1} [1, 2, 5, 6, 9, 10, 13, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 3: 6, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 3, 16: 6, 20: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 5, 20, 3, 16]
#  Learning probs for MM model, A = [9, 4, 7, 57, 70, 77]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 12: 3, 14: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 1, 7, 12, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {6: 0, 8: 0, 10: 0, 13: 0} [6, 8, 10, 13]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 100: 1} [1, 5, 6, 9, 10, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 5: 6, 6: 1, 7: 1, 8: 1, 10: 1, 11: 3, 16: 6, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 5, 16]
empirical probabilities from test set: {9: 0.237, 4: 0.26, 7: 0.243, 57: 0.072, 70: 0.063, 77: 0.068, 0: 0.057}
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.3252701925368997), 4: np.float64(0.15847296851728343), 7: np.float64(0.24114491571253374), 57: np.float64(0.06877798080832076), 70: np.float64(0.06877798080832076), 77: np.float64(0.06877798080832076), 0: np.float64(0.06877798080832076)}
err dic= {9: np.float64(0.08827019253689972), 4: np.float64(0.10152703148271658), 7: np.float64(0.001855084287466252), 57: np.float64(0.0032220191916792346), 70: np.float64(0.0057779808083207596), 77: np.float64(0.0007779808083207551), 0: np.float64(0.011777980808320758)} 

err list= [np.float64(0.08827019253689972), np.float64(0.10152703148271658), np.float64(0.001855084287466252), np.float64(0.0032220191916792346), np.float64(0.0057779808083207596), np.float64(0.0007779808083207551), np.float64(0.011777980808320758)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.3229807486097493), 4: np.float64(0.1664561954546843), 7: np.float64(0.23570591021249757), 57: np.float64(0.06871428643076721), 70: np.float64(0.06871428643076721), 77: np.float64(0.06871428643076721), 0: np.float64(0.06871428643076721)}
err dic= {9: np.float64(0.0859807486097493), 4: np.float64(0.09354380454531572), 7: np.float64(0.007294089787502428), 57: np.float64(0.0032857135692327816), 70: np.float64(0.0057142864307672125), 77: np.float64(0.0007142864307672081), 0: np.float64(0.011714286430767211)} 

err list= [np.float64(0.0859807486097493), np.float64(0.09354380454531572), np.float64(0.007294089787502428), np.float64(0.0032857135692327816), np.float64(0.0057142864307672125), np.float64(0.0007142864307672081), np.float64(0.011714286430767211)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.3173523504365714), 4: np.float64(0.18286759947725192), 7: np.float64(0.22492290722903402), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.08035235043657141), 4: np.float64(0.07713240052274808), 7: np.float64(0.018077092770965975), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.08035235043657141), np.float64(0.07713240052274808), np.float64(0.018077092770965975), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.2972243946774085), 4: np.float64(0.23032269033426073), 7: np.float64(0.19759577213118765), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.06022439467740853), 4: np.float64(0.029677309665739282), 7: np.float64(0.04540422786881235), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.06022439467740853), np.float64(0.029677309665739282), np.float64(0.04540422786881235), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.26774720671976826), 4: np.float64(0.2838698054027964), 7: np.float64(0.17352584502029256), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.030747206719768272), 4: np.float64(0.023869805402796374), 7: np.float64(0.06947415497970744), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.030747206719768272), np.float64(0.023869805402796374), np.float64(0.06947415497970744), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.2529882096568269), 4: np.float64(0.3054820674500458), 7: np.float64(0.1666725800359845), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.0159882096568269), 4: np.float64(0.04548206745004579), 7: np.float64(0.07632741996401549), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.0159882096568269), np.float64(0.04548206745004579), np.float64(0.07632741996401549), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  1 

learned probs for this beta: {9: np.float64(0.24778284513711168), 4: np.float64(0.3121031810730607), 7: np.float64(0.16525683093268484), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.010782845137111696), 4: np.float64(0.05210318107306067), 7: np.float64(0.07774316906731515), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.010782845137111696), np.float64(0.05210318107306067), np.float64(0.07774316906731515), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  1.25 

learned probs for this beta: {9: np.float64(0.24625477485753278), 4: np.float64(0.31387776898779207), 7: np.float64(0.16501031329753216), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.009254774857532788), 4: np.float64(0.05387776898779206), 7: np.float64(0.07798968670246784), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.009254774857532788), np.float64(0.05387776898779206), np.float64(0.07798968670246784), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  1.5 

learned probs for this beta: {9: np.float64(0.24584859227046607), 4: np.float64(0.31432308694983097), 7: np.float64(0.16497117792256), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.008848592270466082), 4: np.float64(0.05432308694983096), 7: np.float64(0.07802882207744), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.008848592270466082), np.float64(0.05432308694983096), np.float64(0.07802882207744), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  1.75 

learned probs for this beta: {9: np.float64(0.24574662383307883), 4: np.float64(0.31443094670373395), 7: np.float64(0.16496528660604398), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.008746623833078837), 4: np.float64(0.05443094670373394), 7: np.float64(0.07803471339395601), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.008746623833078837), np.float64(0.05443094670373394), np.float64(0.07803471339395601), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

