p= 0.025 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(0.1117943704466336), 3: np.float64(0.10903415760556906), 4: np.float64(0.10634209466237093), 59: np.float64(0.1682073443213532), 40: np.float64(0.1682073443213532), 84: np.float64(0.1682073443213532), 0: np.float64(0.1682073443213532)}
err dic= {2: np.float64(0.16320562955336643), 3: np.float64(0.13796584239443094), 4: np.float64(0.14565790533762907), 59: np.float64(0.1092073443213532), 40: np.float64(0.09620734432135321), 84: np.float64(0.1082073443213532), 0: np.float64(0.1332073443213532)} 

err list= [np.float64(0.16320562955336643), np.float64(0.13796584239443094), np.float64(0.14565790533762907), np.float64(0.1092073443213532), np.float64(0.09620734432135321), np.float64(0.1082073443213532), np.float64(0.1332073443213532)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.14790378936237977), 3: np.float64(0.14069043643665116), 4: np.float64(0.13382888288438988), 59: np.float64(0.14439422282914532), 40: np.float64(0.14439422282914532), 84: np.float64(0.14439422282914532), 0: np.float64(0.14439422282914532)}
err dic= {2: np.float64(0.12709621063762025), 3: np.float64(0.10630956356334884), 4: np.float64(0.11817111711561012), 59: np.float64(0.08539422282914533), 40: np.float64(0.07239422282914533), 84: np.float64(0.08439422282914533), 0: np.float64(0.10939422282914532)} 

err list= [np.float64(0.12709621063762025), np.float64(0.10630956356334884), np.float64(0.11817111711561012), np.float64(0.08539422282914533), np.float64(0.07239422282914533), np.float64(0.08439422282914533), np.float64(0.10939422282914532)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.22909899032536502), 3: np.float64(0.20729733888064852), 4: np.float64(0.1875703888784914), 59: np.float64(0.09400832047887428), 40: np.float64(0.09400832047887428), 84: np.float64(0.09400832047887428), 0: np.float64(0.09400832047887428)}
err dic= {2: np.float64(0.04590100967463501), 3: np.float64(0.03970266111935147), 4: np.float64(0.0644296111215086), 59: np.float64(0.03500832047887428), 40: np.float64(0.022008320478874285), 84: np.float64(0.03400832047887428), 0: np.float64(0.05900832047887428)} 

err list= [np.float64(0.04590100967463501), np.float64(0.03970266111935147), np.float64(0.0644296111215086), np.float64(0.03500832047887428), np.float64(0.022008320478874285), np.float64(0.03400832047887428), np.float64(0.05900832047887428)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.39864520749156174), 3: np.float64(0.31046519976209147), 4: np.float64(0.2417905406911363), 59: np.float64(0.012274763013803928), 40: np.float64(0.012274763013803928), 84: np.float64(0.012274763013803928), 0: np.float64(0.012274763013803928)}
err dic= {2: np.float64(0.12364520749156171), 3: np.float64(0.06346519976209147), 4: np.float64(0.010209459308863689), 59: np.float64(0.04672523698619607), 40: np.float64(0.05972523698619607), 84: np.float64(0.04772523698619607), 0: np.float64(0.022725236986196076)} 

err list= [np.float64(0.12364520749156171), np.float64(0.06346519976209147), np.float64(0.010209459308863689), np.float64(0.04672523698619607), np.float64(0.05972523698619607), np.float64(0.04772523698619607), np.float64(0.022725236986196076)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5055739997694526), 3: np.float64(0.30664613161372106), 4: np.float64(0.18599028050599725), 59: np.float64(0.00044739702770750387), 40: np.float64(0.00044739702770750387), 84: np.float64(0.00044739702770750387), 0: np.float64(0.00044739702770750387)}
err dic= {2: np.float64(0.2305739997694526), 3: np.float64(0.059646131613721065), 4: np.float64(0.06600971949400275), 59: np.float64(0.05855260297229249), 40: np.float64(0.07155260297229249), 84: np.float64(0.05955260297229249), 0: np.float64(0.0345526029722925)} 

