p= 0.01 num clusters= 1
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 100]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
empirical probabilities from test set: {2: 0.275, 3: 0.247, 4: 0.252, 59: 0.059, 40: 0.072, 84: 0.06, 0: 0.035}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.10940637967261835), 3: np.float64(0.10670512653383978), 4: np.float64(0.1040705675726914), 59: np.float64(0.16995448155520987), 40: np.float64(0.16995448155520987), 84: np.float64(0.16995448155520987), 0: np.float64(0.16995448155520987)}
err dic= {2: np.float64(0.16559362032738167), 3: np.float64(0.1402948734661602), 4: np.float64(0.1479294324273086), 59: np.float64(0.11095448155520987), 40: np.float64(0.09795448155520987), 84: np.float64(0.10995448155520987), 0: np.float64(0.13495448155520987)} 

err list= [np.float64(0.16559362032738167), np.float64(0.1402948734661602), np.float64(0.1479294324273086), np.float64(0.11095448155520987), np.float64(0.09795448155520987), np.float64(0.10995448155520987), np.float64(0.13495448155520987)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.14252978060998162), 3: np.float64(0.13557852118384572), 4: np.float64(0.12896627868036747), 59: np.float64(0.14823135488145253), 40: np.float64(0.14823135488145253), 84: np.float64(0.14823135488145253), 0: np.float64(0.14823135488145253)}
err dic= {2: np.float64(0.1324702193900184), 3: np.float64(0.11142147881615427), 4: np.float64(0.12303372131963253), 59: np.float64(0.08923135488145253), 40: np.float64(0.07623135488145254), 84: np.float64(0.08823135488145253), 0: np.float64(0.11323135488145253)} 

err list= [np.float64(0.1324702193900184), np.float64(0.11142147881615427), np.float64(0.12303372131963253), np.float64(0.08923135488145253), np.float64(0.07623135488145254), np.float64(0.08823135488145253), np.float64(0.11323135488145253)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.21826254833995293), 3: np.float64(0.19749212069387162), 4: np.float64(0.17869826057108879), 59: np.float64(0.1013867675987675), 40: np.float64(0.1013867675987675), 84: np.float64(0.1013867675987675), 0: np.float64(0.1013867675987675)}
err dic= {2: np.float64(0.056737451660047095), 3: np.float64(0.04950787930612838), 4: np.float64(0.07330173942891122), 59: np.float64(0.0423867675987675), 40: np.float64(0.029386767598767502), 84: np.float64(0.0413867675987675), 0: np.float64(0.0663867675987675)} 

err list= [np.float64(0.056737451660047095), np.float64(0.04950787930612838), np.float64(0.07330173942891122), np.float64(0.0423867675987675), np.float64(0.029386767598767502), np.float64(0.0413867675987675), np.float64(0.0663867675987675)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.39237776551253783), 3: np.float64(0.3055841110409724), 4: np.float64(0.23798914497288826), 59: np.float64(0.016012244618401967), 40: np.float64(0.016012244618401967), 84: np.float64(0.016012244618401967), 0: np.float64(0.016012244618401967)}
err dic= {2: np.float64(0.11737776551253781), 3: np.float64(0.058584111040972386), 4: np.float64(0.014010855027111746), 59: np.float64(0.04298775538159803), 40: np.float64(0.05598775538159803), 84: np.float64(0.043987755381598034), 0: np.float64(0.018987755381598036)} 

err list= [np.float64(0.11737776551253781), np.float64(0.058584111040972386), np.float64(0.014010855027111746), np.float64(0.04298775538159803), np.float64(0.05598775538159803), np.float64(0.043987755381598034), np.float64(0.018987755381598036)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5051788468771481), 3: np.float64(0.3064064592692646), 4: np.float64(0.18584491188079988), 59: np.float64(0.0006424454931975654), 40: np.float64(0.0006424454931975654), 84: np.float64(0.0006424454931975654), 0: np.float64(0.0006424454931975654)}
err dic= {2: np.float64(0.23017884687714807), 3: np.float64(0.05940645926926458), 4: np.float64(0.06615508811920012), 59: np.float64(0.05835755450680243), 40: np.float64(0.07135755450680242), 84: np.float64(0.05935755450680243), 0: np.float64(0.03435755450680244)} 

err list= [np.float64(0.23017884687714807), np.float64(0.05940645926926458), np.float64(0.06615508811920012), np.float64(0.05835755450680243), np.float64(0.07135755450680242), np.float64(0.05935755450680243), np.float64(0.03435755450680244)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5896912542220977), 3: np.float64(0.2785504249384166), 4: np.float64(0.13157790399270525), 59: np.float64(4.5104211695328585e-05), 40: np.float64(4.5104211695328585e-05), 84: np.float64(4.5104211695328585e-05), 0: np.float64(4.5104211695328585e-05)}
err dic= {2: np.float64(0.31469125422209765), 3: np.float64(0.03155042493841659), 4: np.float64(0.12042209600729475), 59: np.float64(0.05895489578830467), 40: np.float64(0.07195489578830466), 84: np.float64(0.05995489578830467), 0: np.float64(0.03495489578830468)} 

err list= [np.float64(0.31469125422209765), np.float64(0.03155042493841659), np.float64(0.12042209600729475), np.float64(0.05895489578830467), np.float64(0.07195489578830466), np.float64(0.05995489578830467), np.float64(0.03495489578830468)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652317878724722), 3: np.float64(0.244725098372005), 4: np.float64(0.0900293324297194), 59: np.float64(3.4453314506555953e-06), 40: np.float64(3.4453314506555953e-06), 84: np.float64(3.4453314506555953e-06), 0: np.float64(3.4453314506555953e-06)}
err dic= {2: np.float64(0.39023178787247215), 3: np.float64(0.002274901627994985), 4: np.float64(0.1619706675702806), 59: np.float64(0.05899655466854934), 40: np.float64(0.07199655466854935), 84: np.float64(0.05999655466854934), 0: np.float64(0.03499655466854935)} 

err list= [np.float64(0.39023178787247215), np.float64(0.002274901627994985), np.float64(0.1619706675702806), np.float64(0.05899655466854934), np.float64(0.07199655466854935), np.float64(0.05999655466854934), np.float64(0.03499655466854935)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.730678346894004), 3: np.float64(0.20934285134700564), 4: np.float64(0.059977731099306895), 59: np.float64(2.676649212329232e-07), 40: np.float64(2.676649212329232e-07), 84: np.float64(2.676649212329232e-07), 0: np.float64(2.676649212329232e-07)}
err dic= {2: np.float64(0.455678346894004), 3: np.float64(0.037657148652994354), 4: np.float64(0.1920222689006931), 59: np.float64(0.05899973233507876), 40: np.float64(0.07199973233507877), 84: np.float64(0.05999973233507876), 0: np.float64(0.03499973233507877)} 

err list= [np.float64(0.455678346894004), np.float64(0.037657148652994354), np.float64(0.1920222689006931), np.float64(0.05899973233507876), np.float64(0.07199973233507877), np.float64(0.05999973233507876), np.float64(0.03499973233507877)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855969693222733), 3: np.float64(0.17529037757700022), 4: np.float64(0.03911257002123472), 59: np.float64(2.0769872297189893e-08), 40: np.float64(2.0769872297189893e-08), 84: np.float64(2.0769872297189893e-08), 0: np.float64(2.0769872297189893e-08)}
err dic= {2: np.float64(0.5105969693222733), 3: np.float64(0.07170962242299977), 4: np.float64(0.21288742997876528), 59: np.float64(0.0589999792301277), 40: np.float64(0.0719999792301277), 84: np.float64(0.059999979230127704), 0: np.float64(0.03499997923012771)} 

err list= [np.float64(0.5105969693222733), np.float64(0.07170962242299977), np.float64(0.21288742997876528), np.float64(0.0589999792301277), np.float64(0.0719999792301277), np.float64(0.059999979230127704), np.float64(0.03499997923012771)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845589057161), 3: np.float64(0.1443339541700947), 4: np.float64(0.02508148038993322), 59: np.float64(1.6335641883786858e-09), 40: np.float64(1.6335641883786858e-09), 84: np.float64(1.6335641883786858e-09), 0: np.float64(1.6335641883786858e-09)}
err dic= {2: np.float64(0.5555845589057161), 3: np.float64(0.1026660458299053), 4: np.float64(0.2269185196100668), 59: np.float64(0.05899999836643581), 40: np.float64(0.07199999836643581), 84: np.float64(0.05999999836643581), 0: np.float64(0.03499999836643582)} 

err list= [np.float64(0.5555845589057161), np.float64(0.1026660458299053), np.float64(0.2269185196100668), np.float64(0.05899999836643581), np.float64(0.07199999836643581), np.float64(0.05999999836643581), np.float64(0.03499999836643582)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133317401002), 3: np.float64(0.11731042776431841), 4: np.float64(0.015876239968092228), 59: np.float64(1.318718180909206e-10), 40: np.float64(1.318718180909206e-10), 84: np.float64(1.318718180909206e-10), 0: np.float64(1.318718180909206e-10)}
err dic= {2: np.float64(0.5918133317401002), 3: np.float64(0.1296895722356816), 4: np.float64(0.23612376003190777), 59: np.float64(0.05899999986812818), 40: np.float64(0.07199999986812818), 84: np.float64(0.05999999986812818), 0: np.float64(0.034999999868128184)} 

err list= [np.float64(0.5918133317401002), np.float64(0.1296895722356816), np.float64(0.23612376003190777), np.float64(0.05899999986812818), np.float64(0.07199999986812818), np.float64(0.05999999986812818), np.float64(0.034999999868128184)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: 0.275, 3: 0.247, 4: 0.252, 59: 0.059, 40: 0.072, 84: 0.06, 0: np.float64(0.2293824027072758)} 

err MNL list= [0.275, 0.247, 0.252, 0.059, 0.072, 0.06, np.float64(0.2293824027072758)]
sampled assortment [3, 4, 8, 74, 40, 87] number: 1
#  Learning probs for MM model, A = [3, 4, 8, 74, 40, 87]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
#  Learning probs for MM model, A = [3, 4, 8, 74, 40, 87]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 100]
empirical probabilities from test set: {3: 0.259, 4: 0.246, 8: 0.256, 74: 0.066, 40: 0.077, 87: 0.047, 0: 0.049}
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.10781310220440632), 4: np.float64(0.10515118722648113), 8: np.float64(0.0955577914634166), 74: np.float64(0.17286947977642148), 40: np.float64(0.17286947977642148), 87: np.float64(0.17286947977642148), 0: np.float64(0.17286947977642148)}
err dic= {3: np.float64(0.1511868977955937), 4: np.float64(0.14084881277351885), 8: np.float64(0.16044220853658342), 74: np.float64(0.10686947977642147), 40: np.float64(0.09586947977642148), 87: np.float64(0.1258694797764215), 0: np.float64(0.12386947977642147)} 

err list= [np.float64(0.1511868977955937), np.float64(0.14084881277351885), np.float64(0.16044220853658342), np.float64(0.10686947977642147), np.float64(0.09586947977642148), np.float64(0.1258694797764215), np.float64(0.12386947977642147)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.13909805155767466), 4: np.float64(0.13231415953237738), 8: np.float64(0.10947568472428836), 74: np.float64(0.15477802604641622), 40: np.float64(0.15477802604641622), 87: np.float64(0.15477802604641622), 0: np.float64(0.15477802604641622)}
err dic= {3: np.float64(0.11990194844232535), 4: np.float64(0.11368584046762262), 8: np.float64(0.14652431527571164), 74: np.float64(0.08877802604641621), 40: np.float64(0.07777802604641622), 87: np.float64(0.10777802604641622), 0: np.float64(0.10577802604641622)} 

err list= [np.float64(0.11990194844232535), np.float64(0.11368584046762262), np.float64(0.14652431527571164), np.float64(0.08877802604641621), np.float64(0.07777802604641622), np.float64(0.10777802604641622), np.float64(0.10577802604641622)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.2126530361987759), 4: np.float64(0.19241642421160773), 8: np.float64(0.13281457860221876), 74: np.float64(0.11552899024684546), 40: np.float64(0.11552899024684546), 87: np.float64(0.11552899024684546), 0: np.float64(0.11552899024684546)}
err dic= {3: np.float64(0.046346963801224106), 4: np.float64(0.05358357578839226), 8: np.float64(0.12318542139778124), 74: np.float64(0.049528990246845456), 40: np.float64(0.03852899024684546), 87: np.float64(0.06852899024684546), 0: np.float64(0.06652899024684546)} 

