p= 0.1 num clusters= 10
linkage completed in  10.69481086730957
silhouette_score of the clusters -0.05335452195273385
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 27: 1, 100: 1} [8, 1, 2, 3, 7, 27, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 10: 0, 12: 0, 16: 0, 20: 0, 21: 0} [3, 5, 7, 10, 12, 16, 20, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 10: 3, 11: 4, 12: 2, 13: 3, 15: 4, 18: 3, 23: 5, 25: 6, 27: 4} [6, 5, 4, 7, 12, 10, 13, 18, 11, 15, 27, 23, 25]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 15: 1, 24: 1} [1, 5, 15, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 11: 1, 13: 2, 17: 2, 18: 2, 21: 2, 23: 2, 100: 2} [9, 11, 5, 13, 17, 18, 21, 23, 100]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 1, 13: 4, 15: 3, 21: 7, 100: 0} [6, 100, 10, 1, 3, 15, 5, 13, 7, 21]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 11: 3, 14: 3, 15: 3, 16: 6, 18: 4, 19: 3, 23: 6, 25: 4, 27: 8, 63: 7} [1, 3, 9, 7, 11, 14, 15, 19, 18, 25, 16, 23, 63, 27]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 11: 2, 14: 2, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 11, 14, 5, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 4, 2: 14, 3: 11, 5: 8, 6: 3, 7: 5, 8: 0, 9: 5, 11: 0, 12: 14, 13: 3, 15: 14, 16: 9, 17: 10, 19: 3, 23: 8, 25: 10, 33: 14, 35: 12, 48: 16, 49: 16, 66: 17, 68: 14, 69: 13, 72: 14, 95: 15, 99: 13, 100: 2} [8, 11, 100, 6, 13, 19, 1, 7, 9, 5, 23, 16, 17, 25, 3, 35, 69, 99, 2, 12, 15, 33, 68, 72, 95, 48, 49, 66]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 17: 1, 22: 0, 25: 0} [3, 5, 7, 22, 25, 17]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 0, 6: 0, 7: 2, 8: 4, 11: 3, 12: 2, 13: 3, 15: 4, 20: 3, 21: 4, 29: 6, 100: 4} [5, 6, 4, 7, 12, 11, 13, 20, 8, 15, 21, 100, 29]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 12: 1, 25: 2} [2, 3, 6, 10, 12, 25]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 24: 1, 26: 1, 100: 1} [1, 5, 6, 10, 12, 13, 24, 26, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {4: 2, 5: 2, 9: 0, 11: 1, 18: 2} [9, 11, 4, 5, 18]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 4: 6, 5: 5, 6: 0, 7: 5, 10: 2, 12: 8, 13: 4, 14: 6, 15: 4, 20: 5, 23: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 20, 4, 14, 23, 12]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 7: 3, 9: 0, 10: 4, 11: 3, 14: 3, 19: 3, 23: 5, 43: 7, 45: 8} [1, 3, 9, 7, 11, 14, 19, 4, 10, 23, 43, 45]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 6: 2, 11: 2, 12: 3, 14: 2, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 11, 14, 12, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 4, 3: 7, 4: 7, 5: 10, 6: 3, 7: 5, 8: 0, 9: 6, 11: 0, 12: 12, 13: 3, 16: 11, 17: 7, 19: 3, 21: 13, 22: 13, 23: 7, 26: 13, 32: 16, 37: 14, 46: 12, 53: 15, 54: 14, 62: 17, 70: 13, 72: 17, 81: 16, 82: 16, 84: 15, 85: 18, 88: 16, 94: 17, 100: 2} [8, 11, 100, 6, 13, 19, 1, 7, 9, 3, 4, 17, 23, 5, 16, 12, 46, 21, 22, 26, 70, 37, 54, 53, 84, 32, 81, 82, 88, 62, 72, 94, 85]
empirical probabilities from test set: {2: 0.27, 3: 0.243, 4: 0.247, 59: 0.069, 40: 0.064, 84: 0.055, 0: 0.052}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.12128453994289581), 3: np.float64(0.10140191711988004), 4: np.float64(0.1426852113468342), 59: np.float64(0.1586570828975969), 40: np.float64(0.1586570828975969), 84: np.float64(0.1586570828975969), 0: np.float64(0.1586570828975969)}
err dic= {2: np.float64(0.1487154600571042), 3: np.float64(0.14159808288011994), 4: np.float64(0.10431478865316579), 59: np.float64(0.08965708289759688), 40: np.float64(0.09465708289759689), 84: np.float64(0.1036570828975969), 0: np.float64(0.1066570828975969)} 

err list= [np.float64(0.1487154600571042), np.float64(0.14159808288011994), np.float64(0.10431478865316579), np.float64(0.08965708289759688), np.float64(0.09465708289759689), np.float64(0.1036570828975969), np.float64(0.1066570828975969)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.1271587558408936), 3: np.float64(0.12730565775061561), 4: np.float64(0.1506181861837323), 59: np.float64(0.14872935005618967), 40: np.float64(0.14872935005618967), 84: np.float64(0.14872935005618967), 0: np.float64(0.14872935005618967)}
err dic= {2: np.float64(0.14284124415910643), 3: np.float64(0.11569434224938438), 4: np.float64(0.0963818138162677), 59: np.float64(0.07972935005618967), 40: np.float64(0.08472935005618967), 84: np.float64(0.09372935005618968), 0: np.float64(0.09672935005618968)} 

err list= [np.float64(0.14284124415910643), np.float64(0.11569434224938438), np.float64(0.0963818138162677), np.float64(0.07972935005618967), np.float64(0.08472935005618967), np.float64(0.09372935005618968), np.float64(0.09672935005618968)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.14499915389537646), 3: np.float64(0.19498713524859507), 4: np.float64(0.1667325290929103), 59: np.float64(0.12332029544077996), 40: np.float64(0.12332029544077996), 84: np.float64(0.12332029544077996), 0: np.float64(0.12332029544077996)}
err dic= {2: np.float64(0.12500084610462356), 3: np.float64(0.04801286475140493), 4: np.float64(0.08026747090708969), 59: np.float64(0.05432029544077996), 40: np.float64(0.05932029544077996), 84: np.float64(0.06832029544077997), 0: np.float64(0.07132029544077997)} 

err list= [np.float64(0.12500084610462356), np.float64(0.04801286475140493), np.float64(0.08026747090708969), np.float64(0.05432029544077996), np.float64(0.05932029544077996), np.float64(0.06832029544077997), np.float64(0.07132029544077997)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.21559322174766485), 3: np.float64(0.39050924277319277), 4: np.float64(0.18453558897120317), 59: np.float64(0.05234048662698489), 40: np.float64(0.05234048662698489), 84: np.float64(0.05234048662698489), 0: np.float64(0.05234048662698489)}
err dic= {2: np.float64(0.05440677825233517), 3: np.float64(0.14750924277319277), 4: np.float64(0.062464411028796823), 59: np.float64(0.016659513373015113), 40: np.float64(0.011659513373015108), 84: np.float64(0.002659513373015107), 0: np.float64(0.0003404866269848955)} 

err list= [np.float64(0.05440677825233517), np.float64(0.14750924277319277), np.float64(0.062464411028796823), np.float64(0.016659513373015113), np.float64(0.011659513373015108), np.float64(0.002659513373015107), np.float64(0.0003404866269848955)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.2593360917442984), 3: np.float64(0.46851881427547126), 4: np.float64(0.18672767784720035), 59: np.float64(0.02135435403325747), 40: np.float64(0.02135435403325747), 84: np.float64(0.02135435403325747), 0: np.float64(0.02135435403325747)}
err dic= {2: np.float64(0.010663908255701626), 3: np.float64(0.22551881427547127), 4: np.float64(0.06027232215279965), 59: np.float64(0.047645645966742534), 40: np.float64(0.04264564596674253), 84: np.float64(0.033645645966742535), 0: np.float64(0.03064564596674253)} 

err list= [np.float64(0.010663908255701626), np.float64(0.22551881427547127), np.float64(0.06027232215279965), np.float64(0.047645645966742534), np.float64(0.04264564596674253), np.float64(0.033645645966742535), np.float64(0.03064564596674253)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.2806023361088501), 3: np.float64(0.4631422455495547), 4: np.float64(0.18219063582683348), 59: np.float64(0.01851619562869043), 40: np.float64(0.01851619562869043), 84: np.float64(0.01851619562869043), 0: np.float64(0.01851619562869043)}
err dic= {2: np.float64(0.010602336108850086), 3: np.float64(0.2201422455495547), 4: np.float64(0.06480936417316652), 59: np.float64(0.050483804371309574), 40: np.float64(0.04548380437130957), 84: np.float64(0.036483804371309575), 0: np.float64(0.03348380437130957)} 

err list= [np.float64(0.010602336108850086), np.float64(0.2201422455495547), np.float64(0.06480936417316652), np.float64(0.050483804371309574), np.float64(0.04548380437130957), np.float64(0.036483804371309575), np.float64(0.03348380437130957)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.30054964081838637), 3: np.float64(0.45085854547167986), 4: np.float64(0.17513745979272308), 59: np.float64(0.01836358847930267), 40: np.float64(0.01836358847930267), 84: np.float64(0.01836358847930267), 0: np.float64(0.01836358847930267)}
err dic= {2: np.float64(0.030549640818386348), 3: np.float64(0.20785854547167987), 4: np.float64(0.07186254020727692), 59: np.float64(0.05063641152069734), 40: np.float64(0.045636411520697334), 84: np.float64(0.036636411520697326), 0: np.float64(0.033636411520697324)} 

err list= [np.float64(0.030549640818386348), np.float64(0.20785854547167987), np.float64(0.07186254020727692), np.float64(0.05063641152069734), np.float64(0.045636411520697334), np.float64(0.036636411520697326), np.float64(0.033636411520697324)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.3183950709622532), 3: np.float64(0.438896172367351), 4: np.float64(0.16927911230072823), 59: np.float64(0.01835741109241684), 40: np.float64(0.01835741109241684), 84: np.float64(0.01835741109241684), 0: np.float64(0.01835741109241684)}
err dic= {2: np.float64(0.048395070962253206), 3: np.float64(0.19589617236735102), 4: np.float64(0.07772088769927177), 59: np.float64(0.050642588907583164), 40: np.float64(0.04564258890758316), 84: np.float64(0.036642588907583165), 0: np.float64(0.03364258890758316)} 

err list= [np.float64(0.048395070962253206), np.float64(0.19589617236735102), np.float64(0.07772088769927177), np.float64(0.050642588907583164), np.float64(0.04564258890758316), np.float64(0.036642588907583165), np.float64(0.03364258890758316)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: np.float64(0.13548223350253807), 3: np.float64(0.10731895093062604), 4: np.float64(0.1124293570219966), 59: np.float64(0.03944966159052453), 40: np.float64(0.05206387478849407), 84: np.float64(0.05133460236886634), 0: np.float64(0.21238240270727582)} 

err MNL list= [np.float64(0.13548223350253807), np.float64(0.10731895093062604), np.float64(0.1124293570219966), np.float64(0.03944966159052453), np.float64(0.05206387478849407), np.float64(0.05133460236886634), np.float64(0.21238240270727582)]
sampled assortment [2, 6, 3, 99, 72, 91] number: 1
#  Learning probs for MM model, A = [2, 6, 3, 99, 72, 91]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 10, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 4: 0, 5: 0, 7: 0, 10: 0, 12: 0, 15: 0, 17: 0, 21: 0} [3, 4, 5, 7, 10, 12, 15, 17, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 11: 3, 12: 2, 13: 3, 15: 4} [6, 5, 4, 7, 12, 11, 13, 15]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 21: 1, 100: 1} [2, 1, 5, 6, 10, 12, 13, 21, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 12: 1, 14: 1, 15: 1, 24: 1} [1, 5, 6, 10, 12, 14, 15, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {4: 2, 7: 2, 9: 0, 10: 2, 11: 1, 13: 2, 18: 2, 24: 3, 100: 1} [9, 11, 100, 4, 7, 10, 13, 18, 24]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 3, 15: 3, 17: 6, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 7: 3, 9: 0, 10: 4, 11: 3, 12: 8, 14: 3, 15: 3, 18: 5, 19: 3, 72: 9} [1, 3, 9, 7, 11, 14, 15, 19, 4, 10, 18, 12, 72]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 12: 3, 14: 3, 15: 3, 16: 3, 19: 1, 25: 3, 100: 0} [100, 3, 4, 19, 12, 14, 15, 16, 25]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 7, 4: 9, 5: 9, 6: 4, 7: 4, 8: 0, 9: 6, 10: 11, 11: 0, 13: 3, 16: 10, 17: 9, 19: 4, 22: 14, 23: 8, 24: 15, 27: 15, 33: 12, 45: 18, 52: 14, 53: 12, 63: 16, 64: 15, 68: 14, 83: 11, 88: 13, 100: 2} [8, 11, 100, 1, 13, 6, 7, 19, 9, 3, 23, 4, 5, 17, 16, 10, 83, 33, 53, 88, 22, 52, 68, 24, 27, 64, 63, 45]
#  Learning probs for MM model, A = [2, 6, 3, 99, 72, 91]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {2: 1, 3: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 2, 3, 7, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 7: 0, 12: 0, 15: 0} [3, 7, 12, 15]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 12: 2, 20: 3, 27: 4} [6, 5, 4, 7, 12, 20, 27]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 100: 1} [2, 1, 3, 6, 10, 11, 12, 13, 14, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 10: 1, 13: 1, 100: 1} [1, 5, 10, 13, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {4: 2, 5: 2, 7: 2, 9: 0, 11: 1, 15: 2, 18: 1, 26: 2, 100: 1} [9, 11, 18, 100, 4, 5, 7, 15, 26]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 4, 14: 5, 15: 3, 17: 7, 20: 5, 100: 0} [6, 100, 1, 3, 10, 15, 13, 5, 7, 14, 20, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 5: 4, 7: 3, 9: 0, 10: 4, 11: 3, 14: 3, 15: 3, 19: 3, 30: 7} [1, 3, 9, 7, 11, 14, 15, 19, 4, 5, 10, 30]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 2, 11: 2, 12: 2, 14: 3, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 11, 12, 5, 14, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 4: 9, 6: 3, 7: 3, 8: 0, 9: 5, 11: 0, 12: 11, 13: 3, 16: 9, 17: 7, 18: 10, 19: 3, 20: 11, 25: 10, 28: 11, 33: 11, 37: 14, 47: 11, 69: 15, 72: 12, 75: 13, 89: 13, 95: 15, 100: 2} [8, 11, 100, 1, 6, 7, 13, 19, 9, 17, 4, 16, 18, 25, 12, 20, 28, 33, 47, 72, 75, 89, 37, 69, 95]
empirical probabilities from test set: {2: 0.284, 6: 0.267, 3: 0.239, 99: 0.061, 72: 0.058, 91: 0.043, 0: 0.048}
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.1282701951425375), 6: np.float64(0.1383915754016827), 3: np.float64(0.10538220072716985), 99: np.float64(0.15698900718215217), 72: np.float64(0.15698900718215217), 91: np.float64(0.15698900718215217), 0: np.float64(0.15698900718215217)}
err dic= {2: np.float64(0.15572980485746246), 6: np.float64(0.1286084245983173), 3: np.float64(0.13361779927283013), 99: np.float64(0.09598900718215217), 72: np.float64(0.09898900718215217), 91: np.float64(0.11398900718215217), 0: np.float64(0.10898900718215217)} 