err list= [np.float64(0.2305739997694526), np.float64(0.059646131613721065), np.float64(0.06600971949400275), np.float64(0.05855260297229249), np.float64(0.07155260297229249), np.float64(0.05955260297229249), np.float64(0.0345526029722925)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5897341374679589), 3: np.float64(0.2785706815494357), 4: np.float64(0.1315874725382221), 59: np.float64(2.6927111094499077e-05), 40: np.float64(2.6927111094499077e-05), 84: np.float64(2.6927111094499077e-05), 0: np.float64(2.6927111094499077e-05)}
err dic= {2: np.float64(0.31473413746795886), 3: np.float64(0.03157068154943571), 4: np.float64(0.12041252746177791), 59: np.float64(0.0589730728889055), 40: np.float64(0.07197307288890549), 84: np.float64(0.0599730728889055), 0: np.float64(0.034973072888905506)} 

err list= [np.float64(0.31473413746795886), np.float64(0.03157068154943571), np.float64(0.12041252746177791), np.float64(0.0589730728889055), np.float64(0.07197307288890549), np.float64(0.0599730728889055), np.float64(0.034973072888905506)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652364028875983), 3: np.float64(0.2447267961411905), 4: np.float64(0.09002995700409867), 59: np.float64(1.7109917782093696e-06), 40: np.float64(1.7109917782093696e-06), 84: np.float64(1.7109917782093696e-06), 0: np.float64(1.7109917782093696e-06)}
err dic= {2: np.float64(0.3902364028875983), 3: np.float64(0.002273203858809497), 4: np.float64(0.16197004299590134), 59: np.float64(0.05899828900822179), 40: np.float64(0.07199828900822179), 84: np.float64(0.05999828900822179), 0: np.float64(0.03499828900822179)} 

err list= [np.float64(0.3902364028875983), np.float64(0.002273203858809497), np.float64(0.16197004299590134), np.float64(0.05899828900822179), np.float64(0.07199828900822179), np.float64(0.05999828900822179), np.float64(0.03499828900822179)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.7306788077533146), 3: np.float64(0.20934298338540885), 4: np.float64(0.05997776892894276), 59: np.float64(1.0998308285518919e-07), 40: np.float64(1.0998308285518919e-07), 84: np.float64(1.0998308285518919e-07), 0: np.float64(1.0998308285518919e-07)}
err dic= {2: np.float64(0.4556788077533146), 3: np.float64(0.03765701661459114), 4: np.float64(0.19202223107105726), 59: np.float64(0.05899989001691714), 40: np.float64(0.07199989001691715), 84: np.float64(0.05999989001691714), 0: np.float64(0.03499989001691715)} 

err list= [np.float64(0.4556788077533146), np.float64(0.03765701661459114), np.float64(0.19202223107105726), np.float64(0.05899989001691714), np.float64(0.07199989001691715), np.float64(0.05999989001691714), np.float64(0.03499989001691715)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855970126768899), 3: np.float64(0.17529038725072257), 4: np.float64(0.03911257217973397), 59: np.float64(6.973163304033093e-09), 40: np.float64(6.973163304033093e-09), 84: np.float64(6.973163304033093e-09), 0: np.float64(6.973163304033093e-09)}
err dic= {2: np.float64(0.5105970126768898), 3: np.float64(0.07170961274927742), 4: np.float64(0.21288742782026604), 59: np.float64(0.05899999302683669), 40: np.float64(0.07199999302683668), 84: np.float64(0.059999993026836694), 0: np.float64(0.0349999930268367)} 

err list= [np.float64(0.5105970126768898), np.float64(0.07170961274927742), np.float64(0.21288742782026604), np.float64(0.05899999302683669), np.float64(0.07199999302683668), np.float64(0.059999993026836694), np.float64(0.0349999930268367)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845629662106), 3: np.float64(0.144333954875703), 4: np.float64(0.0250814805125495), 59: np.float64(4.113842415959547e-10), 40: np.float64(4.113842415959547e-10), 84: np.float64(4.113842415959547e-10), 0: np.float64(4.113842415959547e-10)}
err dic= {2: np.float64(0.5555845629662106), 3: np.float64(0.102666045124297), 4: np.float64(0.2269185194874505), 59: np.float64(0.05899999958861576), 40: np.float64(0.07199999958861575), 84: np.float64(0.05999999958861576), 0: np.float64(0.034999999588615764)} 