err list= [np.float64(0.046346963801224106), np.float64(0.05358357578839226), np.float64(0.12318542139778124), np.float64(0.049528990246845456), np.float64(0.03852899024684546), np.float64(0.06852899024684546), np.float64(0.06652899024684546)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.4194305192069369), 4: np.float64(0.3266528168024079), 8: np.float64(0.1358950602725808), 74: np.float64(0.02950540092952013), 40: np.float64(0.02950540092952013), 87: np.float64(0.02950540092952013), 0: np.float64(0.02950540092952013)}
err dic= {3: np.float64(0.1604305192069369), 4: np.float64(0.08065281680240788), 8: np.float64(0.1201049397274192), 74: np.float64(0.036494599070479875), 40: np.float64(0.04749459907047987), 87: np.float64(0.01749459907047987), 0: np.float64(0.019494599070479873)} 

err list= [np.float64(0.1604305192069369), np.float64(0.08065281680240788), np.float64(0.1201049397274192), np.float64(0.036494599070479875), np.float64(0.04749459907047987), np.float64(0.01749459907047987), np.float64(0.019494599070479873)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5804878219301527), 4: np.float64(0.3520836615904435), 8: np.float64(0.06090285206267064), 74: np.float64(0.0016314161041838247), 40: np.float64(0.0016314161041838247), 87: np.float64(0.0016314161041838247), 0: np.float64(0.0016314161041838247)}
err dic= {3: np.float64(0.3214878219301527), 4: np.float64(0.10608366159044352), 8: np.float64(0.19509714793732935), 74: np.float64(0.06436858389581618), 40: np.float64(0.07536858389581617), 87: np.float64(0.045368583895816175), 0: np.float64(0.04736858389581618)} 

err list= [np.float64(0.3214878219301527), np.float64(0.10608366159044352), np.float64(0.19509714793732935), np.float64(0.06436858389581618), np.float64(0.07536858389581617), np.float64(0.045368583895816175), np.float64(0.04736858389581618)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.6648060623371244), 4: np.float64(0.31403214790751477), 8: np.float64(0.02064066685255919), 74: np.float64(0.00013028072570091213), 40: np.float64(0.00013028072570091213), 87: np.float64(0.00013028072570091213), 0: np.float64(0.00013028072570091213)}
err dic= {3: np.float64(0.40580606233712435), 4: np.float64(0.06803214790751477), 8: np.float64(0.2353593331474408), 74: np.float64(0.06586971927429909), 40: np.float64(0.07686971927429909), 87: np.float64(0.04686971927429909), 0: np.float64(0.04886971927429909)} 

err list= [np.float64(0.40580606233712435), np.float64(0.06803214790751477), np.float64(0.2353593331474408), np.float64(0.06586971927429909), np.float64(0.07686971927429909), np.float64(0.04686971927429909), np.float64(0.04886971927429909)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.7263599799520452), 4: np.float64(0.2672129035140585), 8: np.float64(0.006377883472564332), 74: np.float64(1.2308265332988428e-05), 40: np.float64(1.2308265332988428e-05), 87: np.float64(1.2308265332988428e-05), 0: np.float64(1.2308265332988428e-05)}
err dic= {3: np.float64(0.46735997995204515), 4: np.float64(0.021212903514058523), 8: np.float64(0.24962211652743568), 74: np.float64(0.06598769173466701), 40: np.float64(0.076987691734667), 87: np.float64(0.04698769173466701), 0: np.float64(0.048987691734667015)} 

err list= [np.float64(0.46735997995204515), np.float64(0.021212903514058523), np.float64(0.24962211652743568), np.float64(0.06598769173466701), np.float64(0.076987691734667), np.float64(0.04698769173466701), np.float64(0.048987691734667015)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.7758285649369508), 4: np.float64(0.22227860539559416), 8: np.float64(0.0018881052322648544), 74: np.float64(1.1811087978652984e-06), 40: np.float64(1.1811087978652984e-06), 87: np.float64(1.1811087978652984e-06), 0: np.float64(1.1811087978652984e-06)}
err dic= {3: np.float64(0.5168285649369508), 4: np.float64(0.023721394604405838), 8: np.float64(0.25411189476773516), 74: np.float64(0.06599881889120214), 40: np.float64(0.07699881889120214), 87: np.float64(0.04699881889120214), 0: np.float64(0.04899881889120214)} 

err list= [np.float64(0.5168285649369508), np.float64(0.023721394604405838), np.float64(0.25411189476773516), np.float64(0.06599881889120214), np.float64(0.07699881889120214), np.float64(0.04699881889120214), np.float64(0.04899881889120214)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.8171258311911188), 4: np.float64(0.18232541757509335), 8: np.float64(0.0005482990764495868), 74: np.float64(1.1303933394551425e-07), 40: np.float64(1.1303933394551425e-07), 87: np.float64(1.1303933394551425e-07), 0: np.float64(1.1303933394551425e-07)}
err dic= {3: np.float64(0.5581258311911188), 4: np.float64(0.06367458242490664), 8: np.float64(0.2554517009235504), 74: np.float64(0.06599988696066605), 40: np.float64(0.07699988696066605), 87: np.float64(0.04699988696066605), 0: np.float64(0.04899988696066605)} 

err list= [np.float64(0.5581258311911188), np.float64(0.06367458242490664), np.float64(0.2554517009235504), np.float64(0.06599988696066605), np.float64(0.07699988696066605), np.float64(0.04699988696066605), np.float64(0.04899988696066605)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.8518182121660807), 4: np.float64(0.1480238098310077), 8: np.float64(0.00015793399269048626), 74: np.float64(1.100255527920965e-08), 40: np.float64(1.100255527920965e-08), 87: np.float64(1.100255527920965e-08), 0: np.float64(1.100255527920965e-08)}
err dic= {3: np.float64(0.5928182121660807), 4: np.float64(0.09797619016899228), 8: np.float64(0.2558420660073095), 74: np.float64(0.06599998899744472), 40: np.float64(0.07699998899744472), 87: np.float64(0.046999988997444724), 0: np.float64(0.048999988997444725)} 

err list= [np.float64(0.5928182121660807), np.float64(0.09797619016899228), np.float64(0.2558420660073095), np.float64(0.06599998899744472), np.float64(0.07699998899744472), np.float64(0.046999988997444724), np.float64(0.048999988997444725)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571363484243), 4: np.float64(0.11919751651038199), 8: np.float64(4.534272100704191e-05), 74: np.float64(1.1050463616167664e-09), 40: np.float64(1.1050463616167664e-09), 87: np.float64(1.1050463616167664e-09), 0: np.float64(1.1050463616167664e-09)}
err dic= {3: np.float64(0.6217571363484243), 4: np.float64(0.126802483489618), 8: np.float64(0.25595465727899297), 74: np.float64(0.06599999889495364), 40: np.float64(0.07699999889495364), 87: np.float64(0.04699999889495364), 0: np.float64(0.04899999889495364)} 

err list= [np.float64(0.6217571363484243), np.float64(0.126802483489618), np.float64(0.25595465727899297), np.float64(0.06599999889495364), np.float64(0.07699999889495364), np.float64(0.04699999889495364), np.float64(0.04899999889495364)]
results for assortment [3, 4, 8, 74, 40, 87] :

err MNL dic= {3: 0.259, 4: 0.246, 8: 0.256, 74: 0.066, 40: 0.077, 87: 0.047, 0: np.float64(0.21578843404120113)} 

err MNL list= [0.259, 0.246, 0.256, 0.066, 0.077, 0.047, np.float64(0.21578843404120113)]
sampled assortment [1, 3, 9, 83, 79, 70] number: 2
#  Learning probs for MM model, A = [1, 3, 9, 83, 79, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 5, 6, 7, 8, 10, 11, 100]
#  Learning probs for MM model, A = [1, 3, 9, 83, 79, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 5, 6, 7, 8, 9, 10, 100]
empirical probabilities from test set: {1: 0.265, 3: 0.251, 9: 0.235, 83: 0.052, 79: 0.068, 70: 0.081, 0: 0.048}
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.10326229037052662), 3: np.float64(0.09836473582709888), 9: np.float64(0.08725962924795032), 83: np.float64(0.17777833613860547), 79: np.float64(0.17777833613860547), 70: np.float64(0.17777833613860547), 0: np.float64(0.17777833613860547)}
err dic= {1: np.float64(0.1617377096294734), 3: np.float64(0.15263526417290113), 9: np.float64(0.14774037075204965), 83: np.float64(0.12577833613860548), 79: np.float64(0.10977833613860546), 70: np.float64(0.09677833613860547), 0: np.float64(0.12977833613860545)} 

err list= [np.float64(0.1617377096294734), np.float64(0.15263526417290113), np.float64(0.14774037075204965), np.float64(0.12577833613860548), np.float64(0.10977833613860546), np.float64(0.09677833613860547), np.float64(0.12977833613860545)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1365820686098266), 3: np.float64(0.12403863217031798), 9: np.float64(0.09782106197672372), 83: np.float64(0.16038955931078236), 79: np.float64(0.16038955931078236), 70: np.float64(0.16038955931078236), 0: np.float64(0.16038955931078236)}
err dic= {1: np.float64(0.1284179313901734), 3: np.float64(0.12696136782968204), 9: np.float64(0.13717893802327627), 83: np.float64(0.10838955931078237), 79: np.float64(0.09238955931078235), 70: np.float64(0.07938955931078236), 0: np.float64(0.11238955931078236)} 

err list= [np.float64(0.1284179313901734), np.float64(0.12696136782968204), np.float64(0.13717893802327627), np.float64(0.10838955931078237), np.float64(0.09238955931078235), np.float64(0.07938955931078236), np.float64(0.11238955931078236)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.21991453629845747), 3: np.float64(0.1821576302329121), 9: np.float64(0.1143896609342917), 83: np.float64(0.12088454313358629), 79: np.float64(0.12088454313358629), 70: np.float64(0.12088454313358629), 0: np.float64(0.12088454313358629)}
err dic= {1: np.float64(0.04508546370154254), 3: np.float64(0.06884236976708791), 9: np.float64(0.12061033906570828), 83: np.float64(0.0688845431335863), 79: np.float64(0.05288454313358629), 70: np.float64(0.03988454313358629), 0: np.float64(0.07288454313358629)} 

err list= [np.float64(0.04508546370154254), np.float64(0.06884236976708791), np.float64(0.12061033906570828), np.float64(0.0688845431335863), np.float64(0.05288454313358629), np.float64(0.03988454313358629), np.float64(0.07288454313358629)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.4756976191095952), 3: np.float64(0.30729992643962317), 9: np.float64(0.10184115080499459), 83: np.float64(0.028790325911446615), 79: np.float64(0.028790325911446615), 70: np.float64(0.028790325911446615), 0: np.float64(0.028790325911446615)}
err dic= {1: np.float64(0.21069761910959517), 3: np.float64(0.05629992643962317), 9: np.float64(0.1331588491950054), 83: np.float64(0.023209674088553383), 79: np.float64(0.03920967408855339), 70: np.float64(0.052209674088553384), 0: np.float64(0.019209674088553386)} 

err list= [np.float64(0.21069761910959517), np.float64(0.05629992643962317), np.float64(0.1331588491950054), np.float64(0.023209674088553383), np.float64(0.03920967408855339), np.float64(0.052209674088553384), np.float64(0.019209674088553386)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.673539698768061), 3: np.float64(0.2900652589389458), 9: np.float64(0.031045104663427865), 83: np.float64(0.0013374844073919113), 79: np.float64(0.0013374844073919113), 70: np.float64(0.0013374844073919113), 0: np.float64(0.0013374844073919113)}
err dic= {1: np.float64(0.40853969876806095), 3: np.float64(0.0390652589389458), 9: np.float64(0.20395489533657213), 83: np.float64(0.050662515592608086), 79: np.float64(0.0666625155926081), 70: np.float64(0.07966251559260809), 0: np.float64(0.04666251559260809)} 

err list= [np.float64(0.40853969876806095), np.float64(0.0390652589389458), np.float64(0.20395489533657213), np.float64(0.050662515592608086), np.float64(0.0666625155926081), np.float64(0.07966251559260809), np.float64(0.04666251559260809)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7738548676349581), 3: np.float64(0.2190860395252217), 9: np.float64(0.006709117637521924), 83: np.float64(8.749380057544414e-05), 79: np.float64(8.749380057544414e-05), 70: np.float64(8.749380057544414e-05), 0: np.float64(8.749380057544414e-05)}
err dic= {1: np.float64(0.5088548676349581), 3: np.float64(0.03191396047477829), 9: np.float64(0.22829088236247808), 83: np.float64(0.05191250619942455), 79: np.float64(0.06791250619942456), 70: np.float64(0.08091250619942456), 0: np.float64(0.047912506199424554)} 