err list= [np.float64(0.15572980485746246), np.float64(0.1286084245983173), np.float64(0.13361779927283013), np.float64(0.09598900718215217), np.float64(0.09898900718215217), np.float64(0.11398900718215217), np.float64(0.10898900718215217)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.13880963848650385), 6: np.float64(0.15216483195634062), 3: np.float64(0.1327452720191743), 99: np.float64(0.14407006438449602), 72: np.float64(0.14407006438449602), 91: np.float64(0.14407006438449602), 0: np.float64(0.14407006438449602)}
err dic= {2: np.float64(0.14519036151349612), 6: np.float64(0.1148351680436594), 3: np.float64(0.10625472798082569), 99: np.float64(0.08307006438449602), 72: np.float64(0.08607006438449602), 91: np.float64(0.10107006438449602), 0: np.float64(0.09607006438449602)} 

err list= [np.float64(0.14519036151349612), np.float64(0.1148351680436594), np.float64(0.10625472798082569), np.float64(0.08307006438449602), np.float64(0.08607006438449602), np.float64(0.10107006438449602), np.float64(0.09607006438449602)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.16407927175355044), 6: np.float64(0.17921872473277176), 3: np.float64(0.19746191092888415), 99: np.float64(0.11481002314619884), 72: np.float64(0.11481002314619884), 91: np.float64(0.11481002314619884), 0: np.float64(0.11481002314619884)}
err dic= {2: np.float64(0.11992072824644953), 6: np.float64(0.08778127526722826), 3: np.float64(0.041538089071115836), 99: np.float64(0.05381002314619884), 72: np.float64(0.05681002314619884), 91: np.float64(0.07181002314619885), 0: np.float64(0.06681002314619884)} 

err list= [np.float64(0.11992072824644953), np.float64(0.08778127526722826), np.float64(0.041538089071115836), np.float64(0.05381002314619884), np.float64(0.05681002314619884), np.float64(0.07181002314619885), np.float64(0.06681002314619884)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.22486159765744532), 6: np.float64(0.20121486265124233), 3: np.float64(0.35433080649711857), 99: np.float64(0.05489818329854849), 72: np.float64(0.05489818329854849), 91: np.float64(0.05489818329854849), 0: np.float64(0.05489818329854849)}
err dic= {2: np.float64(0.05913840234255466), 6: np.float64(0.06578513734875768), 3: np.float64(0.11533080649711858), 99: np.float64(0.006101816701451511), 72: np.float64(0.0031018167014515152), 91: np.float64(0.011898183298548491), 0: np.float64(0.006898183298548487)} 

err list= [np.float64(0.05913840234255466), np.float64(0.06578513734875768), np.float64(0.11533080649711858), np.float64(0.006101816701451511), np.float64(0.0031018167014515152), np.float64(0.011898183298548491), np.float64(0.006898183298548487)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.26541451789477244), 6: np.float64(0.17930249133300444), 3: np.float64(0.43097903556990547), 99: np.float64(0.031075988800579487), 72: np.float64(0.031075988800579487), 91: np.float64(0.031075988800579487), 0: np.float64(0.031075988800579487)}
err dic= {2: np.float64(0.018585482105227535), 6: np.float64(0.08769750866699558), 3: np.float64(0.19197903556990548), 99: np.float64(0.02992401119942051), 72: np.float64(0.026924011199420516), 91: np.float64(0.01192401119942051), 0: np.float64(0.016924011199420514)} 

err list= [np.float64(0.018585482105227535), np.float64(0.08769750866699558), np.float64(0.19197903556990548), np.float64(0.02992401119942051), np.float64(0.026924011199420516), np.float64(0.01192401119942051), np.float64(0.016924011199420514)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.2962267180376928), 6: np.float64(0.16185523505973484), 3: np.float64(0.42727778631275193), 99: np.float64(0.0286600651474551), 72: np.float64(0.0286600651474551), 91: np.float64(0.0286600651474551), 0: np.float64(0.0286600651474551)}
err dic= {2: np.float64(0.012226718037692819), 6: np.float64(0.10514476494026517), 3: np.float64(0.18827778631275194), 99: np.float64(0.032339934852544897), 72: np.float64(0.029339934852544904), 91: np.float64(0.014339934852544898), 0: np.float64(0.019339934852544902)} 

err list= [np.float64(0.012226718037692819), np.float64(0.10514476494026517), np.float64(0.18827778631275194), np.float64(0.032339934852544897), np.float64(0.029339934852544904), np.float64(0.014339934852544898), np.float64(0.019339934852544902)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  1 

learned probs for this beta: {2: np.float64(0.3231603400502081), 6: np.float64(0.1508073320226959), 3: np.float64(0.41187235770914926), 99: np.float64(0.028539992554486714), 72: np.float64(0.028539992554486714), 91: np.float64(0.028539992554486714), 0: np.float64(0.028539992554486714)}
err dic= {2: np.float64(0.03916034005020813), 6: np.float64(0.11619266797730413), 3: np.float64(0.17287235770914927), 99: np.float64(0.032460007445513285), 72: np.float64(0.02946000744551329), 91: np.float64(0.014460007445513283), 0: np.float64(0.019460007445513287)} 

err list= [np.float64(0.03916034005020813), np.float64(0.11619266797730413), np.float64(0.17287235770914927), np.float64(0.032460007445513285), np.float64(0.02946000744551329), np.float64(0.014460007445513283), np.float64(0.019460007445513287)]
results for assortment [2, 6, 3, 99, 72, 91] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.3447081464278822), 6: np.float64(0.14411763418682672), 3: np.float64(0.39703078595373653), 99: np.float64(0.02853585835788862), 72: np.float64(0.02853585835788862), 91: np.float64(0.02853585835788862), 0: np.float64(0.02853585835788862)}
err dic= {2: np.float64(0.06070814642788225), 6: np.float64(0.1228823658131733), 3: np.float64(0.15803078595373654), 99: np.float64(0.03246414164211138), 72: np.float64(0.029464141642111384), 91: np.float64(0.014464141642111378), 0: np.float64(0.019464141642111382)} 

err list= [np.float64(0.06070814642788225), np.float64(0.1228823658131733), np.float64(0.15803078595373654), np.float64(0.03246414164211138), np.float64(0.029464141642111384), np.float64(0.014464141642111378), np.float64(0.019464141642111382)]
results for assortment [2, 6, 3, 99, 72, 91] :

err MNL dic= {2: np.float64(0.14829828772603615), 6: np.float64(0.12783106630394195), 3: np.float64(0.10212476662932735), 99: np.float64(0.04664388968901692), 72: np.float64(0.0502306502373713), 91: np.float64(0.06267024057182484), 0: np.float64(0.21870934016109245)} 

err MNL list= [np.float64(0.14829828772603615), np.float64(0.12783106630394195), np.float64(0.10212476662932735), np.float64(0.04664388968901692), np.float64(0.0502306502373713), np.float64(0.06267024057182484), np.float64(0.21870934016109245)]
sampled assortment [1, 4, 6, 79, 56, 88] number: 2
#  Learning probs for MM model, A = [1, 4, 6, 79, 56, 88]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 4, 5, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 16: 0} [3, 5, 7, 12, 16]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 11: 4, 12: 2, 18: 3, 21: 4, 23: 4} [6, 5, 4, 7, 12, 18, 11, 21, 23]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 5: 1, 6: 1, 10: 1, 11: 1} [2, 1, 3, 4, 5, 6, 10, 11]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 24: 1} [1, 4, 5, 6, 10, 12, 13, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 10: 2, 11: 1, 13: 2, 18: 2, 21: 2, 24: 2, 27: 2, 100: 2} [9, 11, 5, 10, 13, 18, 21, 24, 27, 100]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 4: 7, 5: 4, 6: 0, 8: 5, 10: 1, 13: 4, 15: 3, 20: 4, 100: 0} [6, 100, 10, 1, 3, 15, 5, 13, 20, 8, 4]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 11: 3, 12: 6, 14: 3, 15: 3, 17: 6, 18: 3, 33: 8, 97: 8} [1, 3, 9, 7, 11, 14, 15, 18, 12, 17, 33, 97]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 2, 11: 2, 12: 4, 14: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 11, 5, 14, 12]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 8, 5: 8, 6: 4, 7: 5, 8: 0, 9: 7, 11: 0, 13: 3, 16: 8, 19: 4, 22: 14, 34: 12, 35: 10, 38: 12, 39: 12, 41: 11, 47: 13, 51: 12, 80: 13, 84: 10, 89: 15, 94: 13, 100: 2} [8, 11, 100, 1, 13, 6, 19, 7, 9, 3, 5, 16, 35, 84, 41, 34, 38, 39, 51, 47, 80, 94, 22, 89]
#  Learning probs for MM model, A = [1, 4, 6, 79, 56, 88]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 4: 0, 5: 0, 12: 0, 14: 0, 15: 0, 16: 0, 21: 0, 30: 2, 31: 0} [3, 4, 5, 12, 14, 15, 16, 21, 31, 30]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 1, 5: 1, 6: 0, 7: 3, 8: 4, 10: 3, 11: 2, 12: 2, 16: 4, 20: 4, 25: 6, 100: 5} [6, 4, 5, 11, 12, 7, 10, 8, 16, 20, 100, 25]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 100: 1} [2, 1, 3, 6, 10, 11, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 13: 1, 14: 1, 15: 1, 21: 1, 100: 1} [1, 5, 6, 10, 13, 14, 15, 21, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {9: 0, 10: 2, 11: 1, 13: 2, 16: 2, 24: 2, 26: 2} [9, 11, 10, 13, 16, 24, 26]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 3, 14: 5, 15: 3, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 14]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 5: 4, 7: 3, 9: 0, 11: 3, 14: 3, 15: 4, 19: 3, 46: 8} [1, 3, 9, 7, 11, 14, 19, 4, 5, 15, 46]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 2, 7: 4, 11: 3, 14: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 5, 11, 14, 7]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 8, 6: 3, 7: 5, 8: 0, 11: 0, 13: 3, 15: 15, 16: 9, 17: 6, 18: 11, 19: 3, 23: 8, 29: 9, 31: 14, 38: 8, 45: 12, 47: 11, 49: 11, 63: 14, 84: 13, 86: 15, 97: 11, 98: 13, 99: 17, 100: 2} [8, 11, 100, 1, 6, 13, 19, 7, 17, 3, 23, 38, 16, 29, 18, 47, 49, 97, 45, 84, 98, 31, 63, 15, 86, 99]
empirical probabilities from test set: {1: 0.257, 4: 0.254, 6: 0.262, 79: 0.07, 56: 0.068, 88: 0.039, 0: 0.05}
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.11239867507184244), 4: np.float64(0.1430716407644017), 6: np.float64(0.1246812981874442), 79: np.float64(0.15496209649407772), 56: np.float64(0.15496209649407772), 88: np.float64(0.15496209649407772), 0: np.float64(0.15496209649407772)}
err dic= {1: np.float64(0.14460132492815758), 4: np.float64(0.1109283592355983), 6: np.float64(0.13731870181255582), 79: np.float64(0.08496209649407771), 56: np.float64(0.08696209649407771), 88: np.float64(0.11596209649407771), 0: np.float64(0.10496209649407771)} 

err list= [np.float64(0.14460132492815758), np.float64(0.1109283592355983), np.float64(0.13731870181255582), np.float64(0.08496209649407771), np.float64(0.08696209649407771), np.float64(0.11596209649407771), np.float64(0.10496209649407771)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1310153413487882), 4: np.float64(0.15556686487850116), 6: np.float64(0.14295273815352685), 79: np.float64(0.1426162639047967), 56: np.float64(0.1426162639047967), 88: np.float64(0.1426162639047967), 0: np.float64(0.1426162639047967)}
err dic= {1: np.float64(0.1259846586512118), 4: np.float64(0.09843313512149884), 6: np.float64(0.11904726184647316), 79: np.float64(0.0726162639047967), 56: np.float64(0.0746162639047967), 88: np.float64(0.1036162639047967), 0: np.float64(0.0926162639047967)} 

err list= [np.float64(0.1259846586512118), np.float64(0.09843313512149884), np.float64(0.11904726184647316), np.float64(0.0726162639047967), np.float64(0.0746162639047967), np.float64(0.1036162639047967), np.float64(0.0926162639047967)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.18084537099798073), 4: np.float64(0.18600816139686951), 6: np.float64(0.1838415522174677), 79: np.float64(0.11232622884692069), 56: np.float64(0.11232622884692069), 88: np.float64(0.11232622884692069), 0: np.float64(0.11232622884692069)}
err dic= {1: np.float64(0.07615462900201928), 4: np.float64(0.06799183860313049), 6: np.float64(0.07815844778253231), 79: np.float64(0.04232622884692068), 56: np.float64(0.04432622884692068), 88: np.float64(0.0733262288469207), 0: np.float64(0.062326228846920684)} 

err list= [np.float64(0.07615462900201928), np.float64(0.06799183860313049), np.float64(0.07815844778253231), np.float64(0.04232622884692068), np.float64(0.04432622884692068), np.float64(0.0733262288469207), np.float64(0.062326228846920684)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.3407309471194903), 4: np.float64(0.25322866530962496), 6: np.float64(0.2395620701408641), 79: np.float64(0.04161957935750509), 56: np.float64(0.04161957935750509), 88: np.float64(0.04161957935750509), 0: np.float64(0.04161957935750509)}
err dic= {1: np.float64(0.0837309471194903), 4: np.float64(0.0007713346903750473), 6: np.float64(0.022437929859135924), 79: np.float64(0.028380420642494915), 56: np.float64(0.026380420642494913), 88: np.float64(0.002619579357505092), 0: np.float64(0.008380420642494911)} 