err list= [np.float64(0.5555845629662106), np.float64(0.102666045124297), np.float64(0.2269185194874505), np.float64(0.05899999958861576), np.float64(0.07199999958861575), np.float64(0.05999999958861576), np.float64(0.034999999588615764)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321203637), 3: np.float64(0.11731042781578144), 4: np.float64(0.015876239975056997), 59: np.float64(2.2199436635443525e-11), 40: np.float64(2.2199436635443525e-11), 84: np.float64(2.2199436635443525e-11), 0: np.float64(2.2199436635443525e-11)}
err dic= {2: np.float64(0.5918133321203637), 3: np.float64(0.12968957218421856), 4: np.float64(0.236123760024943), 59: np.float64(0.05899999997780056), 40: np.float64(0.07199999997780056), 84: np.float64(0.05999999997780056), 0: np.float64(0.03499999997780057)} 

err list= [np.float64(0.5918133321203637), np.float64(0.12968957218421856), np.float64(0.236123760024943), np.float64(0.05899999997780056), np.float64(0.07199999997780056), np.float64(0.05999999997780056), np.float64(0.03499999997780057)]
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(0.11019415441029441), 4: np.float64(0.10747345104394061), 8: np.float64(0.09767858708281764), 74: np.float64(0.17116345186573403), 40: np.float64(0.17116345186573403), 87: np.float64(0.17116345186573403), 0: np.float64(0.17116345186573403)}
err dic= {3: np.float64(0.1488058455897056), 4: np.float64(0.13852654895605937), 8: np.float64(0.15832141291718238), 74: np.float64(0.10516345186573403), 40: np.float64(0.09416345186573404), 87: np.float64(0.12416345186573403), 0: np.float64(0.12216345186573403)} 

err list= [np.float64(0.1488058455897056), np.float64(0.13852654895605937), np.float64(0.15832141291718238), np.float64(0.10516345186573403), np.float64(0.09416345186573404), np.float64(0.12416345186573403), np.float64(0.12216345186573403)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.14450760037814858), 4: np.float64(0.13745988154368544), 8: np.float64(0.11378732676045004), 74: np.float64(0.15106129782942956), 40: np.float64(0.15106129782942956), 87: np.float64(0.15106129782942956), 0: np.float64(0.15106129782942956)}
err dic= {3: np.float64(0.11449239962185143), 4: np.float64(0.10854011845631456), 8: np.float64(0.14221267323954995), 74: np.float64(0.08506129782942956), 40: np.float64(0.07406129782942956), 87: np.float64(0.10406129782942956), 0: np.float64(0.10206129782942956)} 

err list= [np.float64(0.11449239962185143), np.float64(0.10854011845631456), np.float64(0.14221267323954995), np.float64(0.08506129782942956), np.float64(0.07406129782942956), np.float64(0.10406129782942956), np.float64(0.10206129782942956)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.22433565522637894), 4: np.float64(0.2029872950484419), 8: np.float64(0.14040544404580682), 74: np.float64(0.10806790141984332), 40: np.float64(0.10806790141984332), 87: np.float64(0.10806790141984332), 0: np.float64(0.10806790141984332)}
err dic= {3: np.float64(0.03466434477362107), 4: np.float64(0.043012704951558095), 8: np.float64(0.11559455595419318), 74: np.float64(0.04206790141984332), 40: np.float64(0.031067901419843322), 87: np.float64(0.06106790141984332), 0: np.float64(0.05906790141984332)} 

err list= [np.float64(0.03466434477362107), np.float64(0.043012704951558095), np.float64(0.11559455595419318), np.float64(0.04206790141984332), np.float64(0.031067901419843322), np.float64(0.06106790141984332), np.float64(0.05906790141984332)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.43159907033249356), 4: np.float64(0.336129693947837), 8: np.float64(0.14090326043194773), 74: np.float64(0.02284199382193133), 40: np.float64(0.02284199382193133), 87: np.float64(0.02284199382193133), 0: np.float64(0.02284199382193133)}
err dic= {3: np.float64(0.17259907033249355), 4: np.float64(0.09012969394783699), 8: np.float64(0.11509673956805228), 74: np.float64(0.04315800617806867), 40: np.float64(0.054158006178068666), 87: np.float64(0.02415800617806867), 0: np.float64(0.026158006178068672)} 