beta is  2 

learned probs for this beta: {9: np.float64(0.2457219113417045), 4: np.float64(0.3144565176135137), 7: np.float64(0.16496442818763885), 57: np.float64(0.06871428571428571), 70: np.float64(0.06871428571428571), 77: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {9: np.float64(0.008721911341704525), 4: np.float64(0.054456517613513666), 7: np.float64(0.07803557181236115), 57: np.float64(0.0032857142857142807), 70: np.float64(0.005714285714285713), 77: np.float64(0.000714285714285709), 0: np.float64(0.011714285714285712)} 

err list= [np.float64(0.008721911341704525), np.float64(0.054456517613513666), np.float64(0.07803557181236115), np.float64(0.0032857142857142807), np.float64(0.005714285714285713), np.float64(0.000714285714285709), np.float64(0.011714285714285712)]
results for assortment [9, 4, 7, 57, 70, 77] :

err MNL dic= {9: 0.237, 4: 0.26, 7: 0.243, 57: 0.072, 70: 0.063, 77: 0.068, 0: np.float64(0.4910506761040209)} 

err MNL list= [0.237, 0.26, 0.243, 0.072, 0.063, 0.068, np.float64(0.4910506761040209)]
sampled assortment [9, 3, 7, 91, 11, 66] number: 6
#  Learning probs for MM model, A = [9, 3, 7, 91, 11, 66]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 12: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 1, 12]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {6: 0, 8: 0, 10: 0, 11: 0, 12: 0, 13: 0} [6, 8, 10, 11, 12, 13]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 13: 1, 15: 1, 21: 2, 100: 1} [1, 2, 5, 6, 9, 10, 13, 15, 100, 21]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 6, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 14: 6, 17: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 17, 5, 14]
#  Learning probs for MM model, A = [9, 3, 7, 91, 11, 66]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 1, 9: 2, 11: 2, 16: 4, 100: 0} [3, 4, 100, 8, 2, 5, 6, 9, 11, 16]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 11: 0, 12: 0} [5, 11, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1, 100: 1} [1, 5, 6, 9, 10, 14, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {2: 0, 5: 4, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 13: 4, 17: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 5, 13, 17]
empirical probabilities from test set: {9: 0.232, 3: 0.24, 7: 0.188, 91: 0.04, 11: 0.21, 66: 0.056, 0: 0.034}
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.2555589058107637), 3: np.float64(0.09033318121580418), 7: np.float64(0.0500076423129154), 91: np.float64(9.366011776561708e-05), 11: np.float64(0.6038192903072197), 66: np.float64(9.366011776561708e-05), 0: np.float64(9.366011776561708e-05)}
err dic= {9: np.float64(0.02355890581076367), 3: np.float64(0.1496668187841958), 7: np.float64(0.1379923576870846), 91: np.float64(0.03990633988223438), 11: np.float64(0.39381929030721974), 66: np.float64(0.05590633988223438), 0: np.float64(0.03390633988223438)} 

err list= [np.float64(0.02355890581076367), np.float64(0.1496668187841958), np.float64(0.1379923576870846), np.float64(0.03990633988223438), np.float64(0.39381929030721974), np.float64(0.05590633988223438), np.float64(0.03390633988223438)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.25228374833354794), 3: np.float64(0.09885413203686788), 7: np.float64(0.051728221013562434), 91: np.float64(7.659973103515676e-10), 11: np.float64(0.5971338963180299), 66: np.float64(7.659973103515676e-10), 0: np.float64(7.659973103515676e-10)}
err dic= {9: np.float64(0.02028374833354793), 3: np.float64(0.1411458679631321), 7: np.float64(0.13627177898643755), 91: np.float64(0.039999999234002694), 11: np.float64(0.38713389631802997), 66: np.float64(0.055999999234002694), 0: np.float64(0.033999999234002695)} 