err list= [np.float64(0.0837309471194903), np.float64(0.0007713346903750473), np.float64(0.022437929859135924), np.float64(0.028380420642494915), np.float64(0.026380420642494913), np.float64(0.002619579357505092), np.float64(0.008380420642494911)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.46793656529098676), 4: np.float64(0.27019134593163596), 6: np.float64(0.20822132415126768), 79: np.float64(0.01341269115652753), 56: np.float64(0.01341269115652753), 88: np.float64(0.01341269115652753), 0: np.float64(0.01341269115652753)}
err dic= {1: np.float64(0.21093656529098676), 4: np.float64(0.01619134593163596), 6: np.float64(0.05377867584873233), 79: np.float64(0.056587308843472475), 56: np.float64(0.054587308843472473), 88: np.float64(0.02558730884347247), 0: np.float64(0.03658730884347247)} 

err list= [np.float64(0.21093656529098676), np.float64(0.01619134593163596), np.float64(0.05377867584873233), np.float64(0.056587308843472475), np.float64(0.054587308843472473), np.float64(0.02558730884347247), np.float64(0.03658730884347247)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.5067535518264765), 4: np.float64(0.27340046250878003), 6: np.float64(0.17846073571478455), 79: np.float64(0.010346312487489736), 56: np.float64(0.010346312487489736), 88: np.float64(0.010346312487489736), 0: np.float64(0.010346312487489736)}
err dic= {1: np.float64(0.24975355182647652), 4: np.float64(0.019400462508780025), 6: np.float64(0.08353926428521546), 79: np.float64(0.05965368751251027), 56: np.float64(0.057653687512510265), 88: np.float64(0.028653687512510264), 0: np.float64(0.03965368751251026)} 

err list= [np.float64(0.24975355182647652), np.float64(0.019400462508780025), np.float64(0.08353926428521546), np.float64(0.05965368751251027), np.float64(0.057653687512510265), np.float64(0.028653687512510264), np.float64(0.03965368751251026)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  1 

learned probs for this beta: {1: np.float64(0.5251704971980359), 4: np.float64(0.2774223733049085), 6: np.float64(0.1566689082340701), 79: np.float64(0.010184555315746411), 56: np.float64(0.010184555315746411), 88: np.float64(0.010184555315746411), 0: np.float64(0.010184555315746411)}
err dic= {1: np.float64(0.2681704971980359), 4: np.float64(0.023422373304908484), 6: np.float64(0.10533109176592992), 79: np.float64(0.059815444684253594), 56: np.float64(0.05781544468425359), 88: np.float64(0.028815444684253587), 0: np.float64(0.03981544468425359)} 

err list= [np.float64(0.2681704971980359), np.float64(0.023422373304908484), np.float64(0.10533109176592992), np.float64(0.059815444684253594), np.float64(0.05781544468425359), np.float64(0.028815444684253587), np.float64(0.03981544468425359)]
results for assortment [1, 4, 6, 79, 56, 88] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.5382215595402378), 4: np.float64(0.2804366461895821), 6: np.float64(0.1406266741240046), 79: np.float64(0.010178780036543864), 56: np.float64(0.010178780036543864), 88: np.float64(0.010178780036543864), 0: np.float64(0.010178780036543864)}
err dic= {1: np.float64(0.28122155954023775), 4: np.float64(0.02643664618958208), 6: np.float64(0.12137332587599542), 79: np.float64(0.05982121996345614), 56: np.float64(0.05782121996345614), 88: np.float64(0.028821219963456136), 0: np.float64(0.03982121996345614)} 

err list= [np.float64(0.28122155954023775), np.float64(0.02643664618958208), np.float64(0.12137332587599542), np.float64(0.05982121996345614), np.float64(0.05782121996345614), np.float64(0.028821219963456136), np.float64(0.03982121996345614)]
results for assortment [1, 4, 6, 79, 56, 88] :

err MNL dic= {1: np.float64(0.11900020988561233), 4: np.float64(0.12046027914786439), 6: np.float64(0.125102109350404), 79: np.float64(0.03814356175884143), 56: np.float64(0.044761045230349475), 88: np.float64(0.0693009759680974), 0: np.float64(0.21235701542659252)} 

err MNL list= [np.float64(0.11900020988561233), np.float64(0.12046027914786439), np.float64(0.125102109350404), np.float64(0.03814356175884143), np.float64(0.044761045230349475), np.float64(0.0693009759680974), np.float64(0.21235701542659252)]
sampled assortment [7, 5, 2, 87, 21, 85] number: 3
#  Learning probs for MM model, A = [7, 5, 2, 87, 21, 85]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 3, 4, 5, 6, 7, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 4: 0, 5: 0, 7: 0, 11: 0, 12: 0, 14: 0, 17: 0, 21: 0} [3, 4, 5, 7, 11, 12, 14, 17, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 3, 9: 2, 10: 2, 11: 4, 12: 2, 13: 3, 16: 4, 20: 2, 23: 4} [6, 5, 4, 9, 10, 12, 20, 7, 13, 11, 16, 23]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 4: 1, 6: 1, 7: 1, 10: 1, 21: 1} [2, 1, 4, 6, 7, 10, 21]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 15: 1} [1, 5, 6, 10, 12, 13, 15]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {7: 2, 9: 0, 11: 1, 13: 2, 15: 2, 18: 2, 23: 2} [9, 11, 7, 13, 15, 18, 23]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 1, 13: 5, 14: 5, 15: 2, 16: 6, 100: 0} [6, 100, 10, 1, 3, 15, 5, 7, 13, 14, 16]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 10: 4, 11: 3, 12: 6, 17: 5, 19: 3, 27: 6} [1, 3, 9, 7, 11, 19, 10, 17, 12, 27]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 11: 2, 14: 2, 19: 1, 25: 3, 100: 0} [100, 3, 4, 19, 11, 14, 5, 25]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 4, 4: 6, 6: 4, 7: 4, 8: 0, 9: 5, 10: 13, 11: 0, 13: 3, 14: 9, 15: 14, 17: 9, 18: 10, 19: 3, 23: 7, 26: 11, 27: 14, 32: 12, 33: 9, 43: 13, 46: 14, 54: 14, 55: 13, 58: 13, 59: 13, 69: 14, 71: 10, 89: 14, 96: 12, 100: 2} [8, 11, 100, 13, 19, 1, 6, 7, 9, 4, 23, 14, 17, 33, 18, 71, 26, 32, 96, 10, 43, 55, 58, 59, 15, 27, 46, 54, 69, 89]
#  Learning probs for MM model, A = [7, 5, 2, 87, 21, 85]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 14, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 15: 0, 16: 0, 20: 0, 21: 0} [3, 5, 7, 12, 15, 16, 20, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 10: 3, 12: 2, 13: 3, 18: 4, 20: 3, 21: 5, 23: 4, 25: 4} [6, 5, 4, 7, 12, 10, 13, 20, 18, 23, 25, 21]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 7: 1, 10: 1, 11: 1, 12: 1, 17: 1, 100: 1} [2, 1, 7, 10, 11, 12, 17, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 14: 1, 100: 1} [1, 5, 6, 10, 12, 13, 14, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {7: 1, 9: 0, 10: 1, 11: 1, 12: 2, 13: 2, 18: 2, 23: 2} [9, 7, 10, 11, 12, 13, 18, 23]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 4, 15: 3, 16: 7, 17: 6, 20: 4, 21: 5, 100: 0} [6, 100, 1, 3, 10, 15, 13, 20, 5, 7, 21, 17, 16]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 5: 4, 7: 3, 9: 0, 10: 4, 11: 3, 12: 8, 14: 3, 18: 5, 19: 3} [1, 3, 9, 7, 11, 14, 19, 4, 5, 10, 18, 12]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 2, 11: 2, 14: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 11, 5, 14]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 5, 3: 8, 4: 9, 5: 7, 6: 4, 7: 4, 8: 0, 9: 4, 10: 13, 11: 0, 13: 3, 15: 15, 19: 3, 20: 11, 23: 7, 24: 15, 26: 11, 28: 12, 35: 11, 36: 13, 41: 13, 50: 16, 59: 13, 64: 12, 68: 17, 70: 16, 75: 17, 76: 14, 83: 13, 85: 13, 95: 14, 100: 2} [8, 11, 100, 13, 19, 6, 7, 9, 1, 5, 23, 3, 4, 20, 26, 35, 28, 64, 10, 36, 41, 59, 83, 85, 76, 95, 15, 24, 50, 70, 68, 75]
empirical probabilities from test set: {7: 0.199, 5: 0.25, 2: 0.261, 87: 0.041, 21: 0.166, 85: 0.051, 0: 0.032}
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.11124031607393456), 5: np.float64(0.12889034753616213), 2: np.float64(0.13585872720290243), 87: np.float64(0.16123353403455712), 21: np.float64(0.1403100070833286), 85: np.float64(0.16123353403455712), 0: np.float64(0.16123353403455712)}
err dic= {7: np.float64(0.08775968392606545), 5: np.float64(0.12110965246383787), 2: np.float64(0.12514127279709758), 87: np.float64(0.12023353403455711), 21: np.float64(0.0256899929166714), 85: np.float64(0.11023353403455713), 0: np.float64(0.12923353403455712)} 

err list= [np.float64(0.08775968392606545), np.float64(0.12110965246383787), np.float64(0.12514127279709758), np.float64(0.12023353403455711), np.float64(0.0256899929166714), np.float64(0.11023353403455713), np.float64(0.12923353403455712)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.13753411410855446), 5: np.float64(0.1443188345462607), 2: np.float64(0.1429174295290254), 87: np.float64(0.14616460175270904), 21: np.float64(0.1367358165580327), 85: np.float64(0.14616460175270904), 0: np.float64(0.14616460175270904)}
err dic= {7: np.float64(0.061465885891445554), 5: np.float64(0.10568116545373929), 2: np.float64(0.11808257047097462), 87: np.float64(0.10516460175270903), 21: np.float64(0.029264183441967295), 85: np.float64(0.09516460175270905), 0: np.float64(0.11416460175270904)} 

err list= [np.float64(0.061465885891445554), np.float64(0.10568116545373929), np.float64(0.11808257047097462), np.float64(0.10516460175270903), np.float64(0.029264183441967295), np.float64(0.09516460175270905), np.float64(0.11416460175270904)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.1979537755549628), 5: np.float64(0.1815040743471152), 2: np.float64(0.1649290078550219), 87: np.float64(0.11097540908720993), 21: np.float64(0.12268691498127077), 85: np.float64(0.11097540908720993), 0: np.float64(0.11097540908720993)}
err dic= {7: np.float64(0.0010462244450372138), 5: np.float64(0.06849592565288479), 2: np.float64(0.0960709921449781), 87: np.float64(0.06997540908720992), 21: np.float64(0.04331308501872924), 85: np.float64(0.059975409087209934), 0: np.float64(0.07897540908720993)} 

err list= [np.float64(0.0010462244450372138), np.float64(0.06849592565288479), np.float64(0.0960709921449781), np.float64(0.06997540908720992), np.float64(0.04331308501872924), np.float64(0.059975409087209934), np.float64(0.07897540908720993)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.3117874059578182), 5: np.float64(0.2861249456734368), 2: np.float64(0.23766917171405771), 87: np.float64(0.03353007949046263), 21: np.float64(0.06382823818330029), 85: np.float64(0.03353007949046263), 0: np.float64(0.03353007949046263)}
err dic= {7: np.float64(0.11278740595781817), 5: np.float64(0.036124945673436826), 2: np.float64(0.023330828285942296), 87: np.float64(0.007469920509537369), 21: np.float64(0.10217176181669972), 85: np.float64(0.017469920509537364), 0: np.float64(0.0015300794904626325)} 

err list= [np.float64(0.11278740595781817), np.float64(0.036124945673436826), np.float64(0.023330828285942296), np.float64(0.007469920509537369), np.float64(0.10217176181669972), np.float64(0.017469920509537364), np.float64(0.0015300794904626325)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.2996256602718682), 5: np.float64(0.37840579983869793), 2: np.float64(0.28681714979379735), 87: np.float64(0.004883501299405051), 21: np.float64(0.02050088619742132), 85: np.float64(0.004883501299405051), 0: np.float64(0.004883501299405051)}
err dic= {7: np.float64(0.1006256602718682), 5: np.float64(0.12840579983869793), 2: np.float64(0.025817149793797345), 87: np.float64(0.036116498700594954), 21: np.float64(0.14549911380257868), 85: np.float64(0.04611649870059495), 0: np.float64(0.02711649870059495)} 

err list= [np.float64(0.1006256602718682), np.float64(0.12840579983869793), np.float64(0.025817149793797345), np.float64(0.036116498700594954), np.float64(0.14549911380257868), np.float64(0.04611649870059495), np.float64(0.02711649870059495)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.2553680094123047), 5: np.float64(0.417520714834195), 2: np.float64(0.3172687951852141), 87: np.float64(0.0004521784587258774), 21: np.float64(0.008485945192108447), 85: np.float64(0.0004521784587258774), 0: np.float64(0.0004521784587258774)}
err dic= {7: np.float64(0.05636800941230469), 5: np.float64(0.167520714834195), 2: np.float64(0.056268795185214104), 87: np.float64(0.04054782154127413), 21: np.float64(0.15751405480789157), 85: np.float64(0.05054782154127412), 0: np.float64(0.031547821541274126)} 

err list= [np.float64(0.05636800941230469), np.float64(0.167520714834195), np.float64(0.056268795185214104), np.float64(0.04054782154127413), np.float64(0.15751405480789157), np.float64(0.05054782154127412), np.float64(0.031547821541274126)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  1 

learned probs for this beta: {7: np.float64(0.21946249105740565), 5: np.float64(0.43445024658943776), 2: np.float64(0.3412243150890922), 87: np.float64(2.8299508970101845e-05), 21: np.float64(0.004778048737154233), 85: np.float64(2.8299508970101845e-05), 0: np.float64(2.8299508970101845e-05)}
err dic= {7: np.float64(0.020462491057405635), 5: np.float64(0.18445024658943776), 2: np.float64(0.08022431508909217), 87: np.float64(0.0409717004910299), 21: np.float64(0.16122195126284578), 85: np.float64(0.05097170049102989), 0: np.float64(0.031971700491029896)} 