err list= [np.float64(0.17259907033249355), np.float64(0.09012969394783699), np.float64(0.11509673956805228), np.float64(0.04315800617806867), np.float64(0.054158006178068666), np.float64(0.02415800617806867), np.float64(0.026158006178068672)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5817533960541338), 4: np.float64(0.3528512710987795), 8: np.float64(0.061150421949790694), 74: np.float64(0.0010612277243243966), 40: np.float64(0.0010612277243243966), 87: np.float64(0.0010612277243243966), 0: np.float64(0.0010612277243243966)}
err dic= {3: np.float64(0.3227533960541338), 4: np.float64(0.10685127109877951), 8: np.float64(0.1948495780502093), 74: np.float64(0.06493877227567561), 40: np.float64(0.07593877227567561), 87: np.float64(0.0459387722756756), 0: np.float64(0.047938772275675605)} 

err list= [np.float64(0.3227533960541338), np.float64(0.10685127109877951), np.float64(0.1948495780502093), np.float64(0.06493877227567561), np.float64(0.07593877227567561), np.float64(0.0459387722756756), np.float64(0.047938772275675605)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.664945728035167), 4: np.float64(0.3140981213118357), 8: np.float64(0.020648822959904396), 74: np.float64(7.683192327187928e-05), 40: np.float64(7.683192327187928e-05), 87: np.float64(7.683192327187928e-05), 0: np.float64(7.683192327187928e-05)}
err dic= {3: np.float64(0.40594572803516704), 4: np.float64(0.06809812131183568), 8: np.float64(0.23535117704009562), 74: np.float64(0.06592316807672813), 40: np.float64(0.07692316807672812), 87: np.float64(0.04692316807672812), 0: np.float64(0.04892316807672812)} 

err list= [np.float64(0.40594572803516704), np.float64(0.06809812131183568), np.float64(0.23535117704009562), np.float64(0.06592316807672813), np.float64(0.07692316807672812), np.float64(0.04692316807672812), np.float64(0.04892316807672812)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.726377882743643), 4: np.float64(0.26721948958302716), 8: np.float64(0.006378213625811056), 74: np.float64(6.103511879899805e-06), 40: np.float64(6.103511879899805e-06), 87: np.float64(6.103511879899805e-06), 0: np.float64(6.103511879899805e-06)}
err dic= {3: np.float64(0.467377882743643), 4: np.float64(0.021219489583027162), 8: np.float64(0.24962178637418894), 74: np.float64(0.06599389648812011), 40: np.float64(0.0769938964881201), 87: np.float64(0.0469938964881201), 0: np.float64(0.0489938964881201)} 

err list= [np.float64(0.467377882743643), np.float64(0.021219489583027162), np.float64(0.24962178637418894), np.float64(0.06599389648812011), np.float64(0.0769938964881201), np.float64(0.0469938964881201), np.float64(0.0489938964881201)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.7758307187588294), 4: np.float64(0.22227922247589374), 8: np.float64(0.00188811789535881), 74: np.float64(4.852174787977702e-07), 40: np.float64(4.852174787977702e-07), 87: np.float64(4.852174787977702e-07), 0: np.float64(4.852174787977702e-07)}
err dic= {3: np.float64(0.5168307187588294), 4: np.float64(0.023720777524106257), 8: np.float64(0.2541118821046412), 74: np.float64(0.06599951478252121), 40: np.float64(0.0769995147825212), 87: np.float64(0.0469995147825212), 0: np.float64(0.0489995147825212)} 

err list= [np.float64(0.5168307187588294), np.float64(0.023720777524106257), np.float64(0.2541118821046412), np.float64(0.06599951478252121), np.float64(0.0769995147825212), np.float64(0.0469995147825212), np.float64(0.0489995147825212)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.8171260763896235), 4: np.float64(0.1823254722862747), 8: np.float64(0.0005482995237515067), 74: np.float64(3.7950087561445364e-08), 40: np.float64(3.7950087561445364e-08), 87: np.float64(3.7950087561445364e-08), 0: np.float64(3.7950087561445364e-08)}
err dic= {3: np.float64(0.5581260763896235), 4: np.float64(0.06367452771372531), 8: np.float64(0.2554517004762485), 74: np.float64(0.06599996204991244), 40: np.float64(0.07699996204991244), 87: np.float64(0.04699996204991244), 0: np.float64(0.04899996204991244)} 