err list= [np.float64(0.5088548676349581), np.float64(0.03191396047477829), np.float64(0.22829088236247808), np.float64(0.05191250619942455), np.float64(0.06791250619942456), np.float64(0.08091250619942456), np.float64(0.047912506199424554)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.843098563181478), 3: np.float64(0.1555656210258959), 9: np.float64(0.0013088641973493101), 83: np.float64(6.7378988188944906e-06), 79: np.float64(6.7378988188944906e-06), 70: np.float64(6.7378988188944906e-06), 0: np.float64(6.7378988188944906e-06)}
err dic= {1: np.float64(0.578098563181478), 3: np.float64(0.09543437897410409), 9: np.float64(0.2336911358026507), 83: np.float64(0.051993262101181104), 79: np.float64(0.0679932621011811), 70: np.float64(0.0809932621011811), 0: np.float64(0.04799326210118111)} 

err list= [np.float64(0.578098563181478), np.float64(0.09543437897410409), np.float64(0.2336911358026507), np.float64(0.051993262101181104), np.float64(0.0679932621011811), np.float64(0.0809932621011811), np.float64(0.04799326210118111)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931949751437355), 3: np.float64(0.1065579073294059), 9: np.float64(0.00024500980683408286), 83: np.float64(5.269300059430474e-07), 79: np.float64(5.269300059430474e-07), 70: np.float64(5.269300059430474e-07), 0: np.float64(5.269300059430474e-07)}
err dic= {1: np.float64(0.6281949751437355), 3: np.float64(0.1444420926705941), 9: np.float64(0.2347549901931659), 83: np.float64(0.05199947306999406), 79: np.float64(0.06799947306999406), 70: np.float64(0.08099947306999405), 0: np.float64(0.04799947306999406)} 

err list= [np.float64(0.6281949751437355), np.float64(0.1444420926705941), np.float64(0.2347549901931659), np.float64(0.05199947306999406), np.float64(0.06799947306999406), np.float64(0.08099947306999405), np.float64(0.04799947306999406)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288705810483676), 3: np.float64(0.0710842991257393), 9: np.float64(4.4956024471409485e-05), 83: np.float64(4.095035525562282e-08), 79: np.float64(4.095035525562282e-08), 70: np.float64(4.095035525562282e-08), 0: np.float64(4.095035525562282e-08)}
err dic= {1: np.float64(0.6638705810483676), 3: np.float64(0.1799157008742607), 9: np.float64(0.23495504397552858), 83: np.float64(0.051999959049644745), 79: np.float64(0.06799995904964475), 70: np.float64(0.08099995904964474), 0: np.float64(0.04799995904964475)} 

err list= [np.float64(0.6638705810483676), np.float64(0.1799157008742607), np.float64(0.23495504397552858), np.float64(0.051999959049644745), np.float64(0.06799995904964475), np.float64(0.08099995904964474), np.float64(0.04799995904964475)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535429127880359), 3: np.float64(0.046448924553415455), 9: np.float64(8.149778810038127e-06), 83: np.float64(3.2199346853700018e-09), 79: np.float64(3.2199346853700018e-09), 70: np.float64(3.2199346853700018e-09), 0: np.float64(3.2199346853700018e-09)}
err dic= {1: np.float64(0.6885429127880359), 3: np.float64(0.20455107544658455), 9: np.float64(0.23499185022118996), 83: np.float64(0.05199999678006531), 79: np.float64(0.06799999678006532), 70: np.float64(0.08099999678006532), 0: np.float64(0.047999996780065314)} 

err list= [np.float64(0.6885429127880359), np.float64(0.20455107544658455), np.float64(0.23499185022118996), np.float64(0.05199999678006531), np.float64(0.06799999678006532), np.float64(0.08099999678006532), np.float64(0.047999996780065314)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386578021916), 3: np.float64(0.029859876526105816), 9: np.float64(1.464632883115243e-06), 83: np.float64(2.5970514183111115e-10), 79: np.float64(2.5970514183111115e-10), 70: np.float64(2.5970514183111115e-10), 0: np.float64(2.5970514183111115e-10)}
err dic= {1: np.float64(0.7051386578021915), 3: np.float64(0.2211401234738942), 9: np.float64(0.23499853536711687), 83: np.float64(0.05199999974029486), 79: np.float64(0.06799999974029486), 70: np.float64(0.08099999974029486), 0: np.float64(0.04799999974029486)} 

err list= [np.float64(0.7051386578021915), np.float64(0.2211401234738942), np.float64(0.23499853536711687), np.float64(0.05199999974029486), np.float64(0.06799999974029486), np.float64(0.08099999974029486), np.float64(0.04799999974029486)]
results for assortment [1, 3, 9, 83, 79, 70] :

err MNL dic= {1: 0.265, 3: 0.251, 9: 0.235, 83: 0.052, 79: 0.068, 70: 0.081, 0: np.float64(0.21829740093736688)} 

err MNL list= [0.265, 0.251, 0.235, 0.052, 0.068, 0.081, np.float64(0.21829740093736688)]
sampled assortment [1, 4, 8, 32, 27, 82] number: 3
#  Learning probs for MM model, A = [1, 4, 8, 32, 27, 82]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [1, 4, 8, 32, 27, 82]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 100]
empirical probabilities from test set: {1: 0.222, 4: 0.23, 8: 0.232, 32: 0.102, 27: 0.12, 82: 0.05, 0: 0.044}
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.10340137935132498), 4: np.float64(0.09619791656336497), 8: np.float64(0.08738015068061283), 32: np.float64(0.1782551383511741), 27: np.float64(0.1782551383511741), 82: np.float64(0.1782551383511741), 0: np.float64(0.1782551383511741)}
err dic= {1: np.float64(0.11859862064867502), 4: np.float64(0.13380208343663502), 8: np.float64(0.14461984931938718), 32: np.float64(0.0762551383511741), 27: np.float64(0.0582551383511741), 82: np.float64(0.12825513835117408), 0: np.float64(0.13425513835117409)} 

err list= [np.float64(0.11859862064867502), np.float64(0.13380208343663502), np.float64(0.14461984931938718), np.float64(0.0762551383511741), np.float64(0.0582551383511741), np.float64(0.12825513835117408), np.float64(0.13425513835117409)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1370401403346179), 4: np.float64(0.11880175361630323), 8: np.float64(0.09816604180677119), 32: np.float64(0.16149801606057654), 27: np.float64(0.16149801606057654), 82: np.float64(0.16149801606057654), 0: np.float64(0.16149801606057654)}
err dic= {1: np.float64(0.08495985966538211), 4: np.float64(0.11119824638369678), 8: np.float64(0.13383395819322882), 32: np.float64(0.059498016060576545), 27: np.float64(0.04149801606057654), 82: np.float64(0.11149801606057654), 0: np.float64(0.11749801606057654)} 

err list= [np.float64(0.08495985966538211), np.float64(0.11119824638369678), np.float64(0.13383395819322882), np.float64(0.059498016060576545), np.float64(0.04149801606057654), np.float64(0.11149801606057654), np.float64(0.11749801606057654)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.22207877659738354), 4: np.float64(0.16825021982391797), 8: np.float64(0.11563554260611286), 32: np.float64(0.12350886524314804), 27: np.float64(0.12350886524314804), 82: np.float64(0.12350886524314804), 0: np.float64(0.12350886524314804)}
err dic= {1: np.float64(7.877659738353415e-05), 4: np.float64(0.06174978017608204), 8: np.float64(0.11636445739388715), 32: np.float64(0.021508865243148045), 27: np.float64(0.0035088652431480433), 82: np.float64(0.07350886524314804), 0: np.float64(0.07950886524314804)} 

err list= [np.float64(7.877659738353415e-05), np.float64(0.06174978017608204), np.float64(0.11636445739388715), np.float64(0.021508865243148045), np.float64(0.0035088652431480433), np.float64(0.07350886524314804), np.float64(0.07950886524314804)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.4974726024113874), 4: np.float64(0.2651549873182382), 8: np.float64(0.10804100149441412), 32: np.float64(0.032332852193990055), 27: np.float64(0.032332852193990055), 82: np.float64(0.032332852193990055), 0: np.float64(0.032332852193990055)}
err dic= {1: np.float64(0.2754726024113874), 4: np.float64(0.03515498731823821), 8: np.float64(0.1239589985055859), 32: np.float64(0.06966714780600994), 27: np.float64(0.08766714780600994), 82: np.float64(0.017667147806009947), 0: np.float64(0.011667147806009942)} 

err list= [np.float64(0.2754726024113874), np.float64(0.03515498731823821), np.float64(0.1239589985055859), np.float64(0.06966714780600994), np.float64(0.08766714780600994), np.float64(0.017667147806009947), np.float64(0.011667147806009942)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7340402264736903), 4: np.float64(0.2227388385936477), 8: np.float64(0.0364732920990004), 32: np.float64(0.0016869107084157146), 27: np.float64(0.0016869107084157146), 82: np.float64(0.0016869107084157146), 0: np.float64(0.0016869107084157146)}
err dic= {1: np.float64(0.5120402264736903), 4: np.float64(0.007261161406352301), 8: np.float64(0.1955267079009996), 32: np.float64(0.10031308929158428), 27: np.float64(0.11831308929158428), 82: np.float64(0.04831308929158429), 0: np.float64(0.04231308929158428)} 

err list= [np.float64(0.5120402264736903), np.float64(0.007261161406352301), np.float64(0.1955267079009996), np.float64(0.10031308929158428), np.float64(0.11831308929158428), np.float64(0.04831308929158429), np.float64(0.04231308929158428)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8491442217179457), 4: np.float64(0.14186264079054595), 8: np.float64(0.0085390681933922), 32: np.float64(0.00011351732453010471), 27: np.float64(0.00011351732453010471), 82: np.float64(0.00011351732453010471), 0: np.float64(0.00011351732453010471)}
err dic= {1: np.float64(0.6271442217179457), 4: np.float64(0.08813735920945406), 8: np.float64(0.2234609318066078), 32: np.float64(0.10188648267546989), 27: np.float64(0.11988648267546989), 82: np.float64(0.0498864826754699), 0: np.float64(0.04388648267546989)} 

err list= [np.float64(0.6271442217179457), np.float64(0.08813735920945406), np.float64(0.2234609318066078), np.float64(0.10188648267546989), np.float64(0.11988648267546989), np.float64(0.0498864826754699), np.float64(0.04388648267546989)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159409730851582), 4: np.float64(0.08225738907281689), 8: np.float64(0.001765127692123992), 32: np.float64(9.127537475203945e-06), 27: np.float64(9.127537475203945e-06), 82: np.float64(9.127537475203945e-06), 0: np.float64(9.127537475203945e-06)}
err dic= {1: np.float64(0.6939409730851582), 4: np.float64(0.1477426109271831), 8: np.float64(0.230234872307876), 32: np.float64(0.10199087246252479), 27: np.float64(0.1199908724625248), 82: np.float64(0.0499908724625248), 0: np.float64(0.0439908724625248)} 

err list= [np.float64(0.6939409730851582), np.float64(0.1477426109271831), np.float64(0.230234872307876), np.float64(0.10199087246252479), np.float64(0.1199908724625248), np.float64(0.0499908724625248), np.float64(0.0439908724625248)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545785785003981), 4: np.float64(0.045074906216071464), 8: np.float64(0.0003435558729960172), 32: np.float64(7.398526334401674e-07), 27: np.float64(7.398526334401674e-07), 82: np.float64(7.398526334401674e-07), 0: np.float64(7.398526334401674e-07)}
err dic= {1: np.float64(0.7325785785003981), 4: np.float64(0.18492509378392855), 8: np.float64(0.231656444127004), 32: np.float64(0.10199926014736656), 27: np.float64(0.11999926014736656), 82: np.float64(0.04999926014736656), 0: np.float64(0.043999260147366555)} 

err list= [np.float64(0.7325785785003981), np.float64(0.18492509378392855), np.float64(0.231656444127004), np.float64(0.10199926014736656), np.float64(0.11999926014736656), np.float64(0.04999926014736656), np.float64(0.043999260147366555)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9761793657807561), 4: np.float64(0.023755755608799407), 8: np.float64(6.464297621849226e-05), 32: np.float64(5.8908556330388165e-08), 27: np.float64(5.8908556330388165e-08), 82: np.float64(5.8908556330388165e-08), 0: np.float64(5.8908556330388165e-08)}
err dic= {1: np.float64(0.7541793657807562), 4: np.float64(0.2062442443912006), 8: np.float64(0.2319353570237815), 32: np.float64(0.10199994109144367), 27: np.float64(0.11999994109144367), 82: np.float64(0.04999994109144367), 0: np.float64(0.043999941091443666)} 