err list= [np.float64(0.020462491057405635), np.float64(0.18445024658943776), np.float64(0.08022431508909217), np.float64(0.0409717004910299), np.float64(0.16122195126284578), np.float64(0.05097170049102989), np.float64(0.031971700491029896)]
results for assortment [7, 5, 2, 87, 21, 85] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.1920708051422281), 5: np.float64(0.4471918408950643), 2: np.float64(0.35773489278456), 87: np.float64(1.7409845045177168e-06), 21: np.float64(0.00299723822463387), 85: np.float64(1.7409845045177168e-06), 0: np.float64(1.7409845045177168e-06)}
err dic= {7: np.float64(0.006929194857771909), 5: np.float64(0.1971918408950643), 2: np.float64(0.09673489278455999), 87: np.float64(0.04099825901549548), 21: np.float64(0.16300276177536613), 85: np.float64(0.05099825901549548), 0: np.float64(0.03199825901549548)} 

err list= [np.float64(0.006929194857771909), np.float64(0.1971918408950643), np.float64(0.09673489278455999), np.float64(0.04099825901549548), np.float64(0.16300276177536613), np.float64(0.05099825901549548), np.float64(0.03199825901549548)]
results for assortment [7, 5, 2, 87, 21, 85] :

err MNL dic= {7: np.float64(0.06557310671032798), 5: np.float64(0.11241488642860856), 2: np.float64(0.12876859504132232), 87: np.float64(0.06586626124018921), 21: np.float64(0.04140932480898177), 85: np.float64(0.05441088414158741), 0: np.float64(0.22788876760746404)} 

err MNL list= [np.float64(0.06557310671032798), np.float64(0.11241488642860856), np.float64(0.12876859504132232), np.float64(0.06586626124018921), np.float64(0.04140932480898177), np.float64(0.05441088414158741), np.float64(0.22788876760746404)]
sampled assortment [5, 7, 3, 56, 34, 84] number: 4
#  Learning probs for MM model, A = [5, 7, 3, 56, 34, 84]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 3, 4, 5, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 6: 0, 7: 0, 12: 0, 16: 0, 17: 0, 18: 0, 20: 0} [3, 5, 6, 7, 12, 16, 17, 18, 20]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 9: 3, 10: 2, 12: 2, 13: 2, 19: 4, 20: 3, 24: 6, 27: 4} [6, 5, 4, 7, 10, 12, 13, 9, 20, 19, 27, 24]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 13: 1, 14: 1, 100: 1} [2, 1, 6, 10, 11, 13, 14, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 12: 1, 13: 1, 14: 1} [1, 4, 5, 6, 12, 13, 14]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {4: 2, 5: 2, 9: 0, 11: 1, 13: 2, 15: 2, 18: 2} [9, 11, 4, 5, 13, 15, 18]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 8: 5, 10: 2, 13: 3, 15: 4, 18: 9, 20: 5, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 8, 20, 18]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 7: 3, 9: 0, 11: 3, 15: 4, 19: 3, 22: 4} [1, 3, 9, 7, 11, 19, 4, 15, 22]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 11: 2, 14: 3, 19: 1, 100: 0} [100, 3, 4, 19, 11, 5, 14]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 4, 2: 13, 5: 8, 6: 4, 7: 3, 8: 0, 9: 6, 11: 0, 13: 3, 16: 10, 19: 3, 22: 11, 23: 8, 25: 12, 33: 14, 38: 10, 41: 12, 48: 13, 49: 12, 50: 16, 62: 13, 74: 12, 76: 14, 79: 15, 83: 14, 91: 14, 93: 19, 96: 14, 98: 12, 100: 2} [8, 11, 100, 7, 13, 19, 1, 6, 9, 5, 23, 16, 38, 22, 25, 41, 49, 74, 98, 2, 48, 62, 33, 76, 83, 91, 96, 79, 50, 93]
#  Learning probs for MM model, A = [5, 7, 3, 56, 34, 84]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0} [8, 2, 3, 4, 7]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 13: 0, 21: 0} [3, 5, 7, 12, 13, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 1, 5: 1, 6: 0, 7: 2, 10: 3, 11: 4, 12: 2, 13: 3, 15: 4, 16: 5, 20: 3, 22: 4, 23: 4, 100: 4} [6, 4, 5, 7, 12, 10, 13, 20, 11, 15, 22, 23, 100, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 12: 1, 13: 1, 14: 1, 100: 1} [2, 3, 6, 10, 12, 13, 14, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 14: 1, 19: 1, 100: 1} [1, 5, 6, 10, 14, 19, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 10: 2, 11: 1, 23: 2, 31: 3} [9, 11, 5, 10, 23, 31]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 10: 1, 13: 4, 14: 5, 15: 2, 21: 7, 100: 0} [6, 100, 10, 1, 3, 15, 5, 13, 14, 21]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 10: 4, 11: 3, 15: 3, 16: 6, 19: 3, 23: 6, 30: 6} [1, 3, 9, 7, 11, 15, 19, 10, 16, 23, 30]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 2, 12: 3, 14: 2, 19: 1, 23: 3, 100: 0} [100, 3, 4, 19, 6, 14, 5, 12, 23]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 4: 6, 5: 10, 6: 3, 7: 4, 8: 0, 9: 5, 11: 0, 13: 3, 17: 7, 19: 3, 21: 13, 22: 14, 23: 7, 26: 11, 27: 14, 29: 15, 31: 11, 38: 12, 41: 13, 71: 11, 76: 11, 86: 12, 87: 13, 92: 16, 93: 12, 97: 12, 100: 2} [8, 11, 100, 1, 6, 13, 19, 7, 9, 4, 17, 23, 5, 26, 31, 71, 76, 38, 86, 93, 97, 21, 41, 87, 22, 27, 29, 92]
empirical probabilities from test set: {5: 0.247, 7: 0.221, 3: 0.283, 56: 0.056, 34: 0.105, 84: 0.049, 0: 0.039}
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.12075190264470088), 7: np.float64(0.11820803480894913), 3: np.float64(0.10341255765128868), 56: np.float64(0.16440687622376518), 34: np.float64(0.16440687622376518), 84: np.float64(0.16440687622376518), 0: np.float64(0.16440687622376518)}
err dic= {5: np.float64(0.12624809735529913), 7: np.float64(0.10279196519105087), 3: np.float64(0.1795874423487113), 56: np.float64(0.10840687622376519), 34: np.float64(0.059406876223765184), 84: np.float64(0.11540687622376518), 0: np.float64(0.12540687622376517)} 

err list= [np.float64(0.12624809735529913), np.float64(0.10279196519105087), np.float64(0.1795874423487113), np.float64(0.10840687622376519), np.float64(0.059406876223765184), np.float64(0.11540687622376518), np.float64(0.12540687622376517)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.13648990269921357), 7: np.float64(0.12545552067808682), 3: np.float64(0.12844892598480956), 56: np.float64(0.15240141265947268), 34: np.float64(0.15240141265947268), 84: np.float64(0.15240141265947268), 0: np.float64(0.15240141265947268)}
err dic= {5: np.float64(0.11051009730078643), 7: np.float64(0.09554447932191318), 3: np.float64(0.15455107401519041), 56: np.float64(0.09640141265947269), 34: np.float64(0.04740141265947269), 84: np.float64(0.10340141265947268), 0: np.float64(0.11340141265947268)} 

err list= [np.float64(0.11051009730078643), np.float64(0.09554447932191318), np.float64(0.15455107401519041), np.float64(0.09640141265947269), np.float64(0.04740141265947269), np.float64(0.10340141265947268), np.float64(0.11340141265947268)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.1748256392170818), 7: np.float64(0.14051835223792922), 3: np.float64(0.19565819356623323), 56: np.float64(0.12224945374468901), 34: np.float64(0.12224945374468901), 84: np.float64(0.12224945374468901), 0: np.float64(0.12224945374468901)}
err dic= {5: np.float64(0.0721743607829182), 7: np.float64(0.08048164776207078), 3: np.float64(0.08734180643376674), 56: np.float64(0.06624945374468902), 34: np.float64(0.017249453744689017), 84: np.float64(0.07324945374468901), 0: np.float64(0.083249453744689)} 

err list= [np.float64(0.0721743607829182), np.float64(0.08048164776207078), np.float64(0.08734180643376674), np.float64(0.06624945374468902), np.float64(0.017249453744689017), np.float64(0.07324945374468901), np.float64(0.083249453744689)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.26886349138985727), 7: np.float64(0.1553687983733534), 3: np.float64(0.4073812449761506), 56: np.float64(0.042096616315159735), 34: np.float64(0.042096616315159735), 84: np.float64(0.042096616315159735), 0: np.float64(0.042096616315159735)}
err dic= {5: np.float64(0.02186349138985727), 7: np.float64(0.0656312016266466), 3: np.float64(0.1243812449761506), 56: np.float64(0.013903383684840266), 34: np.float64(0.06290338368484026), 84: np.float64(0.006903383684840267), 0: np.float64(0.003096616315159735)} 

err list= [np.float64(0.02186349138985727), np.float64(0.0656312016266466), np.float64(0.1243812449761506), np.float64(0.013903383684840266), np.float64(0.06290338368484026), np.float64(0.006903383684840267), np.float64(0.003096616315159735)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.3023486924205502), 7: np.float64(0.1296614064109736), 3: np.float64(0.5534910350981216), 56: np.float64(0.0036247165175887293), 34: np.float64(0.0036247165175887293), 84: np.float64(0.0036247165175887293), 0: np.float64(0.0036247165175887293)}
err dic= {5: np.float64(0.05534869242055018), 7: np.float64(0.0913385935890264), 3: np.float64(0.2704910350981216), 56: np.float64(0.05237528348241127), 34: np.float64(0.10137528348241126), 84: np.float64(0.04537528348241127), 0: np.float64(0.03537528348241127)} 

err list= [np.float64(0.05534869242055018), np.float64(0.0913385935890264), np.float64(0.2704910350981216), np.float64(0.05237528348241127), np.float64(0.10137528348241126), np.float64(0.04537528348241127), np.float64(0.03537528348241127)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.2958292749124963), 7: np.float64(0.09804341072320324), 3: np.float64(0.60554734778781), 56: np.float64(0.0001449916441225767), 34: np.float64(0.0001449916441225767), 84: np.float64(0.0001449916441225767), 0: np.float64(0.0001449916441225767)}
err dic= {5: np.float64(0.04882927491249628), 7: np.float64(0.12295658927679676), 3: np.float64(0.3225473477878101), 56: np.float64(0.05585500835587742), 34: np.float64(0.10485500835587742), 84: np.float64(0.04885500835587742), 0: np.float64(0.03885500835587742)} 

err list= [np.float64(0.04882927491249628), np.float64(0.12295658927679676), np.float64(0.3225473477878101), np.float64(0.05585500835587742), np.float64(0.10485500835587742), np.float64(0.04885500835587742), np.float64(0.03885500835587742)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  1 

learned probs for this beta: {5: np.float64(0.286676122283537), 7: np.float64(0.07271191545321631), 3: np.float64(0.6405926098993143), 56: np.float64(4.838090983106368e-06), 34: np.float64(4.838090983106368e-06), 84: np.float64(4.838090983106368e-06), 0: np.float64(4.838090983106368e-06)}
err dic= {5: np.float64(0.03967612228353701), 7: np.float64(0.1482880845467837), 3: np.float64(0.35759260989931435), 56: np.float64(0.0559951619090169), 34: np.float64(0.10499516190901689), 84: np.float64(0.0489951619090169), 0: np.float64(0.0389951619090169)} 

err list= [np.float64(0.03967612228353701), np.float64(0.1482880845467837), np.float64(0.35759260989931435), np.float64(0.0559951619090169), np.float64(0.10499516190901689), np.float64(0.0489951619090169), np.float64(0.0389951619090169)]
results for assortment [5, 7, 3, 56, 34, 84] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.2797548441864071), 7: np.float64(0.05343122811455603), 3: np.float64(0.6668132375571363), 56: np.float64(1.7253547512820535e-07), 34: np.float64(1.7253547512820535e-07), 84: np.float64(1.7253547512820535e-07), 0: np.float64(1.7253547512820535e-07)}
err dic= {5: np.float64(0.03275484418640712), 7: np.float64(0.16756877188544397), 3: np.float64(0.3838132375571363), 56: np.float64(0.05599982746452487), 34: np.float64(0.10499982746452487), 84: np.float64(0.04899982746452487), 0: np.float64(0.03899982746452487)} 

err list= [np.float64(0.03275484418640712), np.float64(0.16756877188544397), np.float64(0.3838132375571363), np.float64(0.05599982746452487), np.float64(0.10499982746452487), np.float64(0.04899982746452487), np.float64(0.03899982746452487)]
results for assortment [5, 7, 3, 56, 34, 84] :

err MNL dic= {5: np.float64(0.10854409457056177), 7: np.float64(0.08672863270216549), 3: np.float64(0.14878093942881052), 56: np.float64(0.056407155560205056), 34: np.float64(0.008924050632911407), 84: np.float64(0.05618882728318862), 0: np.float64(0.22253363322523276)} 