err list= [np.float64(0.02028374833354793), np.float64(0.1411458679631321), np.float64(0.13627177898643755), np.float64(0.039999999234002694), np.float64(0.38713389631802997), np.float64(0.055999999234002694), np.float64(0.033999999234002695)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.2448600857573141), 3: np.float64(0.11648756945833912), 7: np.float64(0.05529478625873569), 91: np.float64(6.511796011031155e-20), 11: np.float64(0.5833575585256112), 66: np.float64(6.511796011031155e-20), 0: np.float64(6.511796011031155e-20)}
err dic= {9: np.float64(0.012860085757314094), 3: np.float64(0.12351243054166088), 7: np.float64(0.13270521374126432), 91: np.float64(0.04), 11: np.float64(0.37335755852561126), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.012860085757314094), np.float64(0.12351243054166088), np.float64(0.13270521374126432), np.float64(0.04), np.float64(0.37335755852561126), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.2211897747305885), 3: np.float64(0.16714519410547993), 7: np.float64(0.06543544363007175), 91: np.float64(9.933134735735095e-50), 11: np.float64(0.5462295875338594), 66: np.float64(9.933134735735095e-50), 0: np.float64(9.933134735735095e-50)}
err dic= {9: np.float64(0.0108102252694115), 3: np.float64(0.07285480589452006), 7: np.float64(0.12256455636992825), 91: np.float64(0.04), 11: np.float64(0.33622958753385945), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.0108102252694115), np.float64(0.07285480589452006), np.float64(0.12256455636992825), np.float64(0.04), np.float64(0.33622958753385945), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.19235543501748417), 3: np.float64(0.22108102285118675), 7: np.float64(0.07902672452392005), 91: np.float64(3.983808435657721e-99), 11: np.float64(0.5075368176074092), 66: np.float64(3.983808435657721e-99), 0: np.float64(3.983808435657721e-99)}
err dic= {9: np.float64(0.03964456498251584), 3: np.float64(0.018918977148813243), 7: np.float64(0.10897327547607995), 91: np.float64(0.04), 11: np.float64(0.29753681760740924), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.03964456498251584), np.float64(0.018918977148813243), np.float64(0.10897327547607995), np.float64(0.04), np.float64(0.29753681760740924), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.18099857915535247), 3: np.float64(0.23986262579317152), 7: np.float64(0.08766815442025237), 91: np.float64(2.0043410920357533e-148), 11: np.float64(0.4914706406312235), 66: np.float64(2.0043410920357533e-148), 0: np.float64(2.0043410920357533e-148)}
err dic= {9: np.float64(0.05100142084464754), 3: np.float64(0.00013737420682846668), 7: np.float64(0.10033184557974763), 91: np.float64(0.04), 11: np.float64(0.2814706406312235), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.05100142084464754), np.float64(0.00013737420682846668), np.float64(0.10033184557974763), np.float64(0.04), np.float64(0.2814706406312235), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  1 

learned probs for this beta: {9: np.float64(0.17788829395857592), 3: np.float64(0.2445349209563472), 7: np.float64(0.09233155018360592), 91: np.float64(1.0853464461478508e-197), 11: np.float64(0.485245234901471), 66: np.float64(1.0853464461478508e-197), 0: np.float64(1.0853464461478508e-197)}
err dic= {9: np.float64(0.054111706041424096), 3: np.float64(0.0045349209563472215), 7: np.float64(0.09566844981639408), 91: np.float64(0.04), 11: np.float64(0.275245234901471), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.054111706041424096), np.float64(0.0045349209563472215), np.float64(0.09566844981639408), np.float64(0.04), np.float64(0.275245234901471), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  1.25 

learned probs for this beta: {9: np.float64(0.17718089366271203), 3: np.float64(0.2455172794351993), 7: np.float64(0.09456912083484455), 91: np.float64(6.161109019724168e-247), 11: np.float64(0.48273270606724394), 66: np.float64(6.161109019724168e-247), 0: np.float64(6.161109019724168e-247)}
err dic= {9: np.float64(0.05481910633728798), 3: np.float64(0.005517279435199307), 7: np.float64(0.09343087916515545), 91: np.float64(0.04), 11: np.float64(0.272732706067244), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.05481910633728798), np.float64(0.005517279435199307), np.float64(0.09343087916515545), np.float64(0.04), np.float64(0.272732706067244), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  1.5 

learned probs for this beta: {9: np.float64(0.17703501588208964), 3: np.float64(0.245707171018532), 7: np.float64(0.09555962816220787), 91: np.float64(3.64136344010652e-296), 11: np.float64(0.4816981849371704), 66: np.float64(3.64136344010652e-296), 0: np.float64(3.64136344010652e-296)}
err dic= {9: np.float64(0.05496498411791037), 3: np.float64(0.00570717101853202), 7: np.float64(0.09244037183779213), 91: np.float64(0.04), 11: np.float64(0.27169818493717046), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.05496498411791037), np.float64(0.00570717101853202), np.float64(0.09244037183779213), np.float64(0.04), np.float64(0.27169818493717046), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  1.75 

learned probs for this beta: {9: np.float64(0.177006566598535), 3: np.float64(0.24574229229774244), 7: np.float64(0.09597487661132018), 91: np.float64(0.0), 11: np.float64(0.4812762644924023), 66: np.float64(0.0), 0: np.float64(0.0)}
err dic= {9: np.float64(0.05499343340146501), 3: np.float64(0.005742292297742452), 7: np.float64(0.09202512338867982), 91: np.float64(0.04), 11: np.float64(0.2712762644924023), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.05499343340146501), np.float64(0.005742292297742452), np.float64(0.09202512338867982), np.float64(0.04), np.float64(0.2712762644924023), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

beta is  2 

learned probs for this beta: {9: np.float64(0.17700120589768978), 3: np.float64(0.2457486309018047), 7: np.float64(0.09614265325584953), 91: np.float64(0.0), 11: np.float64(0.4811075099446557), 66: np.float64(0.0), 0: np.float64(0.0)}
err dic= {9: np.float64(0.05499879410231023), 3: np.float64(0.005748630901804719), 7: np.float64(0.09185734674415047), 91: np.float64(0.04), 11: np.float64(0.2711075099446557), 66: np.float64(0.056), 0: np.float64(0.034)} 

err list= [np.float64(0.05499879410231023), np.float64(0.005748630901804719), np.float64(0.09185734674415047), np.float64(0.04), np.float64(0.2711075099446557), np.float64(0.056), np.float64(0.034)]
results for assortment [9, 3, 7, 91, 11, 66] :