err list= [np.float64(0.7541793657807562), np.float64(0.2062442443912006), np.float64(0.2319353570237815), np.float64(0.10199994109144367), np.float64(0.11999994109144367), np.float64(0.04999994109144367), np.float64(0.043999941091443666)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141516038864), 4: np.float64(0.012173922990355322), 8: np.float64(1.1906586229307759e-05), 32: np.float64(4.704882523044306e-09), 27: np.float64(4.704882523044306e-09), 82: np.float64(4.704882523044306e-09), 0: np.float64(4.704882523044306e-09)}
err dic= {1: np.float64(0.7658141516038864), 4: np.float64(0.21782607700964468), 8: np.float64(0.2319880934137707), 32: np.float64(0.10199999529511747), 27: np.float64(0.11999999529511747), 82: np.float64(0.04999999529511748), 0: np.float64(0.04399999529511747)} 

err list= [np.float64(0.7658141516038864), np.float64(0.21782607700964468), np.float64(0.2319880934137707), np.float64(0.10199999529511747), np.float64(0.11999999529511747), np.float64(0.04999999529511748), np.float64(0.04399999529511747)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855148490313), 4: np.float64(0.006112322366114925), 8: np.float64(2.1612518760247726e-06), 32: np.float64(3.8324467868305223e-10), 27: np.float64(3.8324467868305223e-10), 82: np.float64(3.8324467868305223e-10), 0: np.float64(3.8324467868305223e-10)}
err dic= {1: np.float64(0.7718855148490313), 4: np.float64(0.2238876776338851), 8: np.float64(0.231997838748124), 32: np.float64(0.10199999961675532), 27: np.float64(0.11999999961675532), 82: np.float64(0.049999999616755324), 0: np.float64(0.04399999961675532)} 

err list= [np.float64(0.7718855148490313), np.float64(0.2238876776338851), np.float64(0.231997838748124), np.float64(0.10199999961675532), np.float64(0.11999999961675532), np.float64(0.049999999616755324), np.float64(0.04399999961675532)]
results for assortment [1, 4, 8, 32, 27, 82] :

err MNL dic= {1: 0.222, 4: 0.23, 8: 0.232, 32: 0.102, 27: 0.12, 82: 0.05, 0: np.float64(0.21605096999011808)} 

err MNL list= [0.222, 0.23, 0.232, 0.102, 0.12, 0.05, np.float64(0.21605096999011808)]
sampled assortment [9, 4, 6, 51, 82, 41] number: 4
#  Learning probs for MM model, A = [9, 4, 6, 51, 82, 41]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
#  Learning probs for MM model, A = [9, 4, 6, 51, 82, 41]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 10, 100]
empirical probabilities from test set: {9: 0.221, 4: 0.245, 6: 0.256, 51: 0.086, 82: 0.04, 41: 0.093, 0: 0.059}
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.025 

learned probs for this beta: {9: np.float64(0.16541157482063307), 4: np.float64(0.08858222570750142), 6: np.float64(0.08435990018933383), 51: np.float64(0.16541157482063307), 82: np.float64(0.16541157482063307), 41: np.float64(0.16541157482063307), 0: np.float64(0.16541157482063307)}
err dic= {9: np.float64(0.055588425179366935), 4: np.float64(0.1564177742924986), 6: np.float64(0.1716400998106662), 51: np.float64(0.07941157482063307), 82: np.float64(0.12541157482063306), 41: np.float64(0.07241157482063307), 0: np.float64(0.10641157482063307)} 

err list= [np.float64(0.055588425179366935), np.float64(0.1564177742924986), np.float64(0.1716400998106662), np.float64(0.07941157482063307), np.float64(0.12541157482063306), np.float64(0.07241157482063307), np.float64(0.10641157482063307)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.15817551303234323), 4: np.float64(0.10963967937316557), 6: np.float64(0.09948275546512098), 51: np.float64(0.15817551303234323), 82: np.float64(0.15817551303234323), 41: np.float64(0.15817551303234323), 0: np.float64(0.15817551303234323)}
err dic= {9: np.float64(0.06282448696765677), 4: np.float64(0.13536032062683442), 6: np.float64(0.15651724453487903), 51: np.float64(0.07217551303234324), 82: np.float64(0.11817551303234322), 41: np.float64(0.06517551303234323), 0: np.float64(0.09917551303234323)} 

err list= [np.float64(0.06282448696765677), np.float64(0.13536032062683442), np.float64(0.15651724453487903), np.float64(0.07217551303234324), np.float64(0.11817551303234322), np.float64(0.06517551303234323), np.float64(0.09917551303234323)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.14119569307353097), 4: np.float64(0.16109721060687018), 6: np.float64(0.13292432402547782), 51: np.float64(0.14119569307353097), 82: np.float64(0.14119569307353097), 41: np.float64(0.14119569307353097), 0: np.float64(0.14119569307353097)}
err dic= {9: np.float64(0.07980430692646903), 4: np.float64(0.08390278939312981), 6: np.float64(0.12307567597452218), 51: np.float64(0.05519569307353098), 82: np.float64(0.10119569307353096), 41: np.float64(0.04819569307353097), 0: np.float64(0.08219569307353097)} 

err list= [np.float64(0.07980430692646903), np.float64(0.08390278939312981), np.float64(0.12307567597452218), np.float64(0.05519569307353098), np.float64(0.10119569307353096), np.float64(0.04819569307353097), np.float64(0.08219569307353097)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.08437744398831544), 4: np.float64(0.35446173537314124), 6: np.float64(0.22365104468528255), 51: np.float64(0.08437744398831544), 82: np.float64(0.08437744398831544), 41: np.float64(0.08437744398831544), 0: np.float64(0.08437744398831544)}
err dic= {9: np.float64(0.13662255601168455), 4: np.float64(0.10946173537314124), 6: np.float64(0.03234895531471746), 51: np.float64(0.0016225560116845533), 82: np.float64(0.04437744398831544), 41: np.float64(0.00862255601168456), 0: np.float64(0.025377443988315443)} 

err list= [np.float64(0.13662255601168455), np.float64(0.10946173537314124), np.float64(0.03234895531471746), np.float64(0.0016225560116845533), np.float64(0.04437744398831544), np.float64(0.00862255601168456), np.float64(0.025377443988315443)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.022002263620521666), 4: np.float64(0.6262465284013016), 6: np.float64(0.26374215349609076), 51: np.float64(0.022002263620521666), 82: np.float64(0.022002263620521666), 41: np.float64(0.022002263620521666), 0: np.float64(0.022002263620521666)}
err dic= {9: np.float64(0.19899773637947835), 4: np.float64(0.3812465284013016), 6: np.float64(0.007742153496090753), 51: np.float64(0.06399773637947832), 82: np.float64(0.017997736379478334), 41: np.float64(0.07099773637947833), 0: np.float64(0.03699773637947833)} 

err list= [np.float64(0.19899773637947835), np.float64(0.3812465284013016), np.float64(0.007742153496090753), np.float64(0.06399773637947832), np.float64(0.017997736379478334), np.float64(0.07099773637947833), np.float64(0.03699773637947833)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.003538560400372996), 4: np.float64(0.7664926134938979), 6: np.float64(0.21581458450423882), 51: np.float64(0.003538560400372996), 82: np.float64(0.003538560400372996), 41: np.float64(0.003538560400372996), 0: np.float64(0.003538560400372996)}
err dic= {9: np.float64(0.217461439599627), 4: np.float64(0.5214926134938979), 6: np.float64(0.040185415495761184), 51: np.float64(0.082461439599627), 82: np.float64(0.036461439599627006), 41: np.float64(0.089461439599627), 0: np.float64(0.055461439599627)} 

err list= [np.float64(0.217461439599627), np.float64(0.5214926134938979), np.float64(0.040185415495761184), np.float64(0.082461439599627), np.float64(0.036461439599627006), np.float64(0.089461439599627), np.float64(0.055461439599627)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(0.0005242450455396777), 4: np.float64(0.8421292307743731), 6: np.float64(0.15524954399792848), 51: np.float64(0.0005242450455396777), 82: np.float64(0.0005242450455396777), 41: np.float64(0.0005242450455396777), 0: np.float64(0.0005242450455396777)}
err dic= {9: np.float64(0.2204757549544603), 4: np.float64(0.5971292307743731), 6: np.float64(0.10075045600207153), 51: np.float64(0.08547575495446032), 82: np.float64(0.039475754954460325), 41: np.float64(0.09247575495446032), 0: np.float64(0.05847575495446032)} 

err list= [np.float64(0.2204757549544603), np.float64(0.5971292307743731), np.float64(0.10075045600207153), np.float64(0.08547575495446032), np.float64(0.039475754954460325), np.float64(0.09247575495446032), np.float64(0.05847575495446032)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(8.92200620865743e-05), 4: np.float64(0.8930321175657444), 6: np.float64(0.10652178212382309), 51: np.float64(8.92200620865743e-05), 82: np.float64(8.92200620865743e-05), 41: np.float64(8.92200620865743e-05), 0: np.float64(8.92200620865743e-05)}
err dic= {9: np.float64(0.22091077993791342), 4: np.float64(0.6480321175657444), 6: np.float64(0.14947821787617693), 51: np.float64(0.08591077993791342), 82: np.float64(0.03991077993791343), 41: np.float64(0.09291077993791343), 0: np.float64(0.058910779937913424)} 

err list= [np.float64(0.22091077993791342), np.float64(0.6480321175657444), np.float64(0.14947821787617693), np.float64(0.08591077993791342), np.float64(0.03991077993791343), np.float64(0.09291077993791343), np.float64(0.058910779937913424)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(1.7124658977227113e-05), 4: np.float64(0.9288354341623046), 6: np.float64(0.07107894254280953), 51: np.float64(1.7124658977227113e-05), 82: np.float64(1.7124658977227113e-05), 41: np.float64(1.7124658977227113e-05), 0: np.float64(1.7124658977227113e-05)}
err dic= {9: np.float64(0.2209828753410228), 4: np.float64(0.6838354341623046), 6: np.float64(0.18492105745719048), 51: np.float64(0.08598287534102277), 82: np.float64(0.039982875341022774), 41: np.float64(0.09298287534102277), 0: np.float64(0.05898287534102277)} 

err list= [np.float64(0.2209828753410228), np.float64(0.6838354341623046), np.float64(0.18492105745719048), np.float64(0.08598287534102277), np.float64(0.039982875341022774), np.float64(0.09298287534102277), np.float64(0.05898287534102277)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(3.534121176989124e-06), 4: np.float64(0.9535343425598322), 6: np.float64(0.046447986834283805), 51: np.float64(3.534121176989124e-06), 82: np.float64(3.534121176989124e-06), 41: np.float64(3.534121176989124e-06), 0: np.float64(3.534121176989124e-06)}
err dic= {9: np.float64(0.22099646587882302), 4: np.float64(0.7085343425598322), 6: np.float64(0.2095520131657162), 51: np.float64(0.08599646587882301), 82: np.float64(0.03999646587882301), 41: np.float64(0.09299646587882301), 0: np.float64(0.058996465878823005)} 

err list= [np.float64(0.22099646587882302), np.float64(0.7085343425598322), np.float64(0.2095520131657162), np.float64(0.08599646587882301), np.float64(0.03999646587882301), np.float64(0.09299646587882301), np.float64(0.058996465878823005)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(7.655742544535382e-07), 4: np.float64(0.9701364723476107), 6: np.float64(0.02985969978111657), 51: np.float64(7.655742544535382e-07), 82: np.float64(7.655742544535382e-07), 41: np.float64(7.655742544535382e-07), 0: np.float64(7.655742544535382e-07)}
err dic= {9: np.float64(0.22099923442574554), 4: np.float64(0.7251364723476107), 6: np.float64(0.22614030021888343), 51: np.float64(0.08599923442574554), 82: np.float64(0.039999234425745545), 41: np.float64(0.09299923442574555), 0: np.float64(0.05899923442574554)} 

err list= [np.float64(0.22099923442574554), np.float64(0.7251364723476107), np.float64(0.22614030021888343), np.float64(0.08599923442574554), np.float64(0.039999234425745545), np.float64(0.09299923442574555), np.float64(0.05899923442574554)]
results for assortment [9, 4, 6, 51, 82, 41] :

err MNL dic= {9: 0.221, 4: 0.245, 6: 0.256, 51: 0.086, 82: 0.04, 41: 0.093, 0: np.float64(0.20371542664985287)} 

err MNL list= [0.221, 0.245, 0.256, 0.086, 0.04, 0.093, np.float64(0.20371542664985287)]
sampled assortment [5, 9, 6, 39, 80, 68] number: 5
#  Learning probs for MM model, A = [5, 9, 6, 39, 80, 68]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 100]
#  Learning probs for MM model, A = [5, 9, 6, 39, 80, 68]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 11: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100]
empirical probabilities from test set: {5: 0.245, 9: 0.228, 6: 0.258, 39: 0.1, 80: 0.063, 68: 0.056, 0: 0.05}
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.025 