err MNL list= [np.float64(0.10854409457056177), np.float64(0.08672863270216549), np.float64(0.14878093942881052), np.float64(0.056407155560205056), np.float64(0.008924050632911407), np.float64(0.05618882728318862), np.float64(0.22253363322523276)]
sampled assortment [9, 5, 7, 30, 76, 68] number: 5
#  Learning probs for MM model, A = [9, 5, 7, 30, 76, 68]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 13: 1, 100: 1} [8, 1, 2, 3, 4, 7, 12, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 10: 0, 12: 0, 15: 0, 16: 0} [3, 5, 10, 12, 15, 16]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 11: 3, 12: 2, 13: 3, 16: 4, 18: 4, 20: 4, 21: 4, 24: 6, 28: 6, 30: 5, 100: 4} [6, 5, 4, 7, 12, 11, 13, 16, 18, 20, 21, 100, 30, 24, 28]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 6: 1, 7: 1, 10: 1, 14: 1, 16: 1} [2, 6, 7, 10, 14, 16]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 9: 1, 10: 1, 18: 2, 24: 2, 100: 1} [1, 5, 6, 9, 10, 100, 18, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {4: 2, 7: 2, 9: 0, 10: 2, 11: 1, 12: 2, 18: 2, 100: 2} [9, 11, 4, 7, 10, 12, 18, 100]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 5, 10: 2, 13: 4, 15: 3, 16: 7, 17: 5, 20: 5, 23: 8, 100: 0} [6, 100, 1, 3, 10, 15, 5, 13, 7, 8, 17, 20, 16, 23]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 4, 3: 0, 7: 3, 9: 0, 11: 3, 14: 3, 15: 3, 18: 5, 19: 3, 25: 5, 39: 8} [1, 3, 9, 7, 11, 14, 15, 19, 2, 18, 25, 39]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 2, 11: 2, 14: 2, 16: 3, 100: 0} [100, 3, 4, 5, 11, 14, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 6, 4: 10, 5: 8, 6: 5, 7: 4, 8: 0, 9: 4, 11: 0, 13: 3, 16: 8, 17: 8, 19: 3, 20: 12, 22: 11, 24: 13, 26: 8, 30: 14, 33: 12, 39: 13, 43: 15, 45: 16, 47: 15, 48: 15, 53: 14, 58: 16, 62: 18, 79: 15, 94: 17, 96: 14, 100: 2} [8, 11, 100, 1, 13, 19, 7, 9, 6, 3, 5, 16, 17, 26, 4, 22, 20, 33, 24, 39, 30, 53, 96, 43, 47, 48, 79, 45, 58, 94, 62]
#  Learning probs for MM model, A = [9, 5, 7, 30, 76, 68]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 14: 1, 100: 1} [8, 1, 2, 3, 4, 7, 12, 14, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 14: 0, 20: 0} [3, 4, 5, 6, 7, 14, 20]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 9: 3, 10: 2, 11: 2, 12: 2, 16: 5} [6, 5, 4, 7, 10, 11, 12, 9, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 18: 1, 21: 1, 100: 1} [2, 1, 3, 6, 10, 18, 21, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 18: 1, 100: 1} [1, 4, 5, 6, 10, 12, 13, 18, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 11: 1, 13: 2, 14: 2, 15: 2, 16: 3, 18: 2, 23: 2, 24: 2} [9, 11, 5, 13, 14, 15, 18, 23, 24, 16]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 8: 5, 10: 2, 12: 6, 13: 3, 15: 3, 16: 7, 20: 4, 21: 7, 35: 10, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7, 8, 12, 16, 21, 35]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 3, 3: 0, 7: 3, 9: 0, 11: 3, 14: 3, 17: 4, 18: 4, 19: 3, 22: 6, 37: 5, 70: 9} [1, 3, 9, 2, 7, 11, 14, 19, 17, 18, 37, 22, 70]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 19: 1, 100: 0} [100, 3, 4, 19, 5]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 9, 5: 10, 6: 5, 7: 4, 8: 0, 9: 4, 11: 0, 13: 3, 17: 8, 19: 3, 20: 11, 21: 14, 23: 7, 25: 12, 26: 13, 35: 12, 37: 13, 46: 12, 54: 14, 57: 13, 62: 14, 70: 17, 73: 14, 77: 16, 82: 16, 88: 12, 91: 14, 95: 16, 97: 15, 99: 13, 100: 2} [8, 11, 100, 1, 13, 19, 7, 9, 6, 23, 17, 3, 5, 20, 25, 35, 46, 88, 26, 37, 57, 99, 21, 54, 62, 73, 91, 97, 77, 82, 95, 70]
empirical probabilities from test set: {9: 0.254, 5: 0.25, 7: 0.226, 30: 0.115, 76: 0.06, 68: 0.057, 0: 0.038}
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.14627473095506646), 5: np.float64(0.11609542722640538), 7: np.float64(0.12306665652701285), 30: np.float64(0.15364079632287836), 76: np.float64(0.15364079632287836), 68: np.float64(0.15364079632287836), 0: np.float64(0.15364079632287836)}
err dic= {9: np.float64(0.10772526904493354), 5: np.float64(0.13390457277359463), 7: np.float64(0.10293334347298716), 30: np.float64(0.038640796322878354), 76: np.float64(0.09364079632287836), 68: np.float64(0.09664079632287836), 0: np.float64(0.11564079632287835)} 

err list= [np.float64(0.10772526904493354), np.float64(0.13390457277359463), np.float64(0.10293334347298716), np.float64(0.038640796322878354), np.float64(0.09364079632287836), np.float64(0.09664079632287836), np.float64(0.11564079632287835)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.14876057705418405), 5: np.float64(0.1351605377059875), 7: np.float64(0.13790478039012058), 30: np.float64(0.14454352621242728), 76: np.float64(0.14454352621242728), 68: np.float64(0.14454352621242728), 0: np.float64(0.14454352621242728)}
err dic= {9: np.float64(0.10523942294581595), 5: np.float64(0.11483946229401251), 7: np.float64(0.08809521960987943), 30: np.float64(0.02954352621242727), 76: np.float64(0.08454352621242728), 68: np.float64(0.08754352621242728), 0: np.float64(0.10654352621242727)} 

err list= [np.float64(0.10523942294581595), np.float64(0.11483946229401251), np.float64(0.08809521960987943), np.float64(0.02954352621242727), np.float64(0.08454352621242728), np.float64(0.08754352621242728), np.float64(0.10654352621242727)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.1527346021886226), 5: np.float64(0.18357070232875955), 7: np.float64(0.17240882828061396), 30: np.float64(0.1228214668005011), 76: np.float64(0.1228214668005011), 68: np.float64(0.1228214668005011), 0: np.float64(0.1228214668005011)}
err dic= {9: np.float64(0.10126539781137742), 5: np.float64(0.06642929767124045), 7: np.float64(0.053591171719386044), 30: np.float64(0.007821466800501095), 76: np.float64(0.0628214668005011), 68: np.float64(0.0658214668005011), 0: np.float64(0.0848214668005011)} 

err list= [np.float64(0.10126539781137742), np.float64(0.06642929767124045), np.float64(0.053591171719386044), np.float64(0.007821466800501095), np.float64(0.0628214668005011), np.float64(0.0658214668005011), np.float64(0.0848214668005011)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.1384327727211892), 5: np.float64(0.32504652464723016), 7: np.float64(0.2633897633839333), 30: np.float64(0.06828273481191172), 76: np.float64(0.06828273481191172), 68: np.float64(0.06828273481191172), 0: np.float64(0.06828273481191172)}
err dic= {9: np.float64(0.1155672272788108), 5: np.float64(0.07504652464723016), 7: np.float64(0.03738976338393327), 30: np.float64(0.04671726518808829), 76: np.float64(0.008282734811911718), 68: np.float64(0.011282734811911714), 0: np.float64(0.030282734811911717)} 

err list= [np.float64(0.1155672272788108), np.float64(0.07504652464723016), np.float64(0.03738976338393327), np.float64(0.04671726518808829), np.float64(0.008282734811911718), np.float64(0.011282734811911714), np.float64(0.030282734811911717)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.11412441796954627), 5: np.float64(0.43053833491730015), 7: np.float64(0.3177750330795161), 30: np.float64(0.03439055350840943), 76: np.float64(0.03439055350840943), 68: np.float64(0.03439055350840943), 0: np.float64(0.03439055350840943)}
err dic= {9: np.float64(0.13987558203045375), 5: np.float64(0.18053833491730015), 7: np.float64(0.0917750330795161), 30: np.float64(0.08060944649159058), 76: np.float64(0.025609446491590568), 68: np.float64(0.022609446491590572), 0: np.float64(0.003609446491590569)} 

err list= [np.float64(0.13987558203045375), np.float64(0.18053833491730015), np.float64(0.0917750330795161), np.float64(0.08060944649159058), np.float64(0.025609446491590568), np.float64(0.022609446491590572), np.float64(0.003609446491590569)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.11253717514070945), 5: np.float64(0.4747486217911396), 7: np.float64(0.3081236712807748), 30: np.float64(0.02614763294684406), 76: np.float64(0.02614763294684406), 68: np.float64(0.02614763294684406), 0: np.float64(0.02614763294684406)}
err dic= {9: np.float64(0.14146282485929057), 5: np.float64(0.22474862179113958), 7: np.float64(0.08212367128077477), 30: np.float64(0.08885236705315594), 76: np.float64(0.03385236705315594), 68: np.float64(0.030852367053155944), 0: np.float64(0.01185236705315594)} 

err list= [np.float64(0.14146282485929057), np.float64(0.22474862179113958), np.float64(0.08212367128077477), np.float64(0.08885236705315594), np.float64(0.03385236705315594), np.float64(0.030852367053155944), np.float64(0.01185236705315594)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  1 

learned probs for this beta: {9: np.float64(0.11782270439335667), 5: np.float64(0.4905377293926961), 7: np.float64(0.29052672746092445), 30: np.float64(0.02527820968825574), 76: np.float64(0.02527820968825574), 68: np.float64(0.02527820968825574), 0: np.float64(0.02527820968825574)}
err dic= {9: np.float64(0.13617729560664332), 5: np.float64(0.24053772939269608), 7: np.float64(0.06452672746092444), 30: np.float64(0.08972179031174427), 76: np.float64(0.03472179031174426), 68: np.float64(0.03172179031174426), 0: np.float64(0.012721790311744259)} 

err list= [np.float64(0.13617729560664332), np.float64(0.24053772939269608), np.float64(0.06452672746092444), np.float64(0.08972179031174427), np.float64(0.03472179031174426), np.float64(0.03172179031174426), np.float64(0.012721790311744259)]
results for assortment [9, 5, 7, 30, 76, 68] :

beta is  1.25 

learned probs for this beta: {9: np.float64(0.12264045375938679), 5: np.float64(0.5000343914483621), 7: np.float64(0.27645032923869733), 30: np.float64(0.025218706388388367), 76: np.float64(0.025218706388388367), 68: np.float64(0.025218706388388367), 0: np.float64(0.025218706388388367)}
err dic= {9: np.float64(0.13135954624061322), 5: np.float64(0.25003439144836215), 7: np.float64(0.05045032923869733), 30: np.float64(0.08978129361161163), 76: np.float64(0.03478129361161163), 68: np.float64(0.03178129361161164), 0: np.float64(0.012781293611611632)} 

err list= [np.float64(0.13135954624061322), np.float64(0.25003439144836215), np.float64(0.05045032923869733), np.float64(0.08978129361161163), np.float64(0.03478129361161163), np.float64(0.03178129361161164), np.float64(0.012781293611611632)]
results for assortment [9, 5, 7, 30, 76, 68] :

err MNL dic= {9: np.float64(0.12461392108956698), 5: np.float64(0.11240058221136354), 7: np.float64(0.09255923480792225), 30: np.float64(0.008563965275250815), 76: np.float64(0.04828091698289755), 68: np.float64(0.05081306856578468), 0: np.float64(0.2219157872849197)} 

err MNL list= [np.float64(0.12461392108956698), np.float64(0.11240058221136354), np.float64(0.09255923480792225), np.float64(0.008563965275250815), np.float64(0.04828091698289755), np.float64(0.05081306856578468), np.float64(0.2219157872849197)]
sampled assortment [7, 8, 4, 39, 56, 92] number: 6
#  Learning probs for MM model, A = [7, 8, 4, 39, 56, 92]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 11: 1, 100: 1} [8, 1, 2, 3, 5, 7, 11, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 13: 0, 18: 0} [3, 5, 7, 13, 18]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 3, 9: 2, 12: 2, 13: 3, 16: 4, 18: 3, 20: 4} [6, 5, 4, 9, 12, 7, 13, 18, 16, 20]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 14: 1, 16: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 14, 16, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 9: 1, 12: 1} [1, 4, 5, 9, 12]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 7: 2, 9: 0, 10: 2, 11: 1, 13: 2, 24: 2} [9, 11, 5, 7, 10, 13, 24]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 2, 15: 3, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 15, 5, 7, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 11: 3} [1, 3, 9, 7, 11]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 6: 2, 11: 2, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 6, 11, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 2: 13, 3: 8, 4: 8, 6: 3, 7: 3, 8: 0, 9: 5, 10: 12, 11: 0, 12: 11, 13: 3, 17: 7, 23: 6, 27: 13, 30: 13, 31: 14, 38: 11, 39: 12, 44: 15, 48: 10, 56: 13, 65: 16, 70: 15, 71: 14, 77: 12, 82: 14, 88: 12, 99: 11, 100: 2} [8, 11, 100, 1, 6, 7, 13, 9, 23, 17, 3, 4, 48, 12, 38, 99, 10, 39, 77, 88, 2, 27, 30, 56, 31, 71, 82, 44, 70, 65]
#  Learning probs for MM model, A = [7, 8, 4, 39, 56, 92]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 3, 4, 5, 7, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 14: 0, 15: 0, 17: 0, 21: 0, 25: 0} [3, 5, 7, 14, 15, 17, 21, 25]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 1, 5: 1, 6: 0, 7: 2, 8: 4, 9: 2, 10: 3, 12: 2, 13: 3, 20: 4, 27: 4} [6, 4, 5, 7, 9, 12, 10, 13, 8, 20, 27]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 4: 1, 6: 1, 7: 1, 10: 1, 11: 1, 17: 1, 100: 1} [2, 1, 3, 4, 6, 7, 10, 11, 17, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 10: 1, 13: 1, 26: 1} [1, 4, 5, 6, 10, 13, 26]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {9: 0, 10: 1, 11: 1, 13: 2, 18: 2, 23: 2, 100: 2} [9, 10, 11, 13, 18, 23, 100]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 14: 5, 17: 5, 100: 0} [6, 100, 1, 3, 10, 5, 7, 14, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 10: 5, 11: 3, 14: 3, 17: 5, 18: 4, 19: 3, 22: 4, 23: 5} [1, 3, 9, 7, 11, 14, 19, 18, 22, 10, 17, 23]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 2, 6: 2, 11: 2, 12: 3, 16: 3, 100: 0} [100, 3, 4, 5, 6, 11, 12, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 5: 8, 6: 4, 7: 5, 8: 0, 9: 5, 11: 0, 13: 3, 16: 10, 17: 8, 19: 3, 20: 9, 24: 12, 25: 13, 26: 15, 30: 12, 37: 13, 40: 11, 48: 12, 51: 13, 52: 14, 64: 12, 67: 14, 68: 14, 80: 10, 85: 15, 86: 14, 97: 13, 99: 13, 100: 2} [8, 11, 100, 1, 13, 19, 6, 7, 9, 5, 17, 20, 16, 80, 40, 24, 30, 48, 64, 25, 37, 51, 97, 99, 52, 67, 68, 86, 26, 85]
empirical probabilities from test set: {7: 0.22, 8: 0.266, 4: 0.242, 39: 0.1, 56: 0.066, 92: 0.058, 0: 0.048}
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.11420424073959225), 8: np.float64(0.13503929300179832), 4: np.float64(0.11321564914987826), 39: np.float64(0.15938520427718264), 56: np.float64(0.15938520427718264), 92: np.float64(0.15938520427718264), 0: np.float64(0.15938520427718264)}
err dic= {7: np.float64(0.10579575926040775), 8: np.float64(0.1309607069982017), 4: np.float64(0.12878435085012174), 39: np.float64(0.059385204277182635), 56: np.float64(0.09338520427718264), 92: np.float64(0.10138520427718264), 0: np.float64(0.11138520427718264)} 