err list= [np.float64(0.5581260763896235), np.float64(0.06367452771372531), np.float64(0.2554517004762485), np.float64(0.06599996204991244), np.float64(0.07699996204991244), np.float64(0.04699996204991244), np.float64(0.04899996204991244)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.8518182402051865), 4: np.float64(0.14802381470347376), 8: np.float64(0.00015793400818743883), 74: np.float64(2.7707879992353475e-09), 40: np.float64(2.7707879992353475e-09), 87: np.float64(2.7707879992353475e-09), 0: np.float64(2.7707879992353475e-09)}
err dic= {3: np.float64(0.5928182402051865), 4: np.float64(0.09797618529652624), 8: np.float64(0.2558420659918126), 74: np.float64(0.065999997229212), 40: np.float64(0.076999997229212), 87: np.float64(0.046999997229212), 0: np.float64(0.048999997229212)} 

err list= [np.float64(0.5928182402051865), np.float64(0.09797618529652624), np.float64(0.2558420659918126), np.float64(0.065999997229212), np.float64(0.076999997229212), np.float64(0.046999997229212), np.float64(0.048999997229212)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  2 

learned probs for this beta: {3: np.float64(0.880757139585843), 4: np.float64(0.1191975169485189), 8: np.float64(4.534272153994354e-05), 74: np.float64(1.8602454836417959e-10), 40: np.float64(1.8602454836417959e-10), 87: np.float64(1.8602454836417959e-10), 0: np.float64(1.8602454836417959e-10)}
err dic= {3: np.float64(0.621757139585843), 4: np.float64(0.1268024830514811), 8: np.float64(0.25595465727846006), 74: np.float64(0.06599999981397546), 40: np.float64(0.07699999981397546), 87: np.float64(0.04699999981397545), 0: np.float64(0.04899999981397545)} 

err list= [np.float64(0.621757139585843), np.float64(0.1268024830514811), np.float64(0.25595465727846006), np.float64(0.06599999981397546), np.float64(0.07699999981397546), np.float64(0.04699999981397545), np.float64(0.04899999981397545)]
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(0.10566149021072145), 3: np.float64(0.10065378716066589), 9: np.float64(0.08930227074641536), 83: np.float64(0.1760956129705493), 79: np.float64(0.1760956129705493), 70: np.float64(0.1760956129705493), 0: np.float64(0.1760956129705493)}
err dic= {1: np.float64(0.15933850978927855), 3: np.float64(0.1503462128393341), 9: np.float64(0.14569772925358462), 83: np.float64(0.1240956129705493), 79: np.float64(0.10809561297054929), 70: np.float64(0.09509561297054929), 0: np.float64(0.12809561297054928)} 

err list= [np.float64(0.15933850978927855), np.float64(0.1503462128393341), np.float64(0.14569772925358462), np.float64(0.1240956129705493), np.float64(0.10809561297054929), np.float64(0.09509561297054929), np.float64(0.12809561297054928)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1422376875493713), 3: np.float64(0.12919726734124806), 9: np.float64(0.10195106867452633), 83: np.float64(0.15665349410871332), 79: np.float64(0.15665349410871332), 70: np.float64(0.15665349410871332), 0: np.float64(0.15665349410871332)}
err dic= {1: np.float64(0.12276231245062871), 3: np.float64(0.12180273265875194), 9: np.float64(0.13304893132547366), 83: np.float64(0.10465349410871333), 79: np.float64(0.08865349410871332), 70: np.float64(0.07565349410871332), 0: np.float64(0.10865349410871332)} 