learned probs for this beta: {5: np.float64(0.11198718115379011), 9: np.float64(0.10164497170043355), 6: np.float64(0.10922220779940381), 39: np.float64(0.16928640983658705), 80: np.float64(0.16928640983658705), 68: np.float64(0.16928640983658705), 0: np.float64(0.16928640983658705)}
err dic= {5: np.float64(0.13301281884620988), 9: np.float64(0.12635502829956646), 6: np.float64(0.1487777922005962), 39: np.float64(0.06928640983658704), 80: np.float64(0.10628640983658705), 68: np.float64(0.11328640983658705), 0: np.float64(0.11928640983658705)} 

err list= [np.float64(0.13301281884620988), np.float64(0.12635502829956646), np.float64(0.1487777922005962), np.float64(0.06928640983658704), np.float64(0.10628640983658705), np.float64(0.11328640983658705), np.float64(0.11928640983658705)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.14150872146289253), 9: np.float64(0.11672236371228117), 6: np.float64(0.13460725967897919), 39: np.float64(0.15179041378646727), 80: np.float64(0.15179041378646727), 68: np.float64(0.15179041378646727), 0: np.float64(0.15179041378646727)}
err dic= {5: np.float64(0.10349127853710746), 9: np.float64(0.11127763628771883), 6: np.float64(0.12339274032102082), 39: np.float64(0.05179041378646726), 80: np.float64(0.08879041378646726), 68: np.float64(0.09579041378646727), 0: np.float64(0.10179041378646726)} 

err list= [np.float64(0.10349127853710746), np.float64(0.11127763628771883), np.float64(0.12339274032102082), np.float64(0.05179041378646726), np.float64(0.08879041378646726), np.float64(0.09579041378646727), np.float64(0.10179041378646726)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.20788351543212394), 9: np.float64(0.142176428195937), 6: np.float64(0.18810078335584177), 39: np.float64(0.11545981825402411), 80: np.float64(0.11545981825402411), 68: np.float64(0.11545981825402411), 0: np.float64(0.11545981825402411)}
err dic= {5: np.float64(0.03711648456787606), 9: np.float64(0.085823571804063), 6: np.float64(0.06989921664415824), 39: np.float64(0.015459818254024107), 80: np.float64(0.05245981825402411), 68: np.float64(0.05945981825402411), 0: np.float64(0.06545981825402411)} 

err list= [np.float64(0.03711648456787606), np.float64(0.085823571804063), np.float64(0.06989921664415824), np.float64(0.015459818254024107), np.float64(0.05245981825402411), np.float64(0.05945981825402411), np.float64(0.06545981825402411)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.39224610120664194), 9: np.float64(0.15644878539043544), 6: np.float64(0.30548157077643806), 39: np.float64(0.03645588565661738), 80: np.float64(0.03645588565661738), 68: np.float64(0.03645588565661738), 0: np.float64(0.03645588565661738)}
err dic= {5: np.float64(0.14724610120664194), 9: np.float64(0.07155121460956457), 6: np.float64(0.04748157077643805), 39: np.float64(0.06354411434338263), 80: np.float64(0.02654411434338262), 68: np.float64(0.019544114343382622), 0: np.float64(0.013544114343382624)} 

err list= [np.float64(0.14724610120664194), np.float64(0.07155121460956457), np.float64(0.04748157077643805), np.float64(0.06354411434338263), np.float64(0.02654411434338262), np.float64(0.019544114343382622), np.float64(0.013544114343382624)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5593742014417122), 9: np.float64(0.0902199191535733), 6: np.float64(0.3392776034266687), 39: np.float64(0.0027820689945063292), 80: np.float64(0.0027820689945063292), 68: np.float64(0.0027820689945063292), 0: np.float64(0.0027820689945063292)}
err dic= {5: np.float64(0.31437420144171224), 9: np.float64(0.1377800808464267), 6: np.float64(0.08127760342666868), 39: np.float64(0.09721793100549368), 80: np.float64(0.06021793100549367), 68: np.float64(0.05321793100549367), 0: np.float64(0.04721793100549367)} 

err list= [np.float64(0.31437420144171224), np.float64(0.1377800808464267), np.float64(0.08127760342666868), np.float64(0.09721793100549368), np.float64(0.06021793100549367), np.float64(0.05321793100549367), np.float64(0.04721793100549367)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6512041668665741), 9: np.float64(0.04012269388744294), 6: np.float64(0.30760706743334726), 39: np.float64(0.00026651795316049766), 80: np.float64(0.00026651795316049766), 68: np.float64(0.00026651795316049766), 0: np.float64(0.00026651795316049766)}
err dic= {5: np.float64(0.4062041668665741), 9: np.float64(0.18787730611255707), 6: np.float64(0.04960706743334725), 39: np.float64(0.0997334820468395), 80: np.float64(0.0627334820468395), 68: np.float64(0.055733482046839505), 0: np.float64(0.04973348204683951)} 

err list= [np.float64(0.4062041668665741), np.float64(0.18787730611255707), np.float64(0.04960706743334725), np.float64(0.0997334820468395), np.float64(0.0627334820468395), np.float64(0.055733482046839505), np.float64(0.04973348204683951)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7190080644766125), 9: np.float64(0.016354029146808047), 6: np.float64(0.2645082849574157), 39: np.float64(3.240535479333492e-05), 80: np.float64(3.240535479333492e-05), 68: np.float64(3.240535479333492e-05), 0: np.float64(3.240535479333492e-05)}
err dic= {5: np.float64(0.4740080644766125), 9: np.float64(0.21164597085319195), 6: np.float64(0.006508284957415678), 39: np.float64(0.09996759464520667), 80: np.float64(0.06296759464520667), 68: np.float64(0.05596759464520667), 0: np.float64(0.04996759464520667)} 

err list= [np.float64(0.4740080644766125), np.float64(0.21164597085319195), np.float64(0.006508284957415678), np.float64(0.09996759464520667), np.float64(0.06296759464520667), np.float64(0.05596759464520667), np.float64(0.04996759464520667)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723444542853904), 9: np.float64(0.006358934714384541), 6: np.float64(0.22128039098112992), 39: np.float64(4.055004774434907e-06), 80: np.float64(4.055004774434907e-06), 68: np.float64(4.055004774434907e-06), 0: np.float64(4.055004774434907e-06)}
err dic= {5: np.float64(0.5273444542853905), 9: np.float64(0.22164106528561547), 6: np.float64(0.036719609018870086), 39: np.float64(0.09999594499522557), 80: np.float64(0.06299594499522557), 68: np.float64(0.05599594499522557), 0: np.float64(0.04999594499522557)} 

err list= [np.float64(0.5273444542853905), np.float64(0.22164106528561547), np.float64(0.036719609018870086), np.float64(0.09999594499522557), np.float64(0.06299594499522557), np.float64(0.05599594499522557), np.float64(0.04999594499522557)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.8156040797099404), 9: np.float64(0.0024080324860731163), 6: np.float64(0.18198586892339177), 39: np.float64(5.047201495283916e-07), 80: np.float64(5.047201495283916e-07), 68: np.float64(5.047201495283916e-07), 0: np.float64(5.047201495283916e-07)}
err dic= {5: np.float64(0.5706040797099404), 9: np.float64(0.2255919675139269), 6: np.float64(0.07601413107660823), 39: np.float64(0.09999949527985048), 80: np.float64(0.06299949527985048), 68: np.float64(0.05599949527985047), 0: np.float64(0.049999495279850474)} 

err list= [np.float64(0.5706040797099404), np.float64(0.2255919675139269), np.float64(0.07601413107660823), np.float64(0.09999949527985048), np.float64(0.06299949527985048), np.float64(0.05599949527985047), np.float64(0.049999495279850474)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511866857503095), 9: np.float64(0.0008989927615727657), 6: np.float64(0.1479140669953463), 39: np.float64(6.362319256625755e-08), 80: np.float64(6.362319256625755e-08), 68: np.float64(6.362319256625755e-08), 0: np.float64(6.362319256625755e-08)}
err dic= {5: np.float64(0.6061866857503095), 9: np.float64(0.22710100723842724), 6: np.float64(0.11008593300465372), 39: np.float64(0.09999993637680744), 80: np.float64(0.06299993637680744), 68: np.float64(0.05599993637680743), 0: np.float64(0.049999936376807434)} 

err list= [np.float64(0.6061866857503095), np.float64(0.22710100723842724), np.float64(0.11008593300465372), np.float64(0.09999993637680744), np.float64(0.06299993637680744), np.float64(0.05599993637680743), np.float64(0.049999936376807434)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036116021892), 9: np.float64(0.0003331497295971272), 6: np.float64(0.11916320566704278), 39: np.float64(8.250292498250814e-09), 80: np.float64(8.250292498250814e-09), 68: np.float64(8.250292498250814e-09), 0: np.float64(8.250292498250814e-09)}
err dic= {5: np.float64(0.6355036116021892), 9: np.float64(0.22766685027040287), 6: np.float64(0.13883679433295723), 39: np.float64(0.0999999917497075), 80: np.float64(0.0629999917497075), 68: np.float64(0.0559999917497075), 0: np.float64(0.049999991749707505)} 

err list= [np.float64(0.6355036116021892), np.float64(0.22766685027040287), np.float64(0.13883679433295723), np.float64(0.0999999917497075), np.float64(0.0629999917497075), np.float64(0.0559999917497075), np.float64(0.049999991749707505)]
results for assortment [5, 9, 6, 39, 80, 68] :

err MNL dic= {5: 0.245, 9: 0.228, 6: 0.258, 39: 0.1, 80: 0.063, 68: 0.056, 0: np.float64(0.2117252931323283)} 

err MNL list= [0.245, 0.228, 0.258, 0.1, 0.063, 0.056, np.float64(0.2117252931323283)]
sampled assortment [6, 3, 8, 15, 78, 97] number: 6
#  Learning probs for MM model, A = [6, 3, 8, 15, 78, 97]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [6, 3, 8, 15, 78, 97]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
empirical probabilities from test set: {6: 0.221, 3: 0.235, 8: 0.238, 15: 0.173, 78: 0.056, 97: 0.039, 0: 0.038}
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.025 

learned probs for this beta: {6: np.float64(0.09225334132729197), 3: np.float64(0.09917341137021193), 8: np.float64(0.087864662932401), 15: np.float64(0.18017714609252372), 78: np.float64(0.18017714609252372), 97: np.float64(0.18017714609252372), 0: np.float64(0.18017714609252372)}
err dic= {6: np.float64(0.12874665867270801), 3: np.float64(0.13582658862978805), 8: np.float64(0.150135337067599), 15: np.float64(0.007177146092523734), 78: np.float64(0.12417714609252373), 97: np.float64(0.14117714609252371), 0: np.float64(0.14217714609252372)} 

err list= [np.float64(0.12874665867270801), np.float64(0.13582658862978805), np.float64(0.150135337067599), np.float64(0.007177146092523734), np.float64(0.12417714609252373), np.float64(0.14117714609252371), np.float64(0.14217714609252372)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.10971296780144872), 3: np.float64(0.12663053423057208), 8: np.float64(0.09956485661617964), 15: np.float64(0.16602291033794964), 78: np.float64(0.16602291033794964), 97: np.float64(0.16602291033794964), 0: np.float64(0.16602291033794964)}
err dic= {6: np.float64(0.11128703219855128), 3: np.float64(0.10836946576942791), 8: np.float64(0.13843514338382035), 15: np.float64(0.006977089662050351), 78: np.float64(0.11002291033794964), 97: np.float64(0.12702291033794963), 0: np.float64(0.12802291033794963)} 

err list= [np.float64(0.11128703219855128), np.float64(0.10836946576942791), np.float64(0.13843514338382035), np.float64(0.006977089662050351), np.float64(0.11002291033794964), np.float64(0.12702291033794963), np.float64(0.12802291033794963)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.14645854343973333), 3: np.float64(0.19393585810192157), 8: np.float64(0.1208389719076546), 15: np.float64(0.13469165663767393), 78: np.float64(0.13469165663767393), 97: np.float64(0.13469165663767393), 0: np.float64(0.13469165663767393)}
err dic= {6: np.float64(0.07454145656026667), 3: np.float64(0.041064141898078416), 8: np.float64(0.1171610280923454), 15: np.float64(0.03830834336232605), 78: np.float64(0.07869165663767394), 97: np.float64(0.09569165663767393), 0: np.float64(0.09669165663767393)} 

err list= [np.float64(0.07454145656026667), np.float64(0.041064141898078416), np.float64(0.1171610280923454), np.float64(0.03830834336232605), np.float64(0.07869165663767394), np.float64(0.09569165663767393), np.float64(0.09669165663767393)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2229452702754075), 3: np.float64(0.4276067765385895), 8: np.float64(0.13949022354815235), 15: np.float64(0.05248943240946247), 78: np.float64(0.05248943240946247), 97: np.float64(0.05248943240946247), 0: np.float64(0.05248943240946247)}
err dic= {6: np.float64(0.0019452702754075013), 3: np.float64(0.19260677653858949), 8: np.float64(0.09850977645184764), 15: np.float64(0.12051056759053752), 78: np.float64(0.0035105675905375278), 97: np.float64(0.013489432409462473), 0: np.float64(0.014489432409462474)} 