err MNL dic= {9: 0.232, 3: 0.24, 7: 0.188, 91: 0.04, 11: 0.21, 66: 0.056, 0: np.float64(0.5057116745580689)} 

err MNL list= [0.232, 0.24, 0.188, 0.04, 0.21, 0.056, np.float64(0.5057116745580689)]
sampled assortment [4, 9, 5, 31, 20, 14] number: 7
#  Learning probs for MM model, A = [4, 9, 5, 31, 20, 14]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 2, 14: 3, 100: 0} [3, 4, 8, 100, 1, 5, 6, 9, 11, 7, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {7: 0, 8: 0, 12: 0} [7, 8, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1, 100: 1} [1, 2, 5, 6, 9, 10, 14, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 5: 4, 6: 1, 7: 1, 8: 1, 10: 1, 17: 5, 20: 4, 100: 1} [2, 6, 7, 8, 10, 100, 1, 5, 20, 17]
#  Learning probs for MM model, A = [4, 9, 5, 31, 20, 14]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 1, 9: 2, 11: 2, 13: 3, 14: 3, 16: 3, 100: 0} [3, 4, 100, 8, 2, 5, 6, 9, 11, 7, 13, 14, 16]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 7: 0, 8: 0, 10: 0, 11: 0, 12: 0} [5, 7, 8, 10, 11, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 13: 1, 100: 1} [1, 2, 5, 6, 9, 13, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 6: 1, 7: 1, 8: 0, 10: 1, 11: 2, 13: 6, 20: 5, 100: 1} [2, 8, 6, 7, 10, 100, 11, 1, 20, 13]
empirical probabilities from test set: {4: 0.209, 9: 0.2, 5: 0.189, 31: 0.087, 20: 0.147, 14: 0.141, 0: 0.027}
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.06827215407189474), 9: np.float64(0.1466414770369873), 5: np.float64(0.6336151254359225), 31: np.float64(0.00010590196428778119), 20: np.float64(0.09617791573007833), 14: np.float64(0.055081523796541555), 0: np.float64(0.00010590196428778119)}
err dic= {4: np.float64(0.14072784592810525), 9: np.float64(0.05335852296301272), 5: np.float64(0.44461512543592246), 31: np.float64(0.08689409803571221), 20: np.float64(0.05082208426992166), 14: np.float64(0.08591847620345844), 0: np.float64(0.02689409803571222)} 

err list= [np.float64(0.14072784592810525), np.float64(0.05335852296301272), np.float64(0.44461512543592246), np.float64(0.08689409803571221), np.float64(0.05082208426992166), np.float64(0.08591847620345844), np.float64(0.02689409803571222)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.07517305368597231), 9: np.float64(0.14291993958362212), 5: np.float64(0.6367659119180715), 31: np.float64(1.0429150428718997e-09), 20: np.float64(0.0962499985856108), 14: np.float64(0.04889109414089325), 0: np.float64(1.0429150428718997e-09)}
err dic= {4: np.float64(0.1338269463140277), 9: np.float64(0.05708006041637789), 5: np.float64(0.4477659119180715), 31: np.float64(0.08699999895708495), 20: np.float64(0.05075000141438919), 14: np.float64(0.09210890585910674), 0: np.float64(0.026999998957084957)} 

err list= [np.float64(0.1338269463140277), np.float64(0.05708006041637789), np.float64(0.4477659119180715), np.float64(0.08699999895708495), np.float64(0.05075000141438919), np.float64(0.09210890585910674), np.float64(0.026999998957084957)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.08965020225792295), 9: np.float64(0.13493561192919976), 5: np.float64(0.6412864144408209), 31: np.float64(1.2934827233301e-19), 20: np.float64(0.09625000000000004), 14: np.float64(0.03787777137205657), 0: np.float64(1.2934827233301e-19)}
err dic= {4: np.float64(0.11934979774207705), 9: np.float64(0.06506438807080026), 5: np.float64(0.4522864144408209), 31: np.float64(0.087), 20: np.float64(0.05074999999999995), 14: np.float64(0.10312222862794342), 0: np.float64(0.027)} 

err list= [np.float64(0.11934979774207705), np.float64(0.06506438807080026), np.float64(0.4522864144408209), np.float64(0.087), np.float64(0.05074999999999995), np.float64(0.10312222862794342), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.13293367583666413), 9: np.float64(0.10821234552243035), 5: np.float64(0.6474475052303499), 31: np.float64(7.632926189090847e-49), 20: np.float64(0.09624999999999993), 14: np.float64(0.015156473410555179), 0: np.float64(7.632926189090847e-49)}
err dic= {4: np.float64(0.07606632416333586), 9: np.float64(0.09178765447756966), 5: np.float64(0.4584475052303499), 31: np.float64(0.087), 20: np.float64(0.05075000000000006), 14: np.float64(0.1258435265894448), 0: np.float64(0.027)} 

err list= [np.float64(0.07606632416333586), np.float64(0.09178765447756966), np.float64(0.4584475052303499), np.float64(0.087), np.float64(0.05075000000000006), np.float64(0.1258435265894448), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.18843823426943562), 9: np.float64(0.0690571508380284), 5: np.float64(0.6439912255555595), 31: np.float64(2.517210183843958e-97), 20: np.float64(0.09625000000000003), 14: np.float64(0.0022633893369765185), 0: np.float64(2.517210183843958e-97)}
err dic= {4: np.float64(0.02056176573056437), 9: np.float64(0.13094284916197163), 5: np.float64(0.45499122555555954), 31: np.float64(0.087), 20: np.float64(0.05074999999999996), 14: np.float64(0.13873661066302348), 0: np.float64(0.027)} 