err list= [np.float64(0.10579575926040775), np.float64(0.1309607069982017), np.float64(0.12878435085012174), np.float64(0.059385204277182635), np.float64(0.09338520427718264), np.float64(0.10138520427718264), np.float64(0.11138520427718264)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.13744439825212382), 8: np.float64(0.13806202647540136), 4: np.float64(0.13852402954147955), 39: np.float64(0.1464923864327493), 56: np.float64(0.1464923864327493), 92: np.float64(0.1464923864327493), 0: np.float64(0.1464923864327493)}
err dic= {7: np.float64(0.08255560174787618), 8: np.float64(0.12793797352459865), 4: np.float64(0.10347597045852044), 39: np.float64(0.046492386432749305), 56: np.float64(0.08049238643274931), 92: np.float64(0.08849238643274931), 0: np.float64(0.09849238643274931)} 

err list= [np.float64(0.08255560174787618), np.float64(0.12793797352459865), np.float64(0.10347597045852044), np.float64(0.046492386432749305), np.float64(0.08049238643274931), np.float64(0.08849238643274931), np.float64(0.09849238643274931)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.19095898111210466), 8: np.float64(0.1445983111553705), 4: np.float64(0.20199331274523707), 39: np.float64(0.11561234874682215), 56: np.float64(0.11561234874682215), 92: np.float64(0.11561234874682215), 0: np.float64(0.11561234874682215)}
err dic= {7: np.float64(0.029041018887895342), 8: np.float64(0.12140168884462951), 4: np.float64(0.04000668725476292), 39: np.float64(0.015612348746822144), 56: np.float64(0.049612348746822146), 92: np.float64(0.057612348746822147), 0: np.float64(0.06761234874682215)} 

err list= [np.float64(0.029041018887895342), np.float64(0.12140168884462951), np.float64(0.04000668725476292), np.float64(0.015612348746822144), np.float64(0.049612348746822146), np.float64(0.057612348746822147), np.float64(0.06761234874682215)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.3050554402448509), 8: np.float64(0.1477609759755459), 4: np.float64(0.37246674008777575), 39: np.float64(0.04367921092295705), 56: np.float64(0.04367921092295705), 92: np.float64(0.04367921092295705), 0: np.float64(0.04367921092295705)}
err dic= {7: np.float64(0.08505544024485087), 8: np.float64(0.1182390240244541), 4: np.float64(0.13046674008777576), 39: np.float64(0.05632078907704296), 56: np.float64(0.022320789077042956), 92: np.float64(0.014320789077042956), 0: np.float64(0.004320789077042954)} 

err list= [np.float64(0.08505544024485087), np.float64(0.1182390240244541), np.float64(0.13046674008777576), np.float64(0.05632078907704296), np.float64(0.022320789077042956), np.float64(0.014320789077042956), np.float64(0.004320789077042954)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.33294045785416804), 8: np.float64(0.1518333442461522), 4: np.float64(0.4603307969094655), 39: np.float64(0.013723850247553689), 56: np.float64(0.013723850247553689), 92: np.float64(0.013723850247553689), 0: np.float64(0.013723850247553689)}
err dic= {7: np.float64(0.11294045785416804), 8: np.float64(0.11416665575384782), 4: np.float64(0.2183307969094655), 39: np.float64(0.08627614975244632), 56: np.float64(0.052276149752446315), 92: np.float64(0.044276149752446314), 0: np.float64(0.03427614975244631)} 

err list= [np.float64(0.11294045785416804), np.float64(0.11416665575384782), np.float64(0.2183307969094655), np.float64(0.08627614975244632), np.float64(0.052276149752446315), np.float64(0.044276149752446314), np.float64(0.03427614975244631)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.3129169749403096), 8: np.float64(0.1718828614363129), 4: np.float64(0.473739964330059), 39: np.float64(0.010365049823329647), 56: np.float64(0.010365049823329647), 92: np.float64(0.010365049823329647), 0: np.float64(0.010365049823329647)}
err dic= {7: np.float64(0.09291697494030962), 8: np.float64(0.09411713856368711), 4: np.float64(0.231739964330059), 39: np.float64(0.08963495017667036), 56: np.float64(0.055634950176670354), 92: np.float64(0.047634950176670354), 0: np.float64(0.03763495017667035)} 

err list= [np.float64(0.09291697494030962), np.float64(0.09411713856368711), np.float64(0.231739964330059), np.float64(0.08963495017667036), np.float64(0.055634950176670354), np.float64(0.047634950176670354), np.float64(0.03763495017667035)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  1 

learned probs for this beta: {7: np.float64(0.2926730084601404), 8: np.float64(0.1893071582502237), 4: np.float64(0.4772768061148589), 39: np.float64(0.010185756793694243), 56: np.float64(0.010185756793694243), 92: np.float64(0.010185756793694243), 0: np.float64(0.010185756793694243)}
err dic= {7: np.float64(0.07267300846014038), 8: np.float64(0.07669284174977631), 4: np.float64(0.2352768061148589), 39: np.float64(0.08981424320630577), 56: np.float64(0.055814243206305764), 92: np.float64(0.047814243206305757), 0: np.float64(0.03781424320630576)} 

err list= [np.float64(0.07267300846014038), np.float64(0.07669284174977631), np.float64(0.2352768061148589), np.float64(0.08981424320630577), np.float64(0.055814243206305764), np.float64(0.047814243206305757), np.float64(0.03781424320630576)]
results for assortment [7, 8, 4, 39, 56, 92] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.2786324170994106), 8: np.float64(0.20168507633814353), 4: np.float64(0.47896702070797464), 39: np.float64(0.01017887146361777), 56: np.float64(0.01017887146361777), 92: np.float64(0.01017887146361777), 0: np.float64(0.01017887146361777)}
err dic= {7: np.float64(0.05863241709941061), 8: np.float64(0.06431492366185648), 4: np.float64(0.23696702070797465), 39: np.float64(0.08982112853638223), 56: np.float64(0.055821128536382235), 92: np.float64(0.047821128536382235), 0: np.float64(0.03782112853638223)} 

err list= [np.float64(0.05863241709941061), np.float64(0.06431492366185648), np.float64(0.23696702070797465), np.float64(0.08982112853638223), np.float64(0.055821128536382235), np.float64(0.047821128536382235), np.float64(0.03782112853638223)]
results for assortment [7, 8, 4, 39, 56, 92] :

err MNL dic= {7: np.float64(0.08468820831795898), 8: np.float64(0.13479974698223604), 4: np.float64(0.10784787306942173), 39: np.float64(0.016124611248748102), 56: np.float64(0.047278161404248606), 92: np.float64(0.04837288492962944), 0: np.float64(0.2155601707869907)} 

err MNL list= [np.float64(0.08468820831795898), np.float64(0.13479974698223604), np.float64(0.10784787306942173), np.float64(0.016124611248748102), np.float64(0.047278161404248606), np.float64(0.04837288492962944), np.float64(0.2155601707869907)]
sampled assortment [8, 4, 7, 91, 16, 90] number: 7
#  Learning probs for MM model, A = [8, 4, 7, 91, 16, 90]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {2: 1, 3: 1, 7: 1, 8: 0, 100: 1} [8, 2, 3, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 14: 0, 15: 0, 17: 0, 25: 0} [3, 5, 7, 14, 15, 17, 25]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 1, 5: 1, 6: 0, 7: 2, 9: 2, 10: 3, 11: 4, 12: 2, 16: 4, 20: 4, 21: 5, 22: 4, 23: 5, 27: 5, 100: 5} [6, 4, 5, 7, 9, 12, 10, 11, 16, 20, 22, 21, 23, 27, 100]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 7: 1, 10: 1, 12: 1, 14: 1, 100: 1} [2, 1, 7, 10, 12, 14, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 4: 1, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1} [1, 4, 5, 6, 10, 12, 13]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 10: 2, 11: 1, 13: 2, 17: 3, 21: 2, 24: 2, 100: 1} [9, 11, 100, 5, 10, 13, 21, 24, 17]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 1, 13: 4, 15: 3, 17: 7, 20: 4, 21: 5, 100: 0} [6, 100, 10, 1, 3, 15, 5, 13, 20, 7, 21, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 7: 3, 9: 0, 11: 3, 17: 5, 27: 5, 42: 4} [1, 3, 9, 7, 11, 42, 17, 27]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 2, 6: 2, 11: 2, 14: 3, 16: 3, 22: 4, 100: 0} [100, 3, 4, 5, 6, 11, 14, 16, 22]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 5: 10, 6: 3, 7: 3, 8: 0, 9: 5, 11: 0, 12: 13, 13: 3, 17: 11, 18: 12, 19: 3, 20: 9, 23: 9, 25: 10, 26: 12, 34: 15, 35: 10, 38: 10, 41: 9, 42: 16, 48: 13, 52: 11, 58: 13, 67: 12, 74: 14, 77: 15, 80: 16, 89: 13, 100: 2} [8, 11, 100, 1, 6, 7, 13, 19, 9, 20, 23, 41, 5, 25, 35, 38, 17, 52, 18, 26, 67, 12, 48, 58, 89, 74, 34, 77, 42, 80]
#  Learning probs for MM model, A = [8, 4, 7, 91, 16, 90]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 16: 1, 100: 1} [8, 1, 2, 3, 4, 7, 16, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 15: 0, 27: 0} [3, 5, 7, 12, 15, 27]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 1, 5: 1, 6: 0, 7: 2, 10: 2, 12: 2, 15: 4, 18: 4, 20: 4, 22: 5} [6, 4, 5, 7, 10, 12, 15, 18, 20, 22]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 1, 10: 1, 11: 1, 13: 1, 100: 1} [2, 1, 3, 6, 7, 10, 11, 13, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 7: 1, 10: 1, 11: 1, 12: 1, 15: 1} [1, 5, 6, 7, 10, 11, 12, 15]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 10: 2, 11: 1, 12: 2, 23: 2, 100: 1} [9, 11, 100, 5, 10, 12, 23]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 10: 2, 13: 3, 15: 3, 16: 6, 17: 6, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 16, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 4, 3: 0, 5: 4, 6: 6, 7: 3, 9: 0, 11: 3, 15: 4, 17: 4, 19: 3, 23: 6, 37: 7, 42: 7} [1, 3, 9, 7, 11, 19, 2, 5, 15, 17, 6, 23, 37, 42]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 3, 11: 2, 12: 3, 14: 2, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 11, 14, 5, 6, 12, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 11, 4: 7, 5: 9, 6: 5, 7: 4, 8: 0, 9: 6, 11: 0, 13: 3, 17: 10, 18: 16, 19: 3, 23: 7, 25: 11, 27: 15, 32: 14, 33: 11, 41: 11, 47: 11, 52: 15, 58: 17, 62: 13, 68: 17, 85: 16, 92: 14, 100: 2} [8, 11, 100, 1, 13, 19, 7, 6, 9, 4, 23, 5, 17, 3, 25, 33, 41, 47, 62, 32, 92, 27, 52, 18, 85, 58, 68]
empirical probabilities from test set: {8: 0.258, 4: 0.237, 7: 0.219, 91: 0.05, 16: 0.154, 90: 0.038, 0: 0.044}
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.025 

learned probs for this beta: {8: np.float64(0.139585197733732), 4: np.float64(0.1310987426996696), 7: np.float64(0.106424961367432), 91: np.float64(0.1647763068582258), 16: np.float64(0.12856217762449004), 90: np.float64(0.1647763068582258), 0: np.float64(0.1647763068582258)}
err dic= {8: np.float64(0.118414802266268), 4: np.float64(0.1059012573003304), 7: np.float64(0.112575038632568), 91: np.float64(0.1147763068582258), 16: np.float64(0.025437822375509955), 90: np.float64(0.1267763068582258), 0: np.float64(0.12077630685822581)} 

err list= [np.float64(0.118414802266268), np.float64(0.1059012573003304), np.float64(0.112575038632568), np.float64(0.1147763068582258), np.float64(0.025437822375509955), np.float64(0.1267763068582258), np.float64(0.12077630685822581)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.14220258016634094), 4: np.float64(0.1420354856698802), 7: np.float64(0.13096806169170785), 91: np.float64(0.15076110723900807), 16: np.float64(0.1325105507550492), 90: np.float64(0.15076110723900807), 0: np.float64(0.15076110723900807)}
err dic= {8: np.float64(0.11579741983365907), 4: np.float64(0.09496451433011979), 7: np.float64(0.08803193830829215), 91: np.float64(0.10076110723900807), 16: np.float64(0.021489449244950803), 90: np.float64(0.11276110723900806), 0: np.float64(0.10676110723900807)} 

err list= [np.float64(0.11579741983365907), np.float64(0.09496451433011979), np.float64(0.08803193830829215), np.float64(0.10076110723900807), np.float64(0.021489449244950803), np.float64(0.11276110723900806), np.float64(0.10676110723900807)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.14818849764513087), 4: np.float64(0.16591392424084636), 7: np.float64(0.19188031967715727), 91: np.float64(0.11925901551494691), 16: np.float64(0.13624021189202512), 90: np.float64(0.11925901551494691), 0: np.float64(0.11925901551494691)}
err dic= {8: np.float64(0.10981150235486914), 4: np.float64(0.07108607575915363), 7: np.float64(0.027119680322842732), 91: np.float64(0.06925901551494691), 16: np.float64(0.017759788107974878), 90: np.float64(0.08125901551494691), 0: np.float64(0.07525901551494692)} 

err list= [np.float64(0.10981150235486914), np.float64(0.07108607575915363), np.float64(0.027119680322842732), np.float64(0.06925901551494691), np.float64(0.017759788107974878), np.float64(0.08125901551494691), np.float64(0.07525901551494692)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.15426075736565834), 4: np.float64(0.1997753738810956), 7: np.float64(0.37714150704545885), 91: np.float64(0.05254950373742608), 16: np.float64(0.11117385049550885), 90: np.float64(0.05254950373742608), 0: np.float64(0.05254950373742608)}
err dic= {8: np.float64(0.10373924263434167), 4: np.float64(0.0372246261189044), 7: np.float64(0.15814150704545885), 91: np.float64(0.00254950373742608), 16: np.float64(0.04282614950449115), 90: np.float64(0.014549503737426084), 0: np.float64(0.008549503737426085)} 