err list= [np.float64(0.0019452702754075013), np.float64(0.19260677653858949), np.float64(0.09850977645184764), np.float64(0.12051056759053752), np.float64(0.0035105675905375278), np.float64(0.013489432409462473), np.float64(0.014489432409462474)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.20538575362773495), 3: np.float64(0.6916947114077909), 8: np.float64(0.08111100433093218), 15: np.float64(0.005452132658385691), 78: np.float64(0.005452132658385691), 97: np.float64(0.005452132658385691), 0: np.float64(0.005452132658385691)}
err dic= {6: np.float64(0.01561424637226505), 3: np.float64(0.45669471140779094), 8: np.float64(0.1568889956690678), 15: np.float64(0.1675478673416143), 78: np.float64(0.05054786734161431), 97: np.float64(0.03354786734161431), 0: np.float64(0.03254786734161431)} 

err list= [np.float64(0.01561424637226505), np.float64(0.45669471140779094), np.float64(0.1568889956690678), np.float64(0.1675478673416143), np.float64(0.05054786734161431), np.float64(0.03354786734161431), np.float64(0.03254786734161431)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13630270292060043), 3: np.float64(0.8285677938234203), 8: np.float64(0.033092535042139055), 15: np.float64(0.0005092420534610042), 78: np.float64(0.0005092420534610042), 97: np.float64(0.0005092420534610042), 0: np.float64(0.0005092420534610042)}
err dic= {6: np.float64(0.08469729707939957), 3: np.float64(0.5935677938234203), 8: np.float64(0.20490746495786094), 15: np.float64(0.17249075794653898), 78: np.float64(0.055490757946538995), 97: np.float64(0.03849075794653899), 0: np.float64(0.03749075794653899)} 

err list= [np.float64(0.08469729707939957), np.float64(0.5935677938234203), np.float64(0.20490746495786094), np.float64(0.17249075794653898), np.float64(0.055490757946538995), np.float64(0.03849075794653899), np.float64(0.03749075794653899)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.08062519926082087), 3: np.float64(0.9072887471059109), 8: np.float64(0.011831301530961581), 15: np.float64(6.368802557656234e-05), 78: np.float64(6.368802557656234e-05), 97: np.float64(6.368802557656234e-05), 0: np.float64(6.368802557656234e-05)}
err dic= {6: np.float64(0.14037480073917913), 3: np.float64(0.6722887471059109), 8: np.float64(0.22616869846903842), 15: np.float64(0.1729363119744234), 78: np.float64(0.05593631197442344), 97: np.float64(0.03893631197442344), 0: np.float64(0.03793631197442344)} 

err list= [np.float64(0.14037480073917913), np.float64(0.6722887471059109), np.float64(0.22616869846903842), np.float64(0.1729363119744234), np.float64(0.05593631197442344), np.float64(0.03893631197442344), np.float64(0.03793631197442344)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.044644347480318064), 3: np.float64(0.9513855267129666), 8: np.float64(0.00393571861080462), 15: np.float64(8.601798977361596e-06), 78: np.float64(8.601798977361596e-06), 97: np.float64(8.601798977361596e-06), 0: np.float64(8.601798977361596e-06)}
err dic= {6: np.float64(0.17635565251968194), 3: np.float64(0.7163855267129666), 8: np.float64(0.23406428138919538), 15: np.float64(0.17299139820102263), 78: np.float64(0.05599139820102264), 97: np.float64(0.03899139820102264), 0: np.float64(0.03799139820102264)} 

err list= [np.float64(0.17635565251968194), np.float64(0.7163855267129666), np.float64(0.23406428138919538), np.float64(0.17299139820102263), np.float64(0.05599139820102264), np.float64(0.03899139820102264), np.float64(0.03799139820102264)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023649606227284067), 3: np.float64(0.9750952807462572), 8: np.float64(0.0012505242312344594), 15: np.float64(1.1471988059677106e-06), 78: np.float64(1.1471988059677106e-06), 97: np.float64(1.1471988059677106e-06), 0: np.float64(1.1471988059677106e-06)}
err dic= {6: np.float64(0.19735039377271593), 3: np.float64(0.7400952807462572), 8: np.float64(0.23674947576876554), 15: np.float64(0.172998852801194), 78: np.float64(0.055998852801194036), 97: np.float64(0.038998852801194035), 0: np.float64(0.037998852801194034)} 

err list= [np.float64(0.19735039377271593), np.float64(0.7400952807462572), np.float64(0.23674947576876554), np.float64(0.172998852801194), np.float64(0.055998852801194036), np.float64(0.038998852801194035), np.float64(0.037998852801194034)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.012148779488230932), 3: np.float64(0.9874651252467052), 8: np.float64(0.0003854840387410057), 15: np.float64(1.5280658088162674e-07), 78: np.float64(1.5280658088162674e-07), 97: np.float64(1.5280658088162674e-07), 0: np.float64(1.5280658088162674e-07)}
err dic= {6: np.float64(0.20885122051176908), 3: np.float64(0.7524651252467052), 8: np.float64(0.237614515961259), 15: np.float64(0.1729998471934191), 78: np.float64(0.05599984719341912), 97: np.float64(0.03899984719341912), 0: np.float64(0.03799984719341912)} 

err list= [np.float64(0.20885122051176908), np.float64(0.7524651252467052), np.float64(0.237614515961259), np.float64(0.1729998471934191), np.float64(0.05599984719341912), np.float64(0.03899984719341912), np.float64(0.03799984719341912)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.006106506739426317), 3: np.float64(0.9937769931697109), 8: np.float64(0.00011641739028545906), 15: np.float64(2.067514456526064e-08), 78: np.float64(2.067514456526064e-08), 97: np.float64(2.067514456526064e-08), 0: np.float64(2.067514456526064e-08)}
err dic= {6: np.float64(0.2148934932605737), 3: np.float64(0.7587769931697109), 8: np.float64(0.23788358260971454), 15: np.float64(0.17299997932485542), 78: np.float64(0.05599997932485543), 97: np.float64(0.03899997932485543), 0: np.float64(0.03799997932485543)} 

err list= [np.float64(0.2148934932605737), np.float64(0.7587769931697109), np.float64(0.23788358260971454), np.float64(0.17299997932485542), np.float64(0.05599997932485543), np.float64(0.03899997932485543), np.float64(0.03799997932485543)]
results for assortment [6, 3, 8, 15, 78, 97] :

err MNL dic= {6: 0.221, 3: 0.235, 8: 0.238, 15: 0.173, 78: 0.056, 97: 0.039, 0: np.float64(0.22226755504658788)} 

err MNL list= [0.221, 0.235, 0.238, 0.173, 0.056, 0.039, np.float64(0.22226755504658788)]
sampled assortment [8, 2, 4, 95, 11, 22] number: 7
#  Learning probs for MM model, A = [8, 2, 4, 95, 11, 22]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 100]
#  Learning probs for MM model, A = [8, 2, 4, 95, 11, 22]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 10: 0, 11: 0, 14: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 100]
empirical probabilities from test set: {8: 0.235, 2: 0.202, 4: 0.197, 95: 0.042, 11: 0.166, 22: 0.137, 0: 0.021}
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.025 

learned probs for this beta: {8: np.float64(0.10166324000970663), 2: np.float64(0.11735209862679108), 4: np.float64(0.11181924414091485), 95: np.float64(0.19077207583229), 11: np.float64(0.09684918972570102), 22: np.float64(0.19077207583229), 0: np.float64(0.19077207583229)}
err dic= {8: np.float64(0.13333675999029337), 2: np.float64(0.08464790137320893), 4: np.float64(0.08518075585908516), 95: np.float64(0.14877207583229), 11: np.float64(0.069150810274299), 22: np.float64(0.05377207583228999), 0: np.float64(0.16977207583229)} 

err list= [np.float64(0.13333675999029337), np.float64(0.08464790137320893), np.float64(0.08518075585908516), np.float64(0.14877207583229), np.float64(0.069150810274299), np.float64(0.05377207583228999), np.float64(0.16977207583229)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.11613813566969493), 2: np.float64(0.15425203401132964), 4: np.float64(0.1401961850431624), 95: np.float64(0.1613223472517882), 11: np.float64(0.10544660352045852), 22: np.float64(0.1613223472517882), 0: np.float64(0.1613223472517882)}
err dic= {8: np.float64(0.11886186433030506), 2: np.float64(0.04774796598867037), 4: np.float64(0.05680381495683762), 95: np.float64(0.1193223472517882), 11: np.float64(0.060553396479541485), 22: np.float64(0.024322347251788196), 0: np.float64(0.14032234725178822)} 

err list= [np.float64(0.11886186433030506), np.float64(0.04774796598867037), np.float64(0.05680381495683762), np.float64(0.1193223472517882), np.float64(0.060553396479541485), np.float64(0.024322347251788196), np.float64(0.14032234725178822)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.13729227298709876), 2: np.float64(0.23880222324022388), 4: np.float64(0.19823345745036522), 95: np.float64(0.1041042980356609), 11: np.float64(0.1133591522153275), 22: np.float64(0.1041042980356609), 0: np.float64(0.1041042980356609)}
err dic= {8: np.float64(0.09770772701290123), 2: np.float64(0.036802223240223864), 4: np.float64(0.0012334574503652107), 95: np.float64(0.0621042980356609), 11: np.float64(0.05264084778467251), 22: np.float64(0.03289570196433911), 0: np.float64(0.0831042980356609)} 

err list= [np.float64(0.09770772701290123), np.float64(0.036802223240223864), np.float64(0.0012334574503652107), np.float64(0.0621042980356609), np.float64(0.05264084778467251), np.float64(0.03289570196433911), np.float64(0.0831042980356609)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.12308840559208752), 2: np.float64(0.4574766496226866), 4: np.float64(0.29577503358002255), 95: np.float64(0.015734900272187408), 11: np.float64(0.07645521038862356), 22: np.float64(0.015734900272187408), 0: np.float64(0.015734900272187408)}
err dic= {8: np.float64(0.11191159440791247), 2: np.float64(0.25547664962268657), 4: np.float64(0.09877503358002254), 95: np.float64(0.026265099727812595), 11: np.float64(0.08954478961137645), 22: np.float64(0.1212650997278126), 0: np.float64(0.005265099727812594)} 

err list= [np.float64(0.11191159440791247), np.float64(0.25547664962268657), np.float64(0.09877503358002254), np.float64(0.026265099727812595), np.float64(0.08954478961137645), np.float64(0.1212650997278126), np.float64(0.005265099727812594)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04695344187557957), 2: np.float64(0.6533327313355354), 4: np.float64(0.2801127887433343), 95: np.float64(0.0006330215069814404), 11: np.float64(0.017701973524586027), 22: np.float64(0.0006330215069814404), 0: np.float64(0.0006330215069814404)}
err dic= {8: np.float64(0.18804655812442042), 2: np.float64(0.45133273133553536), 4: np.float64(0.08311278874333428), 95: np.float64(0.04136697849301856), 11: np.float64(0.14829802647541399), 22: np.float64(0.13636697849301857), 0: np.float64(0.02036697849301856)} 

err list= [np.float64(0.18804655812442042), np.float64(0.45133273133553536), np.float64(0.08311278874333428), np.float64(0.04136697849301856), np.float64(0.14829802647541399), np.float64(0.13636697849301857), np.float64(0.02036697849301856)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013533300392681386), 2: np.float64(0.7667678944262509), 4: np.float64(0.2165199473631327), 95: np.float64(3.938651964155305e-05), 11: np.float64(0.00306069825901611), 22: np.float64(3.938651964155305e-05), 0: np.float64(3.938651964155305e-05)}
err dic= {8: np.float64(0.2214666996073186), 2: np.float64(0.5647678944262509), 4: np.float64(0.0195199473631327), 95: np.float64(0.04196061348035845), 11: np.float64(0.1629393017409839), 22: np.float64(0.13696061348035846), 0: np.float64(0.020960613480358447)} 

err list= [np.float64(0.2214666996073186), np.float64(0.5647678944262509), np.float64(0.0195199473631327), np.float64(0.04196061348035845), np.float64(0.1629393017409839), np.float64(0.13696061348035846), np.float64(0.020960613480358447)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034774830517678413), 2: np.float64(0.8410270318182933), 4: np.float64(0.15501470544219142), 95: np.float64(2.475713073721977e-06), 11: np.float64(0.0004733525485350635), 22: np.float64(2.475713073721977e-06), 0: np.float64(2.475713073721977e-06)}
err dic= {8: np.float64(0.23152251694823214), 2: np.float64(0.6390270318182933), 4: np.float64(0.04198529455780858), 95: np.float64(0.04199752428692628), 11: np.float64(0.16552664745146495), 22: np.float64(0.1369975242869263), 0: np.float64(0.020997524286926278)} 