err list= [np.float64(0.12276231245062871), np.float64(0.12180273265875194), np.float64(0.13304893132547366), np.float64(0.10465349410871333), np.float64(0.08865349410871332), np.float64(0.07565349410871332), np.float64(0.10865349410871332)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.23296717633290082), 3: np.float64(0.19313537522149415), 9: np.float64(0.1216169626022124), 83: np.float64(0.11307012146084935), 79: np.float64(0.11307012146084935), 70: np.float64(0.11307012146084935), 0: np.float64(0.11307012146084935)}
err dic= {1: np.float64(0.0320328236670992), 3: np.float64(0.057864624778505847), 9: np.float64(0.11338303739778759), 83: np.float64(0.06107012146084936), 79: np.float64(0.04507012146084935), 70: np.float64(0.03207012146084935), 0: np.float64(0.06507012146084935)} 

err list= [np.float64(0.0320328236670992), np.float64(0.057864624778505847), np.float64(0.11338303739778759), np.float64(0.06107012146084936), np.float64(0.04507012146084935), np.float64(0.03207012146084935), np.float64(0.06507012146084935)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.48880516450429323), 3: np.float64(0.3166376335250655), 9: np.float64(0.10601773707406519), 83: np.float64(0.022134866224143995), 79: np.float64(0.022134866224143995), 70: np.float64(0.022134866224143995), 0: np.float64(0.022134866224143995)}
err dic= {1: np.float64(0.22380516450429322), 3: np.float64(0.06563763352506552), 9: np.float64(0.1289822629259348), 83: np.float64(0.029865133775856003), 79: np.float64(0.04586513377585601), 70: np.float64(0.058865133775856004), 0: np.float64(0.025865133775856006)} 

err list= [np.float64(0.22380516450429322), np.float64(0.06563763352506552), np.float64(0.1289822629259348), np.float64(0.029865133775856003), np.float64(0.04586513377585601), np.float64(0.058865133775856004), np.float64(0.025865133775856006)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6746744656630185), 3: np.float64(0.2906674067387031), 9: np.float64(0.03120038850565729), 83: np.float64(0.0008644347731551913), 79: np.float64(0.0008644347731551913), 70: np.float64(0.0008644347731551913), 0: np.float64(0.0008644347731551913)}
err dic= {1: np.float64(0.40967446566301846), 3: np.float64(0.039667406738703115), 9: np.float64(0.2037996114943427), 83: np.float64(0.05113556522684481), 79: np.float64(0.06713556522684481), 70: np.float64(0.08013556522684481), 0: np.float64(0.04713556522684481)} 

err list= [np.float64(0.40967446566301846), np.float64(0.039667406738703115), np.float64(0.2037996114943427), np.float64(0.05113556522684481), np.float64(0.06713556522684481), np.float64(0.08013556522684481), np.float64(0.04713556522684481)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.7739586699926175), 3: np.float64(0.21912455050929533), 9: np.float64(0.006712093360761442), 83: np.float64(5.1171534331724505e-05), 79: np.float64(5.1171534331724505e-05), 70: np.float64(5.1171534331724505e-05), 0: np.float64(5.1171534331724505e-05)}
err dic= {1: np.float64(0.5089586699926175), 3: np.float64(0.03187544949070467), 9: np.float64(0.22828790663923854), 83: np.float64(0.05194882846566827), 79: np.float64(0.06794882846566828), 70: np.float64(0.08094882846566828), 0: np.float64(0.047948828465668274)} 

err list= [np.float64(0.5089586699926175), np.float64(0.03187544949070467), np.float64(0.22828790663923854), np.float64(0.05194882846566827), np.float64(0.06794882846566828), np.float64(0.08094882846566828), np.float64(0.047948828465668274)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8431093097464795), 3: np.float64(0.15556850731440486), 9: np.float64(0.001308928536665716), 83: np.float64(3.313600612131847e-06), 79: np.float64(3.313600612131847e-06), 70: np.float64(3.313600612131847e-06), 0: np.float64(3.313600612131847e-06)}
err dic= {1: np.float64(0.5781093097464794), 3: np.float64(0.09543149268559514), 9: np.float64(0.23369107146333426), 83: np.float64(0.05199668639938786), 79: np.float64(0.06799668639938787), 70: np.float64(0.08099668639938787), 0: np.float64(0.04799668639938787)} 