err list= [np.float64(0.10373924263434167), np.float64(0.0372246261189044), np.float64(0.15814150704545885), np.float64(0.00254950373742608), np.float64(0.04282614950449115), np.float64(0.014549503737426084), np.float64(0.008549503737426085)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.17166623561134695), 4: np.float64(0.18916632974989486), 7: np.float64(0.5161612489434095), 91: np.float64(0.0169245138170278), 16: np.float64(0.07223264424426554), 90: np.float64(0.0169245138170278), 0: np.float64(0.0169245138170278)}
err dic= {8: np.float64(0.08633376438865306), 4: np.float64(0.047833670250105126), 7: np.float64(0.29716124894340956), 91: np.float64(0.0330754861829722), 16: np.float64(0.08176735575573446), 90: np.float64(0.021075486182972197), 0: np.float64(0.027075486182972196)} 

err list= [np.float64(0.08633376438865306), np.float64(0.047833670250105126), np.float64(0.29716124894340956), np.float64(0.0330754861829722), np.float64(0.08176735575573446), np.float64(0.021075486182972197), np.float64(0.027075486182972196)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.1975913003652114), 4: np.float64(0.18000768200676254), 7: np.float64(0.5270828735969181), 91: np.float64(0.01066353610702862), 16: np.float64(0.06332753571002209), 90: np.float64(0.01066353610702862), 0: np.float64(0.01066353610702862)}
err dic= {8: np.float64(0.06040869963478862), 4: np.float64(0.05699231799323745), 7: np.float64(0.3080828735969181), 91: np.float64(0.03933646389297138), 16: np.float64(0.09067246428997791), 90: np.float64(0.02733646389297138), 0: np.float64(0.033336463892971374)} 

err list= [np.float64(0.06040869963478862), np.float64(0.05699231799323745), np.float64(0.3080828735969181), np.float64(0.03933646389297138), np.float64(0.09067246428997791), np.float64(0.02733646389297138), np.float64(0.033336463892971374)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  1 

learned probs for this beta: {8: np.float64(0.21354896674787305), 4: np.float64(0.17582618619106188), 7: np.float64(0.5199103910338998), 91: np.float64(0.010203314070603667), 16: np.float64(0.060104513815354366), 90: np.float64(0.010203314070603667), 0: np.float64(0.010203314070603667)}
err dic= {8: np.float64(0.04445103325212696), 4: np.float64(0.061173813808938104), 7: np.float64(0.3009103910338998), 91: np.float64(0.039796685929396336), 16: np.float64(0.09389548618464563), 90: np.float64(0.027796685929396332), 0: np.float64(0.03379668592939633)} 

err list= [np.float64(0.04445103325212696), np.float64(0.061173813808938104), np.float64(0.3009103910338998), np.float64(0.039796685929396336), np.float64(0.09389548618464563), np.float64(0.027796685929396332), np.float64(0.03379668592939633)]
results for assortment [8, 4, 7, 91, 16, 90] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.22081215852760533), 4: np.float64(0.17424287432072336), 7: np.float64(0.5153569083348919), 91: np.float64(0.010179922062680136), 16: np.float64(0.05904829262873888), 90: np.float64(0.010179922062680136), 0: np.float64(0.010179922062680136)}
err dic= {8: np.float64(0.03718784147239468), 4: np.float64(0.06275712567927663), 7: np.float64(0.2963569083348919), 91: np.float64(0.03982007793731987), 16: np.float64(0.09495170737126112), 90: np.float64(0.027820077937319863), 0: np.float64(0.033820077937319865)} 

err list= [np.float64(0.03718784147239468), np.float64(0.06275712567927663), np.float64(0.2963569083348919), np.float64(0.03982007793731987), np.float64(0.09495170737126112), np.float64(0.027820077937319863), np.float64(0.033820077937319865)]
results for assortment [8, 4, 7, 91, 16, 90] :

err MNL dic= {8: np.float64(0.12726147704590815), 4: np.float64(0.1033199915957558), 7: np.float64(0.08416440802605313), 91: np.float64(0.054055047799138584), 16: np.float64(0.028986868368526097), 90: np.float64(0.07104506775921843), 0: np.float64(0.21863262947788636)} 

err MNL list= [np.float64(0.12726147704590815), np.float64(0.1033199915957558), np.float64(0.08416440802605313), np.float64(0.054055047799138584), np.float64(0.028986868368526097), np.float64(0.07104506775921843), np.float64(0.21863262947788636)]
sampled assortment [6, 5, 4, 80, 96, 47] number: 8
#  Learning probs for MM model, A = [6, 5, 4, 80, 96, 47]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 13, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 6: 0, 7: 0, 11: 0, 16: 0, 20: 0} [3, 5, 6, 7, 11, 16, 20]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 3, 9: 2, 12: 2, 13: 3, 18: 3} [6, 5, 4, 9, 12, 7, 13, 18]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 14: 1, 17: 1, 100: 1} [2, 1, 3, 6, 10, 14, 17, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 12: 1} [1, 5, 6, 10, 12]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 7: 2, 9: 0, 10: 1, 11: 1, 18: 1, 19: 2, 24: 2} [9, 10, 11, 18, 5, 7, 19, 24]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 4: 5, 6: 0, 7: 5, 10: 2, 13: 3, 16: 5, 17: 6, 100: 0} [6, 100, 1, 3, 10, 13, 4, 7, 16, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 3: 0, 4: 4, 5: 4, 7: 3, 9: 0, 10: 3, 11: 3, 14: 3, 18: 5, 19: 3} [1, 3, 9, 7, 10, 11, 14, 19, 4, 5, 18]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 6: 3, 11: 2, 14: 3, 16: 3, 19: 1, 100: 0} [100, 3, 4, 19, 11, 5, 6, 14, 16]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 5: 6, 6: 4, 7: 6, 8: 0, 9: 6, 11: 0, 13: 3, 19: 3, 35: 11, 44: 10, 45: 11, 48: 11, 52: 10, 53: 13, 57: 13, 58: 11, 59: 13, 62: 12, 64: 12, 77: 12, 78: 12, 84: 11, 85: 10, 88: 12, 92: 11, 99: 13, 100: 2} [8, 11, 100, 1, 13, 19, 6, 5, 7, 9, 44, 52, 85, 35, 45, 48, 58, 84, 92, 62, 64, 77, 78, 88, 53, 57, 59, 99]
#  Learning probs for MM model, A = [6, 5, 4, 80, 96, 47]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 14: 1} [8, 1, 2, 3, 4, 7, 10, 14]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 6: 0, 7: 0, 14: 0, 15: 0, 16: 0, 24: 2} [3, 5, 6, 7, 14, 15, 16, 24]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 3, 10: 2, 12: 2, 13: 3, 20: 3, 23: 6, 27: 4} [6, 5, 4, 10, 12, 7, 13, 20, 27, 23]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 9: 1, 10: 1, 11: 1, 13: 1, 15: 1} [2, 1, 6, 9, 10, 11, 13, 15]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 6: 1, 10: 1, 22: 1, 24: 1} [1, 5, 6, 10, 22, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {9: 0, 11: 1, 13: 2, 17: 2, 18: 2, 22: 3, 100: 1} [9, 11, 100, 13, 17, 18, 22]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 5, 6: 0, 7: 5, 10: 2, 13: 3, 14: 5, 15: 3, 20: 4, 100: 0} [6, 100, 1, 3, 10, 13, 15, 20, 5, 7, 14]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 3, 3: 0, 4: 4, 5: 4, 7: 3, 9: 0, 11: 3, 14: 3, 15: 3, 17: 3, 25: 3} [1, 3, 9, 2, 7, 11, 14, 15, 17, 25, 4, 5]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 3, 14: 2, 100: 0} [100, 3, 4, 14, 5]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 4, 2: 13, 4: 9, 5: 9, 6: 4, 7: 4, 8: 0, 9: 5, 11: 0, 13: 3, 17: 9, 19: 4, 20: 11, 22: 12, 23: 8, 30: 14, 34: 15, 37: 15, 38: 16, 39: 13, 42: 15, 46: 13, 50: 16, 51: 15, 56: 17, 58: 15, 62: 11, 68: 13, 91: 17, 97: 14, 100: 2} [8, 11, 100, 13, 1, 6, 7, 19, 9, 23, 4, 5, 17, 20, 62, 22, 2, 39, 46, 68, 30, 97, 34, 37, 42, 51, 58, 38, 50, 56, 91]
empirical probabilities from test set: {6: 0.254, 5: 0.249, 4: 0.25, 80: 0.049, 96: 0.052, 47: 0.101, 0: 0.045}
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.1219124808248407), 5: np.float64(0.11583710504155888), 4: np.float64(0.12844567882786115), 80: np.float64(0.15845118382643497), 96: np.float64(0.15845118382643497), 47: np.float64(0.15845118382643497), 0: np.float64(0.15845118382643497)}
err dic= {6: np.float64(0.13208751917515932), 5: np.float64(0.13316289495844114), 4: np.float64(0.12155432117213885), 80: np.float64(0.10945118382643497), 96: np.float64(0.10645118382643498), 47: np.float64(0.057451183826434965), 0: np.float64(0.11345118382643497)} 

err list= [np.float64(0.13208751917515932), np.float64(0.13316289495844114), np.float64(0.12155432117213885), np.float64(0.10945118382643497), np.float64(0.10645118382643498), np.float64(0.057451183826434965), np.float64(0.11345118382643497)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.14248758225762861), 5: np.float64(0.13067267451529221), 4: np.float64(0.13556430744741468), 80: np.float64(0.14781885894491636), 96: np.float64(0.14781885894491636), 47: np.float64(0.14781885894491636), 0: np.float64(0.14781885894491636)}
err dic= {6: np.float64(0.11151241774237139), 5: np.float64(0.11832732548470778), 4: np.float64(0.11443569255258532), 80: np.float64(0.09881885894491636), 96: np.float64(0.09581885894491637), 47: np.float64(0.04681885894491636), 0: np.float64(0.10281885894491637)} 

err list= [np.float64(0.11151241774237139), np.float64(0.11832732548470778), np.float64(0.11443569255258532), np.float64(0.09881885894491636), np.float64(0.09581885894491637), np.float64(0.04681885894491636), np.float64(0.10281885894491637)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.1946425222764418), 5: np.float64(0.16545215619094372), 4: np.float64(0.15242443102091646), 80: np.float64(0.12187022262792446), 96: np.float64(0.12187022262792446), 47: np.float64(0.12187022262792446), 0: np.float64(0.12187022262792446)}
err dic= {6: np.float64(0.059357477723558205), 5: np.float64(0.08354784380905628), 4: np.float64(0.09757556897908354), 80: np.float64(0.07287022262792446), 96: np.float64(0.06987022262792447), 47: np.float64(0.020870222627924456), 0: np.float64(0.07687022262792446)} 

err list= [np.float64(0.059357477723558205), np.float64(0.08354784380905628), np.float64(0.09757556897908354), np.float64(0.07287022262792446), np.float64(0.06987022262792447), np.float64(0.020870222627924456), np.float64(0.07687022262792446)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.32648943988086), 5: np.float64(0.24106842207494686), 4: np.float64(0.2185352497224645), 80: np.float64(0.05347672208043221), 96: np.float64(0.05347672208043221), 47: np.float64(0.05347672208043221), 0: np.float64(0.05347672208043221)}
err dic= {6: np.float64(0.07248943988085998), 5: np.float64(0.00793157792505314), 4: np.float64(0.03146475027753551), 80: np.float64(0.004476722080432205), 96: np.float64(0.0014767220804322093), 47: np.float64(0.0475232779195678), 0: np.float64(0.008476722080432209)} 

err list= [np.float64(0.07248943988085998), np.float64(0.00793157792505314), np.float64(0.03146475027753551), np.float64(0.004476722080432205), np.float64(0.0014767220804322093), np.float64(0.0475232779195678), np.float64(0.008476722080432209)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.3698209644710695), 5: np.float64(0.2564645937917433), 4: np.float64(0.3126809745560441), 80: np.float64(0.015258366795285801), 96: np.float64(0.015258366795285801), 47: np.float64(0.015258366795285801), 0: np.float64(0.015258366795285801)}
err dic= {6: np.float64(0.11582096447106949), 5: np.float64(0.007464593791743301), 4: np.float64(0.0626809745560441), 80: np.float64(0.0337416332047142), 96: np.float64(0.0367416332047142), 47: np.float64(0.0857416332047142), 0: np.float64(0.029741633204714197)} 

err list= [np.float64(0.11582096447106949), np.float64(0.007464593791743301), np.float64(0.0626809745560441), np.float64(0.0337416332047142), np.float64(0.0367416332047142), np.float64(0.0857416332047142), np.float64(0.029741633204714197)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.3631980162761908), 5: np.float64(0.2564273182976752), 4: np.float64(0.3385886789398697), 80: np.float64(0.010446496621566059), 96: np.float64(0.010446496621566059), 47: np.float64(0.010446496621566059), 0: np.float64(0.010446496621566059)}
err dic= {6: np.float64(0.1091980162761908), 5: np.float64(0.007427318297675178), 4: np.float64(0.08858867893986971), 80: np.float64(0.03855350337843394), 96: np.float64(0.04155350337843394), 47: np.float64(0.09055350337843394), 0: np.float64(0.034553503378433936)} 

err list= [np.float64(0.1091980162761908), np.float64(0.007427318297675178), np.float64(0.08858867893986971), np.float64(0.03855350337843394), np.float64(0.04155350337843394), np.float64(0.09055350337843394), np.float64(0.034553503378433936)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  1 

learned probs for this beta: {6: np.float64(0.3530626348821645), 5: np.float64(0.2595710455360614), 4: np.float64(0.3466106060865517), 80: np.float64(0.010188928373805634), 96: np.float64(0.010188928373805634), 47: np.float64(0.010188928373805634), 0: np.float64(0.010188928373805634)}
err dic= {6: np.float64(0.09906263488216449), 5: np.float64(0.010571045536061419), 4: np.float64(0.0966106060865517), 80: np.float64(0.03881107162619437), 96: np.float64(0.041811071626194365), 47: np.float64(0.09081107162619437), 0: np.float64(0.034811071626194366)} 

err list= [np.float64(0.09906263488216449), np.float64(0.010571045536061419), np.float64(0.0966106060865517), np.float64(0.03881107162619437), np.float64(0.041811071626194365), np.float64(0.09081107162619437), np.float64(0.034811071626194366)]
results for assortment [6, 5, 4, 80, 96, 47] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.34348136052177536), 5: np.float64(0.26355520588348025), 4: np.float64(0.3522475093438912), 80: np.float64(0.010178981062713274), 96: np.float64(0.010178981062713274), 47: np.float64(0.010178981062713274), 0: np.float64(0.010178981062713274)}
err dic= {6: np.float64(0.08948136052177535), 5: np.float64(0.014555205883480249), 4: np.float64(0.10224750934389121), 80: np.float64(0.038821018937286726), 96: np.float64(0.04182101893728672), 47: np.float64(0.09082101893728674), 0: np.float64(0.03482101893728672)} 