err list= [np.float64(0.02056176573056437), np.float64(0.13094284916197163), np.float64(0.45499122555555954), np.float64(0.087), np.float64(0.05074999999999996), np.float64(0.13873661066302348), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.2194916636095576), 9: np.float64(0.044137851686424236), 5: np.float64(0.6398594237263715), 31: np.float64(8.587391729426764e-146), 20: np.float64(0.09624999999999997), 14: np.float64(0.0002610609776467386), 0: np.float64(8.587391729426764e-146)}
err dic= {4: np.float64(0.010491663609557611), 9: np.float64(0.15586214831357578), 5: np.float64(0.4508594237263715), 31: np.float64(0.087), 20: np.float64(0.05075000000000002), 14: np.float64(0.14073893902235324), 0: np.float64(0.027)} 

err list= [np.float64(0.010491663609557611), np.float64(0.15586214831357578), np.float64(0.4508594237263715), np.float64(0.087), np.float64(0.05075000000000002), np.float64(0.14073893902235324), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  1 

learned probs for this beta: {4: np.float64(0.23448440039396218), 9: np.float64(0.02900291881400122), 5: np.float64(0.6402361377605184), 31: np.float64(2.973224152199598e-194), 20: np.float64(0.09625000000000003), 14: np.float64(2.6543031518315217e-05), 0: np.float64(2.973224152199598e-194)}
err dic= {4: np.float64(0.025484400393962187), 9: np.float64(0.1709970811859988), 5: np.float64(0.45123613776051835), 31: np.float64(0.087), 20: np.float64(0.05074999999999996), 14: np.float64(0.14097345696848168), 0: np.float64(0.027)} 

err list= [np.float64(0.025484400393962187), np.float64(0.1709970811859988), np.float64(0.45123613776051835), np.float64(0.087), np.float64(0.05074999999999996), np.float64(0.14097345696848168), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.24112084389098937), 9: np.float64(0.019237226903469816), 5: np.float64(0.6433894141922442), 31: np.float64(1.0421609912779463e-242), 20: np.float64(0.09624999999999997), 14: np.float64(2.5150132963833248e-06), 0: np.float64(1.0421609912779463e-242)}
err dic= {4: np.float64(0.032120843890989376), 9: np.float64(0.1807627730965302), 5: np.float64(0.45438941419224416), 31: np.float64(0.087), 20: np.float64(0.05075000000000002), 14: np.float64(0.14099748498670361), 0: np.float64(0.027)} 

err list= [np.float64(0.032120843890989376), np.float64(0.1807627730965302), np.float64(0.45438941419224416), np.float64(0.087), np.float64(0.05075000000000002), np.float64(0.14099748498670361), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  1.5 

learned probs for this beta: {4: np.float64(0.24390179503614995), 9: np.float64(0.012674472969402037), 5: np.float64(0.6471735039178714), 31: np.float64(3.6915333825062154e-291), 20: np.float64(0.09624999999999996), 14: np.float64(2.2807657675801165e-07), 0: np.float64(3.6915333825062154e-291)}
err dic= {4: np.float64(0.03490179503614996), 9: np.float64(0.18732552703059796), 5: np.float64(0.4581735039178714), 31: np.float64(0.087), 20: np.float64(0.05075000000000003), 14: np.float64(0.14099977192342322), 0: np.float64(0.027)} 

err list= [np.float64(0.03490179503614996), np.float64(0.18732552703059796), np.float64(0.4581735039178714), np.float64(0.087), np.float64(0.05075000000000003), np.float64(0.14099977192342322), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  1.75 

learned probs for this beta: {4: np.float64(0.24502665816789723), 9: np.float64(0.008243582941346311), 5: np.float64(0.6504797387955977), 31: np.float64(0.0), 20: np.float64(0.09624999999999999), 14: np.float64(2.0095158574010915e-08), 0: np.float64(0.0)}
err dic= {4: np.float64(0.03602665816789724), 9: np.float64(0.1917564170586537), 5: np.float64(0.4614797387955977), 31: np.float64(0.087), 20: np.float64(0.05075), 14: np.float64(0.14099997990484142), 0: np.float64(0.027)} 

err list= [np.float64(0.03602665816789724), np.float64(0.1917564170586537), np.float64(0.4614797387955977), np.float64(0.087), np.float64(0.05075), np.float64(0.14099997990484142), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

beta is  2 

learned probs for this beta: {4: np.float64(0.24547094428797367), 9: np.float64(0.005290386813918349), 5: np.float64(0.6529886671619493), 31: np.float64(0.0), 20: np.float64(0.09624999999999999), 14: np.float64(1.736158644216704e-09), 0: np.float64(0.0)}
err dic= {4: np.float64(0.03647094428797368), 9: np.float64(0.19470961318608165), 5: np.float64(0.46398866716194925), 31: np.float64(0.087), 20: np.float64(0.05075), 14: np.float64(0.14099999826384135), 0: np.float64(0.027)} 