err list= [np.float64(0.5781093097464794), np.float64(0.09543149268559514), np.float64(0.23369107146333426), np.float64(0.05199668639938786), np.float64(0.06799668639938787), np.float64(0.08099668639938787), np.float64(0.04799668639938787)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931960192560988), 3: np.float64(0.10655811273968482), 9: np.float64(0.000245011230038648), 83: np.float64(2.1419354448626897e-07), 79: np.float64(2.1419354448626897e-07), 70: np.float64(2.1419354448626897e-07), 0: np.float64(2.1419354448626897e-07)}
err dic= {1: np.float64(0.6281960192560988), 3: np.float64(0.14444188726031518), 9: np.float64(0.23475498876996134), 83: np.float64(0.05199978580645551), 79: np.float64(0.06799978580645552), 70: np.float64(0.08099978580645552), 0: np.float64(0.04799978580645552)} 

err list= [np.float64(0.6281960192560988), np.float64(0.14444188726031518), np.float64(0.23475498876996134), np.float64(0.05199978580645551), np.float64(0.06799978580645552), np.float64(0.08099978580645552), np.float64(0.04799978580645552)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288706767576653), 3: np.float64(0.07108431300901136), 9: np.float64(4.4956054188102486e-05), 83: np.float64(1.35447838974135e-08), 79: np.float64(1.35447838974135e-08), 70: np.float64(1.35447838974135e-08), 0: np.float64(1.35447838974135e-08)}
err dic= {1: np.float64(0.6638706767576653), 3: np.float64(0.17991568699098864), 9: np.float64(0.23495504394581188), 83: np.float64(0.0519999864552161), 79: np.float64(0.06799998645521611), 70: np.float64(0.08099998645521611), 0: np.float64(0.0479999864552161)} 

err list= [np.float64(0.6638706767576653), np.float64(0.17991568699098864), np.float64(0.23495504394581188), np.float64(0.0519999864552161), np.float64(0.06799998645521611), np.float64(0.08099998645521611), np.float64(0.0479999864552161)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.95354292155026), 3: np.float64(0.04644892549709868), 9: np.float64(8.149779423246367e-06), 83: np.float64(7.933043992860899e-10), 79: np.float64(7.933043992860899e-10), 70: np.float64(7.933043992860899e-10), 0: np.float64(7.933043992860899e-10)}
err dic= {1: np.float64(0.68854292155026), 3: np.float64(0.20455107450290133), 9: np.float64(0.23499185022057675), 83: np.float64(0.051999999206695596), 79: np.float64(0.06799999920669561), 70: np.float64(0.08099999920669561), 0: np.float64(0.0479999992066956)} 

err list= [np.float64(0.68854292155026), np.float64(0.20455107450290133), np.float64(0.23499185022057675), np.float64(0.051999999206695596), np.float64(0.06799999920669561), np.float64(0.08099999920669561), np.float64(0.0479999992066956)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386586064735), 3: np.float64(0.02985987659087278), 9: np.float64(1.4646328957145254e-06), 83: np.float64(4.243941740116503e-11), 79: np.float64(4.243941740116503e-11), 70: np.float64(4.243941740116503e-11), 0: np.float64(4.243941740116503e-11)}
err dic= {1: np.float64(0.7051386586064735), 3: np.float64(0.22114012340912723), 9: np.float64(0.23499853536710427), 83: np.float64(0.05199999995756058), 79: np.float64(0.06799999995756059), 70: np.float64(0.08099999995756059), 0: np.float64(0.04799999995756058)} 

err list= [np.float64(0.7051386586064735), np.float64(0.22114012340912723), np.float64(0.23499853536710427), np.float64(0.05199999995756058), np.float64(0.06799999995756059), np.float64(0.08099999995756059), np.float64(0.04799999995756058)]
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(0.10580747869330649), 4: np.float64(0.09844345171694308), 8: np.float64(0.08942879379256428), 32: np.float64(0.17658006894929698), 27: np.float64(0.17658006894929698), 82: np.float64(0.17658006894929698), 0: np.float64(0.17658006894929698)}
err dic= {1: np.float64(0.11619252130669351), 4: np.float64(0.13155654828305693), 8: np.float64(0.14257120620743574), 32: np.float64(0.07458006894929699), 27: np.float64(0.056580068949296985), 82: np.float64(0.12658006894929696), 0: np.float64(0.13258006894929697)} 