err list= [np.float64(0.08948136052177535), np.float64(0.014555205883480249), np.float64(0.10224750934389121), np.float64(0.038821018937286726), np.float64(0.04182101893728672), np.float64(0.09082101893728674), np.float64(0.03482101893728672)]
results for assortment [6, 5, 4, 80, 96, 47] :

err MNL dic= {6: np.float64(0.11738883652738505), 5: np.float64(0.11039909938213427), 4: np.float64(0.116739972772018), 80: np.float64(0.0600166509582155), 96: np.float64(0.053560791705937784), 47: np.float64(0.014142946905435105), 0: np.float64(0.2168075191119489)} 

err MNL list= [np.float64(0.11738883652738505), np.float64(0.11039909938213427), np.float64(0.116739972772018), np.float64(0.0600166509582155), np.float64(0.053560791705937784), np.float64(0.014142946905435105), np.float64(0.2168075191119489)]
sampled assortment [6, 5, 7, 98, 79, 33] number: 9
#  Learning probs for MM model, A = [6, 5, 7, 98, 79, 33]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 1, 3, 4, 5, 7, 12, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 15: 0, 20: 0} [3, 5, 7, 12, 15, 20]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 7: 2, 9: 3, 10: 3, 12: 2, 13: 3, 16: 5, 18: 3, 20: 3, 27: 4} [6, 5, 4, 7, 12, 9, 10, 13, 18, 20, 27, 16]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {2: 0, 3: 1, 6: 1, 10: 1, 13: 1, 100: 1} [2, 3, 6, 10, 13, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 7: 1, 12: 1, 13: 1, 15: 1, 16: 1, 100: 1} [1, 5, 7, 12, 13, 15, 16, 100]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 11: 1, 15: 1, 18: 1, 24: 2} [9, 11, 15, 18, 5, 24]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 10: 1, 13: 3, 15: 3, 17: 7, 20: 5, 100: 0} [6, 100, 10, 1, 3, 13, 15, 5, 7, 20, 17]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 3, 3: 0, 4: 4, 7: 3, 9: 0, 10: 4, 11: 3, 12: 6, 16: 6, 19: 3, 53: 6} [1, 3, 9, 2, 7, 11, 19, 4, 10, 12, 16, 53]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 5: 2, 6: 2, 14: 2, 19: 1, 100: 0} [100, 3, 4, 19, 5, 6, 14]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 3: 8, 4: 9, 6: 4, 7: 5, 8: 0, 9: 5, 11: 0, 12: 12, 13: 3, 17: 9, 19: 4, 21: 11, 22: 13, 23: 9, 28: 13, 33: 11, 38: 13, 48: 11, 59: 13, 62: 14, 80: 11, 85: 13, 88: 13, 92: 12, 94: 16, 100: 2} [8, 11, 100, 1, 13, 6, 19, 7, 9, 3, 4, 17, 23, 21, 33, 48, 80, 12, 92, 22, 28, 38, 59, 85, 88, 62, 94]
#  Learning probs for MM model, A = [6, 5, 7, 98, 79, 33]
#cluster  8 with weight 0.2095
Learned cluster center of cluster 8:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 100: 1} [8, 1, 2, 3, 5, 7, 100]
#cluster  7 with weight 0.15725
Learned cluster center of cluster 7:  {3: 0, 5: 0, 7: 0, 12: 0, 15: 0, 20: 0, 21: 0} [3, 5, 7, 12, 15, 20, 21]
#cluster  4 with weight 0.053
Learned cluster center of cluster 4:  {4: 2, 5: 1, 6: 0, 8: 4, 9: 2, 10: 3, 11: 3, 12: 2, 27: 4} [6, 5, 4, 9, 12, 10, 11, 8, 27]
#cluster  1 with weight 0.1765
Learned cluster center of cluster 1:  {1: 1, 2: 0, 6: 1, 7: 1, 10: 1, 11: 1, 100: 1} [2, 1, 6, 7, 10, 11, 100]
#cluster  2 with weight 0.1285
Learned cluster center of cluster 2:  {1: 0, 5: 1, 12: 1, 15: 1, 24: 1} [1, 5, 12, 15, 24]
#cluster  6 with weight 0.07125
Learned cluster center of cluster 6:  {5: 2, 9: 0, 10: 2, 11: 1, 12: 2, 18: 2} [9, 11, 5, 10, 12, 18]
#cluster  10 with weight 0.0485
Learned cluster center of cluster 10:  {1: 2, 3: 2, 5: 4, 6: 0, 7: 5, 8: 4, 10: 2, 13: 4, 14: 5, 15: 3, 17: 5, 21: 6, 100: 0} [6, 100, 1, 3, 10, 15, 5, 8, 13, 7, 14, 17, 21]
#cluster  3 with weight 0.03625
Learned cluster center of cluster 3:  {1: 0, 2: 3, 3: 0, 4: 3, 7: 3, 9: 0, 11: 4, 13: 7, 14: 3, 15: 3, 19: 3, 45: 8, 50: 8} [1, 3, 9, 2, 4, 7, 14, 15, 19, 11, 13, 45, 50]
#cluster  5 with weight 0.11325
Learned cluster center of cluster 5:  {3: 1, 4: 1, 6: 2, 16: 3, 19: 1, 25: 3, 100: 0} [100, 3, 4, 19, 6, 16, 25]
#cluster  9 with weight 0.006
Learned cluster center of cluster 9:  {1: 3, 5: 9, 6: 4, 7: 4, 8: 0, 9: 6, 11: 0, 13: 3, 15: 12, 17: 9, 19: 4, 23: 8, 37: 12, 39: 14, 41: 11, 51: 11, 58: 12, 60: 13, 69: 14, 76: 13, 77: 12, 81: 12, 88: 11, 97: 13, 98: 12, 99: 14, 100: 2} [8, 11, 100, 1, 13, 6, 7, 19, 9, 23, 5, 17, 41, 51, 88, 15, 37, 58, 77, 81, 98, 60, 76, 97, 39, 69, 99]
empirical probabilities from test set: {6: 0.266, 5: 0.246, 7: 0.216, 98: 0.058, 79: 0.06, 33: 0.115, 0: 0.039}
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.13494796615113977), 5: np.float64(0.10774083657366078), 7: np.float64(0.1115294119358976), 98: np.float64(0.16144544633482477), 79: np.float64(0.16144544633482477), 33: np.float64(0.16144544633482477), 0: np.float64(0.16144544633482477)}
err dic= {6: np.float64(0.13105203384886024), 5: np.float64(0.1382591634263392), 7: np.float64(0.1044705880641024), 98: np.float64(0.10344544633482478), 79: np.float64(0.10144544633482477), 33: np.float64(0.046445446334824766), 0: np.float64(0.12244544633482476)} 

err list= [np.float64(0.13105203384886024), np.float64(0.1382591634263392), np.float64(0.1044705880641024), np.float64(0.10344544633482478), np.float64(0.10144544633482477), np.float64(0.046445446334824766), np.float64(0.12244544633482476)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.14476270883635894), 5: np.float64(0.12559674958101066), 7: np.float64(0.12775851125642115), 98: np.float64(0.150470507581552), 79: np.float64(0.150470507581552), 33: np.float64(0.150470507581552), 0: np.float64(0.150470507581552)}
err dic= {6: np.float64(0.12123729116364107), 5: np.float64(0.12040325041898933), 7: np.float64(0.08824148874357884), 98: np.float64(0.09247050758155201), 79: np.float64(0.090470507581552), 33: np.float64(0.035470507581552), 0: np.float64(0.111470507581552)} 

err list= [np.float64(0.12123729116364107), np.float64(0.12040325041898933), np.float64(0.08824148874357884), np.float64(0.09247050758155201), np.float64(0.090470507581552), np.float64(0.035470507581552), np.float64(0.111470507581552)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.1691074570626135), 5: np.float64(0.1711426128959426), 7: np.float64(0.16576829732472081), 98: np.float64(0.12349540817918113), 79: np.float64(0.12349540817918113), 33: np.float64(0.12349540817918113), 0: np.float64(0.12349540817918113)}
err dic= {6: np.float64(0.09689254293738653), 5: np.float64(0.0748573871040574), 7: np.float64(0.05023170267527918), 98: np.float64(0.06549540817918112), 79: np.float64(0.06349540817918113), 33: np.float64(0.008495408179181124), 0: np.float64(0.08449540817918114)} 

err list= [np.float64(0.09689254293738653), np.float64(0.0748573871040574), np.float64(0.05023170267527918), np.float64(0.06549540817918112), np.float64(0.06349540817918113), np.float64(0.008495408179181124), np.float64(0.08449540817918114)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.23411550628668143), 5: np.float64(0.31808046020110103), 7: np.float64(0.25052773185617533), 98: np.float64(0.04931907541401062), 79: np.float64(0.04931907541401062), 33: np.float64(0.04931907541401062), 0: np.float64(0.04931907541401062)}
err dic= {6: np.float64(0.031884493713318585), 5: np.float64(0.07208046020110104), 7: np.float64(0.03452773185617533), 98: np.float64(0.008680924585989382), 79: np.float64(0.010680924585989376), 33: np.float64(0.06568092458598938), 0: np.float64(0.010319075414010621)} 

err list= [np.float64(0.031884493713318585), np.float64(0.07208046020110104), np.float64(0.03452773185617533), np.float64(0.008680924585989382), np.float64(0.010680924585989376), np.float64(0.06568092458598938), np.float64(0.010319075414010621)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.2913344115029916), 5: np.float64(0.43688772706268225), 7: np.float64(0.24646426503227073), 98: np.float64(0.0063283991005139055), 79: np.float64(0.0063283991005139055), 33: np.float64(0.0063283991005139055), 0: np.float64(0.0063283991005139055)}
err dic= {6: np.float64(0.025334411502991594), 5: np.float64(0.19088772706268226), 7: np.float64(0.030464265032270732), 98: np.float64(0.051671600899486095), 79: np.float64(0.05367160089948609), 33: np.float64(0.1086716008994861), 0: np.float64(0.03267160089948609)} 

err list= [np.float64(0.025334411502991594), np.float64(0.19088772706268226), np.float64(0.030464265032270732), np.float64(0.051671600899486095), np.float64(0.05367160089948609), np.float64(0.1086716008994861), np.float64(0.03267160089948609)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.3189949694941537), 5: np.float64(0.46659856954246387), 7: np.float64(0.21284050427302265), 98: np.float64(0.0003914891725899334), 79: np.float64(0.0003914891725899334), 33: np.float64(0.0003914891725899334), 0: np.float64(0.0003914891725899334)}
err dic= {6: np.float64(0.052994969494153665), 5: np.float64(0.22059856954246387), 7: np.float64(0.0031594957269773516), 98: np.float64(0.05760851082741007), 79: np.float64(0.05960851082741007), 33: np.float64(0.11460851082741007), 0: np.float64(0.03860851082741007)} 

err list= [np.float64(0.052994969494153665), np.float64(0.22059856954246387), np.float64(0.0031594957269773516), np.float64(0.05760851082741007), np.float64(0.05960851082741007), np.float64(0.11460851082741007), np.float64(0.03860851082741007)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  1 

learned probs for this beta: {6: np.float64(0.33340141163649206), 5: np.float64(0.4825398089175819), 7: np.float64(0.18399042762389917), 98: np.float64(1.7087955506734825e-05), 79: np.float64(1.7087955506734825e-05), 33: np.float64(1.7087955506734825e-05), 0: np.float64(1.7087955506734825e-05)}
err dic= {6: np.float64(0.06740141163649205), 5: np.float64(0.23653980891758192), 7: np.float64(0.03200957237610083), 98: np.float64(0.05798291204449327), 79: np.float64(0.05998291204449326), 33: np.float64(0.11498291204449328), 0: np.float64(0.038982912044493265)} 

err list= [np.float64(0.06740141163649205), np.float64(0.23653980891758192), np.float64(0.03200957237610083), np.float64(0.05798291204449327), np.float64(0.05998291204449326), np.float64(0.11498291204449328), np.float64(0.038982912044493265)]
results for assortment [6, 5, 7, 98, 79, 33] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.3446830623653132), 5: np.float64(0.49674522432475027), 7: np.float64(0.15856877061501337), 98: np.float64(7.356737307680729e-07), 79: np.float64(7.356737307680729e-07), 33: np.float64(7.356737307680729e-07), 0: np.float64(7.356737307680729e-07)}
err dic= {6: np.float64(0.0786830623653132), 5: np.float64(0.25074522432475027), 7: np.float64(0.057431229384986626), 98: np.float64(0.057999264326269236), 79: np.float64(0.05999926432626923), 33: np.float64(0.11499926432626924), 0: np.float64(0.03899926432626923)} 

err list= [np.float64(0.0786830623653132), np.float64(0.25074522432475027), np.float64(0.057431229384986626), np.float64(0.057999264326269236), np.float64(0.05999926432626923), np.float64(0.11499926432626924), np.float64(0.03899926432626923)]
results for assortment [6, 5, 7, 98, 79, 33] :

err MNL dic= {6: np.float64(0.12983089770354905), 5: np.float64(0.10784759916492695), 7: np.float64(0.08202296450939459), 98: np.float64(0.048158663883089765), 79: np.float64(0.04756784968684759), 33: np.float64(0.00201461377870564), 0: np.float64(0.22196033402922752)} 

err MNL list= [np.float64(0.12983089770354905), np.float64(0.10784759916492695), np.float64(0.08202296450939459), np.float64(0.048158663883089765), np.float64(0.04756784968684759), np.float64(0.00201461377870564), np.float64(0.22196033402922752)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25]
 mean error for all betas:

mean_err= [0.1067948  0.1005234  0.08815671 0.07446948 0.07367195 0.07442156
 0.07619567 0.07843651]
mean_std= [0.         0.00627139 0.01822335 0.02847962 0.02552283 0.02335927
 0.02205877 0.02146894]
MNL: [0.10149444 0.10807261 0.10416074 0.09947598 0.09830105 0.09416393
 0.09352452 0.09820936 0.09843655 0.09134327]
 mean error for MNL:

mean_err_MNL= 0.09871824347894989
mean_std_MNL= 0.0047752006160125485