err list= [np.float64(0.03647094428797368), np.float64(0.19470961318608165), np.float64(0.46398866716194925), np.float64(0.087), np.float64(0.05075), np.float64(0.14099999826384135), np.float64(0.027)]
results for assortment [4, 9, 5, 31, 20, 14] :

err MNL dic= {4: 0.209, 9: 0.2, 5: 0.189, 31: 0.087, 20: 0.147, 14: 0.141, 0: np.float64(0.5060519397978726)} 

err MNL list= [0.209, 0.2, 0.189, 0.087, 0.147, 0.141, np.float64(0.5060519397978726)]
sampled assortment [4, 1, 6, 54, 64, 98] number: 8
#  Learning probs for MM model, A = [4, 1, 6, 54, 64, 98]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 2, 12: 3, 14: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 11, 7, 12, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {7: 0, 8: 0, 10: 0, 12: 0} [7, 8, 10, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 6: 1, 9: 1, 10: 1, 13: 1, 14: 1, 100: 1} [1, 6, 9, 10, 13, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 4: 5, 5: 5, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 13: 5, 20: 5, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 4, 5, 13, 20]
#  Learning probs for MM model, A = [4, 1, 6, 54, 64, 98]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {1: 3, 2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 11: 3, 14: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 1, 7, 11, 14]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {8: 0, 12: 0} [8, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 2: 1, 5: 1, 6: 1, 9: 1, 10: 1, 14: 1, 15: 1, 100: 1} [1, 2, 5, 6, 9, 10, 14, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 4: 6, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 17: 5, 25: 6, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 17, 4, 25]
empirical probabilities from test set: {4: 0.243, 1: 0.253, 6: 0.261, 54: 0.076, 64: 0.071, 98: 0.056, 0: 0.04}
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.18724962215876373), 1: np.float64(0.26780327635991924), 6: np.float64(0.27000474652200235), 54: np.float64(0.06873558873982863), 64: np.float64(0.06873558873982863), 98: np.float64(0.06873558873982863), 0: np.float64(0.06873558873982863)}
err dic= {4: np.float64(0.055750377841236265), 1: np.float64(0.014803276359919237), 6: np.float64(0.009004746522002338), 54: np.float64(0.007264411260171369), 64: np.float64(0.0022644112601713645), 98: np.float64(0.012735588739828628), 0: np.float64(0.02873558873982863)} 

err list= [np.float64(0.055750377841236265), np.float64(0.014803276359919237), np.float64(0.009004746522002338), np.float64(0.007264411260171369), np.float64(0.0022644112601713645), np.float64(0.012735588739828628), np.float64(0.02873558873982863)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.19199895503676004), 1: np.float64(0.2644129606314081), 6: np.float64(0.26873094034312217), 54: np.float64(0.06871428599717742), 64: np.float64(0.06871428599717742), 98: np.float64(0.06871428599717742), 0: np.float64(0.06871428599717742)}
err dic= {4: np.float64(0.051001044963239955), 1: np.float64(0.01141296063140812), 6: np.float64(0.007730940343122161), 54: np.float64(0.007285714002822574), 64: np.float64(0.0022857140028225698), 98: np.float64(0.012714285997177423), 0: np.float64(0.028714285997177423)} 

err list= [np.float64(0.051001044963239955), np.float64(0.01141296063140812), np.float64(0.007730940343122161), np.float64(0.007285714002822574), np.float64(0.0022857140028225698), np.float64(0.012714285997177423), np.float64(0.028714285997177423)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.20191203724379495), 1: np.float64(0.25754877715853863), 6: np.float64(0.26568204274052376), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.04108796275620505), 1: np.float64(0.0045487771585386305), 6: np.float64(0.004682042740523751), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.04108796275620505), np.float64(0.0045487771585386305), np.float64(0.004682042740523751), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.23296756547746106), 1: np.float64(0.2391642384638904), 6: np.float64(0.2530110532015055), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.010032434522538936), 1: np.float64(0.013835761536109603), 6: np.float64(0.00798894679849449), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.010032434522538936), np.float64(0.013835761536109603), np.float64(0.00798894679849449), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.2760331027370933), 1: np.float64(0.22439653425187903), 6: np.float64(0.22471322015388498), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.03303310273709331), 1: np.float64(0.028603465748120976), 6: np.float64(0.03628677984611503), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.03303310273709331), np.float64(0.028603465748120976), np.float64(0.03628677984611503), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.29956522683440945), 1: np.float64(0.22608077424658285), 6: np.float64(0.1994968560618649), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.056565226834409454), 1: np.float64(0.026919225753417153), 6: np.float64(0.06150314393813511), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.056565226834409454), np.float64(0.026919225753417153), np.float64(0.06150314393813511), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  1 

learned probs for this beta: {4: np.float64(0.30931877780324085), 1: np.float64(0.2325684697336975), 6: np.float64(0.1832556096059189), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.06631877780324086), 1: np.float64(0.02043153026630251), 6: np.float64(0.0777443903940811), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.06631877780324086), np.float64(0.02043153026630251), np.float64(0.0777443903940811), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.31279848926378934), 1: np.float64(0.2380731778556192), 6: np.float64(0.17427119002344849), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.06979848926378934), 1: np.float64(0.014926822144380791), 6: np.float64(0.08672880997655152), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.06979848926378934), np.float64(0.014926822144380791), np.float64(0.08672880997655152), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  1.5 