err list= [np.float64(0.23152251694823214), np.float64(0.6390270318182933), np.float64(0.04198529455780858), np.float64(0.04199752428692628), np.float64(0.16552664745146495), np.float64(0.1369975242869263), np.float64(0.020997524286926278)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467378969217879), 2: np.float64(0.8926348985987295), 4: np.float64(0.10644825017728599), 95: np.float64(1.5319474323953942e-07), 11: np.float64(6.965374283562279e-05), 22: np.float64(1.5319474323953942e-07), 0: np.float64(1.5319474323953942e-07)}
err dic= {8: np.float64(0.23415326210307819), 2: np.float64(0.6906348985987294), 4: np.float64(0.09055174982271402), 95: np.float64(0.041999846805256764), 11: np.float64(0.16593034625716438), 22: np.float64(0.13699984680525676), 0: np.float64(0.020999846805256763)} 

err list= [np.float64(0.23415326210307819), np.float64(0.6906348985987294), np.float64(0.09055174982271402), np.float64(0.041999846805256764), np.float64(0.16593034625716438), np.float64(0.13699984680525676), np.float64(0.020999846805256763)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066371835668158), 2: np.float64(0.9287259444538888), 4: np.float64(0.07106336603689684), 95: np.float64(9.345456789754078e-09), 11: np.float64(9.997754489822545e-06), 22: np.float64(9.345456789754078e-09), 0: np.float64(9.345456789754078e-09)}
err dic= {8: np.float64(0.23479933628164332), 2: np.float64(0.7267259444538887), 4: np.float64(0.12593663396310317), 95: np.float64(0.04199999065454321), 11: np.float64(0.1659900022455102), 22: np.float64(0.1369999906545432), 0: np.float64(0.02099999065454321)} 

err list= [np.float64(0.23479933628164332), np.float64(0.7267259444538887), np.float64(0.12593663396310317), np.float64(0.04199999065454321), np.float64(0.1659900022455102), np.float64(0.1369999906545432), np.float64(0.02099999065454321)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.6823878298096384e-05), 2: np.float64(0.9535067286398906), 4: np.float64(0.04644503146625975), 95: np.float64(5.74845973961152e-10), 11: np.float64(1.414291013115667e-06), 22: np.float64(5.74845973961152e-10), 0: np.float64(5.74845973961152e-10)}
err dic= {8: np.float64(0.23495317612170188), 2: np.float64(0.7515067286398907), 4: np.float64(0.15055496853374026), 95: np.float64(0.041999999425154026), 11: np.float64(0.1659985857089869), 22: np.float64(0.13699999942515403), 0: np.float64(0.02099999942515403)} 

err list= [np.float64(0.23495317612170188), np.float64(0.7515067286398907), np.float64(0.15055496853374026), np.float64(0.041999999425154026), np.float64(0.1659985857089869), np.float64(0.13699999942515403), np.float64(0.02099999942515403)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.0815608593254931e-05), 2: np.float64(0.9701298209550606), 4: np.float64(0.02985916521843081), 95: np.float64(3.622280716538441e-11), 11: np.float64(1.981092453377738e-07), 22: np.float64(3.622280716538441e-11), 0: np.float64(3.622280716538441e-11)}
err dic= {8: np.float64(0.23498918439140673), 2: np.float64(0.7681298209550607), 4: np.float64(0.1671408347815692), 95: np.float64(0.04199999996377719), 11: np.float64(0.16599980189075467), 22: np.float64(0.1369999999637772), 0: np.float64(0.020999999963777195)} 

err list= [np.float64(0.23498918439140673), np.float64(0.7681298209550607), np.float64(0.1671408347815692), np.float64(0.04199999996377719), np.float64(0.16599980189075467), np.float64(0.1369999999637772), np.float64(0.020999999963777195)]
results for assortment [8, 2, 4, 95, 11, 22] :

err MNL dic= {8: 0.235, 2: 0.202, 4: 0.197, 95: 0.042, 11: 0.166, 22: 0.137, 0: np.float64(0.2356339886054509)} 

err MNL list= [0.235, 0.202, 0.197, 0.042, 0.166, 0.137, np.float64(0.2356339886054509)]
sampled assortment [1, 3, 9, 100, 22, 58] number: 8
#  Learning probs for MM model, A = [1, 3, 9, 100, 22, 58]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 100]
#  Learning probs for MM model, A = [1, 3, 9, 100, 22, 58]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 11: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 100]
empirical probabilities from test set: {1: 0.218, 3: 0.181, 9: 0.197, 100: 0.222, 22: 0.113, 58: 0.041, 0: 0.028}
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.12021437043689051), 3: np.float64(0.11455099697132673), 9: np.float64(0.09938436094908736), 100: np.float64(0.09246914519561009), 22: np.float64(0.1911270421490235), 58: np.float64(0.1911270421490235), 0: np.float64(0.1911270421490235)}
err dic= {1: np.float64(0.09778562956310949), 3: np.float64(0.06644900302867326), 9: np.float64(0.09761563905091265), 100: np.float64(0.12953085480438992), 22: np.float64(0.07812704214902351), 58: np.float64(0.1501270421490235), 0: np.float64(0.16312704214902352)} 

err list= [np.float64(0.09778562956310949), np.float64(0.06644900302867326), np.float64(0.09761563905091265), np.float64(0.12953085480438992), np.float64(0.07812704214902351), np.float64(0.1501270421490235), np.float64(0.16312704214902352)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.16146671693667028), 3: np.float64(0.14678183197045364), 9: np.float64(0.11088931596372156), 100: np.float64(0.09605703631550416), 22: np.float64(0.1616016996045545), 58: np.float64(0.1616016996045545), 0: np.float64(0.1616016996045545)}
err dic= {1: np.float64(0.05653328306332972), 3: np.float64(0.03421816802954636), 9: np.float64(0.08611068403627845), 100: np.float64(0.12594296368449584), 22: np.float64(0.0486016996045545), 58: np.float64(0.1206016996045545), 0: np.float64(0.1336016996045545)} 

err list= [np.float64(0.05653328306332972), np.float64(0.03421816802954636), np.float64(0.08611068403627845), np.float64(0.12594296368449584), np.float64(0.0486016996045545), np.float64(0.1206016996045545), np.float64(0.1336016996045545)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.2581400583067269), 3: np.float64(0.21450727634048197), 9: np.float64(0.12431364126745997), 100: np.float64(0.09346973207651026), 22: np.float64(0.10318976400293972), 58: np.float64(0.10318976400293972), 0: np.float64(0.10318976400293972)}
err dic= {1: np.float64(0.04014005830672693), 3: np.float64(0.03350727634048198), 9: np.float64(0.07268635873254004), 100: np.float64(0.12853026792348976), 22: np.float64(0.009810235997060282), 58: np.float64(0.06218976400293972), 0: np.float64(0.07518976400293972)} 

err list= [np.float64(0.04014005830672693), np.float64(0.03350727634048198), np.float64(0.07268635873254004), np.float64(0.12853026792348976), np.float64(0.009810235997060282), np.float64(0.06218976400293972), np.float64(0.07518976400293972)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5006502374384827), 3: np.float64(0.32535121203324713), 9: np.float64(0.08848419742767491), 100: np.float64(0.04323828806041621), 22: np.float64(0.014092021680053827), 58: np.float64(0.014092021680053827), 0: np.float64(0.014092021680053827)}
err dic= {1: np.float64(0.2826502374384827), 3: np.float64(0.14435121203324713), 9: np.float64(0.1085158025723251), 100: np.float64(0.1787617119395838), 22: np.float64(0.09890797831994617), 58: np.float64(0.026907978319946173), 0: np.float64(0.013907978319946173)} 

err list= [np.float64(0.2826502374384827), np.float64(0.14435121203324713), np.float64(0.1085158025723251), np.float64(0.1787617119395838), np.float64(0.09890797831994617), np.float64(0.026907978319946173), np.float64(0.013907978319946173)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.680665578227172), 3: np.float64(0.2936656146744148), 9: np.float64(0.019834616379134067), 100: np.float64(0.004526807926198721), 22: np.float64(0.0004357942643535205), 58: np.float64(0.0004357942643535205), 0: np.float64(0.0004357942643535205)}
err dic= {1: np.float64(0.462665578227172), 3: np.float64(0.11266561467441483), 9: np.float64(0.17716538362086595), 100: np.float64(0.21747319207380128), 22: np.float64(0.11256420573564649), 58: np.float64(0.04056420573564648), 0: np.float64(0.02756420573564648)} 

err list= [np.float64(0.462665578227172), np.float64(0.11266561467441483), np.float64(0.17716538362086595), np.float64(0.21747319207380128), np.float64(0.11256420573564649), np.float64(0.04056420573564648), np.float64(0.02756420573564648)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7763469451092907), 3: np.float64(0.21999724641729548), 9: np.float64(0.003251269202772069), 100: np.float64(0.00034516303137026994), 22: np.float64(1.979207975990561e-05), 58: np.float64(1.979207975990561e-05), 0: np.float64(1.979207975990561e-05)}
err dic= {1: np.float64(0.5583469451092907), 3: np.float64(0.03899724641729549), 9: np.float64(0.19374873079722793), 100: np.float64(0.22165483696862973), 22: np.float64(0.11298020792024009), 58: np.float64(0.0409802079202401), 0: np.float64(0.027980207920240096)} 

err list= [np.float64(0.5583469451092907), np.float64(0.03899724641729549), np.float64(0.19374873079722793), np.float64(0.22165483696862973), np.float64(0.11298020792024009), np.float64(0.0409802079202401), np.float64(0.027980207920240096)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437471579262177), 3: np.float64(0.15573933161292922), 9: np.float64(0.0004864413208523247), 100: np.float64(2.4260407244633742e-05), 22: np.float64(9.36244254609842e-07), 58: np.float64(9.36244254609842e-07), 0: np.float64(9.36244254609842e-07)}
err dic= {1: np.float64(0.6257471579262177), 3: np.float64(0.025260668387070778), 9: np.float64(0.1965135586791477), 100: np.float64(0.22197573959275538), 22: np.float64(0.1129990637557454), 58: np.float64(0.04099906375574539), 0: np.float64(0.02799906375574539)} 

err list= [np.float64(0.6257471579262177), np.float64(0.025260668387070778), np.float64(0.1965135586791477), np.float64(0.22197573959275538), np.float64(0.1129990637557454), np.float64(0.04099906375574539), np.float64(0.02799906375574539)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933411230356627), 3: np.float64(0.10658664064433768), 9: np.float64(7.044581483896259e-05), 100: np.float64(1.6573235688063181e-06), 22: np.float64(4.43938651515032e-08), 58: np.float64(4.43938651515032e-08), 0: np.float64(4.43938651515032e-08)}
err dic= {1: np.float64(0.6753411230356627), 3: np.float64(0.07441335935566232), 9: np.float64(0.19692955418516103), 100: np.float64(0.2219983426764312), 22: np.float64(0.11299995560613485), 58: np.float64(0.04099995560613485), 0: np.float64(0.02799995560613485)} 

err list= [np.float64(0.6753411230356627), np.float64(0.07441335935566232), np.float64(0.19692955418516103), np.float64(0.2219983426764312), np.float64(0.11299995560613485), np.float64(0.04099995560613485), np.float64(0.02799995560613485)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011124715495), 3: np.float64(0.07108872719152484), 9: np.float64(1.0042483390878864e-05), 100: np.float64(1.1156967265792228e-07), 22: np.float64(2.0946219336278777e-09), 58: np.float64(2.0946219336278777e-09), 0: np.float64(2.0946219336278777e-09)}
err dic= {1: np.float64(0.7109011124715495), 3: np.float64(0.10991127280847515), 9: np.float64(0.19698995751660914), 100: np.float64(0.22199988843032734), 22: np.float64(0.11299999790537807), 58: np.float64(0.04099999790537807), 0: np.float64(0.027999997905378066)} 

err list= [np.float64(0.7109011124715495), np.float64(0.10991127280847515), np.float64(0.19698995751660914), np.float64(0.22199988843032734), np.float64(0.11299999790537807), np.float64(0.04099999790537807), np.float64(0.027999997905378066)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.953548995880374), 3: np.float64(0.04644957966991993), 9: np.float64(1.4167151765326684e-06), 100: np.float64(7.434334660764014e-09), 22: np.float64(1.0006485408116786e-10), 58: np.float64(1.0006485408116786e-10), 0: np.float64(1.0006485408116786e-10)}
err dic= {1: np.float64(0.735548995880374), 3: np.float64(0.13455042033008008), 9: np.float64(0.19699858328482348), 100: np.float64(0.22199999256566535), 22: np.float64(0.11299999989993514), 58: np.float64(0.04099999989993515), 0: np.float64(0.027999999899935145)} 