learned probs for this beta: {4: np.float64(0.31394475348250467), 1: np.float64(0.24158670438406774), 6: np.float64(0.16961139927628455), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.07094475348250467), 1: np.float64(0.011413295615932267), 6: np.float64(0.09138860072371546), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.07094475348250467), np.float64(0.011413295615932267), np.float64(0.09138860072371546), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  1.75 

learned probs for this beta: {4: np.float64(0.31430594707993714), 1: np.float64(0.24357681040751655), 6: np.float64(0.16726009965540323), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.07130594707993715), 1: np.float64(0.00942318959248345), 6: np.float64(0.09373990034459678), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.07130594707993715), np.float64(0.00942318959248345), np.float64(0.09373990034459678), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

beta is  2 

learned probs for this beta: {4: np.float64(0.31441676425471227), 1: np.float64(0.2446362475913489), 6: np.float64(0.16608984529679577), 54: np.float64(0.06871428571428571), 64: np.float64(0.06871428571428571), 98: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {4: np.float64(0.07141676425471227), 1: np.float64(0.008363752408651115), 6: np.float64(0.09491015470320424), 54: np.float64(0.007285714285714284), 64: np.float64(0.00228571428571428), 98: np.float64(0.012714285714285713), 0: np.float64(0.028714285714285713)} 

err list= [np.float64(0.07141676425471227), np.float64(0.008363752408651115), np.float64(0.09491015470320424), np.float64(0.007285714285714284), np.float64(0.00228571428571428), np.float64(0.012714285714285713), np.float64(0.028714285714285713)]
results for assortment [4, 1, 6, 54, 64, 98] :

err MNL dic= {4: 0.243, 1: 0.253, 6: 0.261, 54: 0.076, 64: 0.071, 98: 0.056, 0: np.float64(0.5064551088815856)} 

err MNL list= [0.243, 0.253, 0.261, 0.076, 0.071, 0.056, np.float64(0.5064551088815856)]
sampled assortment [3, 2, 6, 75, 62, 44] number: 9
#  Learning probs for MM model, A = [3, 2, 6, 75, 62, 44]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 8: 0, 9: 2, 12: 3, 15: 3, 100: 0} [3, 4, 8, 100, 2, 5, 6, 9, 12, 15]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 8: 0, 10: 0, 11: 0, 12: 0, 100: 0} [5, 8, 10, 11, 12, 100]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 6: 1, 9: 1, 10: 1, 15: 1, 100: 1} [1, 5, 6, 9, 10, 15, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 4, 2: 0, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 14: 6, 17: 5, 100: 2} [2, 6, 7, 8, 10, 11, 100, 1, 17, 14]
#  Learning probs for MM model, A = [3, 2, 6, 75, 62, 44]
#cluster  4 with weight 0.24575
Learned cluster center of cluster 4:  {2: 2, 3: 0, 4: 0, 5: 2, 6: 2, 7: 3, 8: 0, 9: 2, 12: 4, 14: 3, 100: 1} [3, 4, 8, 100, 2, 5, 6, 9, 7, 14, 12]
#cluster  2 with weight 0.481
Learned cluster center of cluster 2:  {5: 0, 8: 0, 10: 0, 12: 0} [5, 8, 10, 12]
#cluster  1 with weight 0.177
Learned cluster center of cluster 1:  {1: 0, 5: 1, 6: 1, 9: 1, 14: 1, 100: 1} [1, 5, 6, 9, 14, 100]
#cluster  3 with weight 0.09625
Learned cluster center of cluster 3:  {1: 3, 2: 0, 6: 1, 7: 1, 8: 1, 10: 1, 11: 2, 16: 6, 17: 5, 24: 6, 100: 1} [2, 6, 7, 8, 10, 100, 11, 1, 17, 16, 24]
empirical probabilities from test set: {3: 0.23, 2: 0.275, 6: 0.24, 75: 0.055, 62: 0.069, 44: 0.085, 0: 0.046}
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.15634615779486655), 2: np.float64(0.1982445225186959), 6: np.float64(0.37039235281143046), 75: np.float64(0.06875424171875175), 62: np.float64(0.06875424171875175), 44: np.float64(0.06875424171875175), 0: np.float64(0.06875424171875175)}
err dic= {3: np.float64(0.07365384220513346), 2: np.float64(0.07675547748130412), 6: np.float64(0.13039235281143047), 75: np.float64(0.013754241718751746), 62: np.float64(0.0002457582812482595), 44: np.float64(0.01624575828124826), 0: np.float64(0.022754241718751747)} 

err list= [np.float64(0.07365384220513346), np.float64(0.07675547748130412), np.float64(0.13039235281143047), np.float64(0.013754241718751746), np.float64(0.0002457582812482595), np.float64(0.01624575828124826), np.float64(0.022754241718751747)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.1621417983448515), 2: np.float64(0.19755347042674776), 6: np.float64(0.3654475868084689), 75: np.float64(0.06871428610498298), 62: np.float64(0.06871428610498298), 44: np.float64(0.06871428610498298), 0: np.float64(0.06871428610498298)}
err dic= {3: np.float64(0.0678582016551485), 2: np.float64(0.07744652957325227), 6: np.float64(0.1254475868084689), 75: np.float64(0.01371428610498298), 62: np.float64(0.0002857138950170257), 44: np.float64(0.016285713895017026), 0: np.float64(0.02271428610498298)} 

err list= [np.float64(0.0678582016551485), np.float64(0.07744652957325227), np.float64(0.1254475868084689), np.float64(0.01371428610498298), np.float64(0.0002857138950170257), np.float64(0.016285713895017026), np.float64(0.02271428610498298)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.17400973014424795), 2: np.float64(0.19567557025202031), 6: np.float64(0.35545755674658897), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.05599026985575206), 2: np.float64(0.07932442974797971), 6: np.float64(0.11545755674658897), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.05599026985575206), np.float64(0.07932442974797971), np.float64(0.11545755674658897), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.2096077233242466), 2: np.float64(0.18689291797619137), 6: np.float64(0.328642215842419), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.020392276675753412), 2: np.float64(0.08810708202380865), 6: np.float64(0.08864221584241899), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.020392276675753412), np.float64(0.08810708202380865), np.float64(0.08864221584241899), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.2586851431028026), 2: np.float64(0.1686317199032143), 6: np.float64(0.29782599413684036), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.028685143102802596), 2: np.float64(0.10636828009678573), 6: np.float64(0.057825994136840364), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.028685143102802596), np.float64(0.10636828009678573), np.float64(0.057825994136840364), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.28841047253783625), 2: np.float64(0.15510248998407844), 6: np.float64(0.28162989462094246), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.05841047253783624), 2: np.float64(0.11989751001592158), 6: np.float64(0.041629894620942465), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.05841047253783624), np.float64(0.11989751001592158), np.float64(0.041629894620942465), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  1 

learned probs for this beta: {3: np.float64(0.3032213267000663), 2: np.float64(0.14890323182344326), 6: np.float64(0.2730182986193476), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.07322132670006629), 2: np.float64(0.12609676817655677), 6: np.float64(0.03301829861934763), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.07322132670006629), np.float64(0.12609676817655677), np.float64(0.03301829861934763), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.30983738739242506), 2: np.float64(0.14778698056107364), 6: np.float64(0.26751848918935833), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.07983738739242505), 2: np.float64(0.12721301943892638), 6: np.float64(0.02751848918935834), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.07983738739242505), np.float64(0.12721301943892638), np.float64(0.02751848918935834), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.31261629218259374), 2: np.float64(0.1491622810573142), 6: np.float64(0.26336428390294914), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.08261629218259373), 2: np.float64(0.12583771894268583), 6: np.float64(0.023364283902949146), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.08261629218259373), np.float64(0.12583771894268583), np.float64(0.023364283902949146), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.31374096290822706), 2: np.float64(0.15141608283822164), 6: np.float64(0.25998581139640825), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.08374096290822705), 2: np.float64(0.12358391716177838), 6: np.float64(0.01998581139640826), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.08374096290822705), np.float64(0.12358391716177838), np.float64(0.01998581139640826), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

beta is  2 

learned probs for this beta: {3: np.float64(0.31418523166994544), 2: np.float64(0.1537648891770248), 6: np.float64(0.2571927362958868), 75: np.float64(0.06871428571428571), 62: np.float64(0.06871428571428571), 44: np.float64(0.06871428571428571), 0: np.float64(0.06871428571428571)}
err dic= {3: np.float64(0.08418523166994543), 2: np.float64(0.12123511082297522), 6: np.float64(0.0171927362958868), 75: np.float64(0.013714285714285714), 62: np.float64(0.0002857142857142919), 44: np.float64(0.016285714285714292), 0: np.float64(0.022714285714285715)} 

err list= [np.float64(0.08418523166994543), np.float64(0.12123511082297522), np.float64(0.0171927362958868), np.float64(0.013714285714285714), np.float64(0.0002857142857142919), np.float64(0.016285714285714292), np.float64(0.022714285714285715)]
results for assortment [3, 2, 6, 75, 62, 44] :

err MNL dic= {3: 0.23, 2: 0.275, 6: 0.24, 75: 0.055, 62: 0.069, 44: 0.085, 0: np.float64(0.49553302191908327)} 

err MNL list= [0.23, 0.275, 0.24, 0.055, 0.069, 0.085, np.float64(0.49553302191908327)]
****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= [0.04768595 0.04696814 0.04577744 0.04326671 0.04163849 0.04119726
 0.04113513 0.0411284  0.0410795  0.04097599 0.04083029]
mean_std= [0.         0.00071781 0.00178299 0.00461472 0.00525745 0.00489974
 0.00453883 0.00424572 0.00400529 0.00381242 0.00366409]
MNL: [0.2092327  0.21187732 0.2087814  0.20815204 0.21217844 0.20486438
 0.21024452 0.21129313 0.20949359 0.20707615]
 mean error for MNL:

mean_err_MNL= 0.20931936740958118
mean_std_MNL= 0.0021456451779391364