err list= [np.float64(0.735548995880374), np.float64(0.13455042033008008), np.float64(0.19699858328482348), np.float64(0.22199999256566535), np.float64(0.11299999989993514), np.float64(0.04099999989993515), np.float64(0.027999999899935145)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303120761), 3: np.float64(0.029859970944554406), 9: np.float64(1.9823727023715938e-07), 100: np.float64(4.91382207643679e-10), 22: np.float64(4.9053953908400946e-12), 58: np.float64(4.9053953908400946e-12), 0: np.float64(4.9053953908400946e-12)}
err dic= {1: np.float64(0.7521398303120761), 3: np.float64(0.1511400290554456), 9: np.float64(0.19699980176272977), 100: np.float64(0.2219999995086178), 22: np.float64(0.11299999999509461), 58: np.float64(0.040999999995094606), 0: np.float64(0.027999999995094605)} 

err list= [np.float64(0.7521398303120761), np.float64(0.1511400290554456), np.float64(0.19699980176272977), np.float64(0.2219999995086178), np.float64(0.11299999999509461), np.float64(0.040999999995094606), np.float64(0.027999999995094605)]
results for assortment [1, 3, 9, 100, 22, 58] :

err MNL dic= {1: 0.218, 3: 0.181, 9: 0.197, 100: 0.222, 22: 0.113, 58: 0.041, 0: np.float64(0.22401612903225807)} 

err MNL list= [0.218, 0.181, 0.197, 0.222, 0.113, 0.041, np.float64(0.22401612903225807)]
sampled assortment [7, 6, 8, 16, 83, 70] number: 9
#  Learning probs for MM model, A = [7, 6, 8, 16, 83, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0, 10: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]
#  Learning probs for MM model, A = [7, 6, 8, 16, 83, 70]
#cluster  1 with weight 1.0
Learned cluster center of cluster 1:  {1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 12: 0, 100: 0} [1, 2, 3, 4, 5, 6, 7, 8, 12, 100]
empirical probabilities from test set: {7: 0.207, 6: 0.246, 8: 0.249, 16: 0.148, 83: 0.048, 70: 0.058, 0: 0.044}
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.09057187980278185), 6: np.float64(0.09286471785611336), 8: np.float64(0.08833565212269191), 16: np.float64(0.18205693755460284), 83: np.float64(0.18205693755460284), 70: np.float64(0.18205693755460284), 0: np.float64(0.18205693755460284)}
err dic= {7: np.float64(0.11642812019721814), 6: np.float64(0.15313528214388664), 8: np.float64(0.1606643478773081), 16: np.float64(0.034056937554602845), 83: np.float64(0.13405693755460285), 70: np.float64(0.12405693755460284), 0: np.float64(0.13805693755460285)} 

err list= [np.float64(0.11642812019721814), np.float64(0.15313528214388664), np.float64(0.1606643478773081), np.float64(0.034056937554602845), np.float64(0.13405693755460285), np.float64(0.12405693755460284), np.float64(0.13805693755460285)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.10606539278812033), 6: np.float64(0.11150348176392089), 8: np.float64(0.10089252254128589), 16: np.float64(0.1703846507266682), 83: np.float64(0.1703846507266682), 70: np.float64(0.1703846507266682), 0: np.float64(0.1703846507266682)}
err dic= {7: np.float64(0.10093460721187966), 6: np.float64(0.1344965182360791), 8: np.float64(0.1481074774587141), 16: np.float64(0.022384650726668204), 83: np.float64(0.1223846507266682), 70: np.float64(0.1123846507266682), 0: np.float64(0.1263846507266682)} 

err list= [np.float64(0.10093460721187966), np.float64(0.1344965182360791), np.float64(0.1481074774587141), np.float64(0.022384650726668204), np.float64(0.1223846507266682), np.float64(0.1123846507266682), np.float64(0.1263846507266682)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.13885317760149588), 6: np.float64(0.15345649376756632), 8: np.float64(0.12563955070702598), 16: np.float64(0.14551269448097887), 83: np.float64(0.14551269448097887), 70: np.float64(0.14551269448097887), 0: np.float64(0.14551269448097887)}
err dic= {7: np.float64(0.06814682239850411), 6: np.float64(0.09254350623243368), 8: np.float64(0.12336044929297402), 16: np.float64(0.002487305519021127), 83: np.float64(0.09751269448097886), 70: np.float64(0.08751269448097887), 0: np.float64(0.10151269448097887)} 

err list= [np.float64(0.06814682239850411), np.float64(0.09254350623243368), np.float64(0.12336044929297402), np.float64(0.002487305519021127), np.float64(0.09751269448097886), np.float64(0.08751269448097887), np.float64(0.10151269448097887)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.2216703418961291), 6: np.float64(0.28463035312049123), 8: np.float64(0.17263703585241127), 16: np.float64(0.08026556728274185), 83: np.float64(0.08026556728274185), 70: np.float64(0.08026556728274185), 0: np.float64(0.08026556728274185)}
err dic= {7: np.float64(0.014670341896129119), 6: np.float64(0.038630353120491234), 8: np.float64(0.07636296414758872), 16: np.float64(0.06773443271725814), 83: np.float64(0.03226556728274185), 70: np.float64(0.02226556728274185), 0: np.float64(0.036265567282741856)} 

err list= [np.float64(0.014670341896129119), np.float64(0.038630353120491234), np.float64(0.07636296414758872), np.float64(0.06773443271725814), np.float64(0.03226556728274185), np.float64(0.02226556728274185), np.float64(0.036265567282741856)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.28241332705345573), 6: np.float64(0.4656208594422241), 8: np.float64(0.17129234156937215), 16: np.float64(0.020168367983737254), 83: np.float64(0.020168367983737254), 70: np.float64(0.020168367983737254), 0: np.float64(0.020168367983737254)}
err dic= {7: np.float64(0.07541332705345574), 6: np.float64(0.2196208594422241), 8: np.float64(0.07770765843062785), 16: np.float64(0.12783163201626274), 83: np.float64(0.027831632016262747), 70: np.float64(0.037831632016262745), 0: np.float64(0.023831632016262743)} 

err list= [np.float64(0.07541332705345574), np.float64(0.2196208594422241), np.float64(0.07770765843062785), np.float64(0.12783163201626274), np.float64(0.027831632016262747), np.float64(0.037831632016262745), np.float64(0.023831632016262743)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.27522641076789794), 6: np.float64(0.5826543161678875), 8: np.float64(0.1300077508777143), 16: np.float64(0.003027880546626195), 83: np.float64(0.003027880546626195), 70: np.float64(0.003027880546626195), 0: np.float64(0.003027880546626195)}
err dic= {7: np.float64(0.06822641076789795), 6: np.float64(0.33665431616788755), 8: np.float64(0.1189922491222857), 16: np.float64(0.1449721194533738), 83: np.float64(0.04497211945337381), 70: np.float64(0.05497211945337381), 0: np.float64(0.040972119453373805)} 

err list= [np.float64(0.06822641076789795), np.float64(0.33665431616788755), np.float64(0.1189922491222857), np.float64(0.1449721194533738), np.float64(0.04497211945337381), np.float64(0.05497211945337381), np.float64(0.040972119453373805)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24417726867808764), 6: np.float64(0.6637426323704081), 8: np.float64(0.08982779714806408), 16: np.float64(0.0005630754508598186), 83: np.float64(0.0005630754508598186), 70: np.float64(0.0005630754508598186), 0: np.float64(0.0005630754508598186)}
err dic= {7: np.float64(0.037177268678087655), 6: np.float64(0.4177426323704081), 8: np.float64(0.15917220285193592), 16: np.float64(0.14743692454914017), 83: np.float64(0.04743692454914018), 70: np.float64(0.057436924549140185), 0: np.float64(0.04343692454914018)} 

err list= [np.float64(0.037177268678087655), np.float64(0.4177426323704081), np.float64(0.15917220285193592), np.float64(0.14743692454914017), np.float64(0.04743692454914018), np.float64(0.057436924549140185), np.float64(0.04343692454914018)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.2092261518659578), 6: np.float64(0.7302710256821867), 8: np.float64(0.05994429613819556), 16: np.float64(0.0001396315784145561), 83: np.float64(0.0001396315784145561), 70: np.float64(0.0001396315784145561), 0: np.float64(0.0001396315784145561)}
err dic= {7: np.float64(0.002226151865957815), 6: np.float64(0.4842710256821867), 8: np.float64(0.18905570386180442), 16: np.float64(0.14786036842158543), 83: np.float64(0.04786036842158545), 70: np.float64(0.05786036842158545), 0: np.float64(0.043860368421585444)} 

err list= [np.float64(0.002226151865957815), np.float64(0.4842710256821867), np.float64(0.18905570386180442), np.float64(0.14786036842158543), np.float64(0.04786036842158545), np.float64(0.05786036842158545), np.float64(0.043860368421585444)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17526431149601146), 6: np.float64(0.7854801492520017), 8: np.float64(0.03910675389240939), 16: np.float64(3.719633989431292e-05), 83: np.float64(3.719633989431292e-05), 70: np.float64(3.719633989431292e-05), 0: np.float64(3.719633989431292e-05)}
err dic= {7: np.float64(0.03173568850398853), 6: np.float64(0.5394801492520017), 8: np.float64(0.2098932461075906), 16: np.float64(0.14796280366010567), 83: np.float64(0.04796280366010569), 70: np.float64(0.05796280366010569), 0: np.float64(0.04396280366010569)} 

err list= [np.float64(0.03173568850398853), np.float64(0.5394801492520017), np.float64(0.2098932461075906), np.float64(0.14796280366010567), np.float64(0.04796280366010569), np.float64(0.05796280366010569), np.float64(0.04396280366010569)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.14432808318961995), 6: np.float64(0.8305507737457649), 8: np.float64(0.025080460166504177), 16: np.float64(1.0170724527955505e-05), 83: np.float64(1.0170724527955505e-05), 70: np.float64(1.0170724527955505e-05), 0: np.float64(1.0170724527955505e-05)}
err dic= {7: np.float64(0.06267191681038004), 6: np.float64(0.5845507737457649), 8: np.float64(0.22391953983349583), 16: np.float64(0.14798982927547202), 83: np.float64(0.047989829275472046), 70: np.float64(0.05798982927547205), 0: np.float64(0.04398982927547204)} 

err list= [np.float64(0.06267191681038004), np.float64(0.5845507737457649), np.float64(0.22391953983349583), np.float64(0.14798982927547202), np.float64(0.047989829275472046), np.float64(0.05798982927547205), np.float64(0.04398982927547204)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11730908543357699), 6: np.float64(0.8668034131829487), 8: np.float64(0.015876058303381152), 16: np.float64(2.8607700233052266e-06), 83: np.float64(2.8607700233052266e-06), 70: np.float64(2.8607700233052266e-06), 0: np.float64(2.8607700233052266e-06)}
err dic= {7: np.float64(0.089690914566423), 6: np.float64(0.6208034131829487), 8: np.float64(0.23312394169661885), 16: np.float64(0.14799713922997668), 83: np.float64(0.0479971392299767), 70: np.float64(0.0579971392299767), 0: np.float64(0.043997139229976695)} 

err list= [np.float64(0.089690914566423), np.float64(0.6208034131829487), np.float64(0.23312394169661885), np.float64(0.14799713922997668), np.float64(0.0479971392299767), np.float64(0.0579971392299767), np.float64(0.043997139229976695)]
results for assortment [7, 6, 8, 16, 83, 70] :

err MNL dic= {7: 0.207, 6: 0.246, 8: 0.249, 16: 0.148, 83: 0.048, 70: 0.058, 0: np.float64(0.21812319790301443)} 

err MNL list= [0.207, 0.246, 0.249, 0.148, 0.048, 0.058, np.float64(0.21812319790301443)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2]
 mean error for all betas:

mean_err= [0.12292221 0.11625234 0.1047909  0.08888585 0.08796777 0.09258651
 0.09792803 0.10306192 0.10873695 0.11456471 0.1202745 ]
mean_std= [0.         0.00666988 0.01709934 0.03127623 0.02803451 0.02759725
 0.02870536 0.03009147 0.03259652 0.03552386 0.0383828 ]
MNL: [0.17062606 0.16668406 0.16718534 0.16743585 0.16353078 0.16596076
 0.16918108 0.17351914 0.17085945 0.16773189]
 mean error for MNL:

mean_err_MNL= 0.16827143997207789
mean_std_MNL= 0.0027038801497929975