err list= [np.float64(0.11619252130669351), np.float64(0.13155654828305693), np.float64(0.14257120620743574), np.float64(0.07458006894929699), np.float64(0.056580068949296985), np.float64(0.12658006894929696), np.float64(0.13258006894929697)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1427375682356494), 4: np.float64(0.1237831754829653), 8: np.float64(0.10232785656845898), 32: np.float64(0.1577878499282313), 27: np.float64(0.1577878499282313), 82: np.float64(0.1577878499282313), 0: np.float64(0.1577878499282313)}
err dic= {1: np.float64(0.0792624317643506), 4: np.float64(0.10621682451703471), 8: np.float64(0.12967214343154104), 32: np.float64(0.05578784992823131), 27: np.float64(0.03778784992823131), 82: np.float64(0.1077878499282313), 0: np.float64(0.11378784992823131)} 

err list= [np.float64(0.0792624317643506), np.float64(0.10621682451703471), np.float64(0.12967214343154104), np.float64(0.05578784992823131), np.float64(0.03778784992823131), np.float64(0.1077878499282313), np.float64(0.11378784992823131)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.23543623687065607), 4: np.float64(0.1786710482379466), 8: np.float64(0.1230443485932169), 32: np.float64(0.11571209157454633), 27: np.float64(0.11571209157454633), 82: np.float64(0.11571209157454633), 0: np.float64(0.11571209157454633)}
err dic= {1: np.float64(0.013436236870656065), 4: np.float64(0.051328951762053404), 8: np.float64(0.10895565140678311), 32: np.float64(0.013712091574546337), 27: np.float64(0.004287908425453665), 82: np.float64(0.06571209157454633), 0: np.float64(0.07171209157454633)} 

err list= [np.float64(0.013436236870656065), np.float64(0.051328951762053404), np.float64(0.10895565140678311), np.float64(0.013712091574546337), np.float64(0.004287908425453665), np.float64(0.06571209157454633), np.float64(0.07171209157454633)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5124388136605267), 4: np.float64(0.2747993931833751), 8: np.float64(0.1128921490583027), 32: np.float64(0.024967411024448754), 27: np.float64(0.024967411024448754), 82: np.float64(0.024967411024448754), 0: np.float64(0.024967411024448754)}
err dic= {1: np.float64(0.2904388136605267), 4: np.float64(0.044799393183375086), 8: np.float64(0.11910785094169732), 32: np.float64(0.07703258897555124), 27: np.float64(0.09503258897555124), 82: np.float64(0.02503258897555125), 0: np.float64(0.019032588975551244)} 

err list= [np.float64(0.2904388136605267), np.float64(0.044799393183375086), np.float64(0.11910785094169732), np.float64(0.07703258897555124), np.float64(0.09503258897555124), np.float64(0.02503258897555125), np.float64(0.019032588975551244)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7355650293577753), 4: np.float64(0.22345912311288035), 8: np.float64(0.0367079956150098), 32: np.float64(0.0010669629785837686), 27: np.float64(0.0010669629785837686), 82: np.float64(0.0010669629785837686), 0: np.float64(0.0010669629785837686)}
err dic= {1: np.float64(0.5135650293577754), 4: np.float64(0.0065408768871196565), 8: np.float64(0.19529200438499023), 32: np.float64(0.10093303702141622), 27: np.float64(0.11893303702141622), 82: np.float64(0.048933037021416236), 0: np.float64(0.04293303702141623)} 

err list= [np.float64(0.5135650293577754), np.float64(0.0065408768871196565), np.float64(0.19529200438499023), np.float64(0.10093303702141622), np.float64(0.11893303702141622), np.float64(0.048933037021416236), np.float64(0.04293303702141623)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8492872564998697), 4: np.float64(0.14190500256776173), 8: np.float64(0.008544477292741567), 32: np.float64(6.581590990708968e-05), 27: np.float64(6.581590990708968e-05), 82: np.float64(6.581590990708968e-05), 0: np.float64(6.581590990708968e-05)}
err dic= {1: np.float64(0.6272872564998697), 4: np.float64(0.08809499743223828), 8: np.float64(0.22345552270725844), 32: np.float64(0.1019341840900929), 27: np.float64(0.1199341840900929), 82: np.float64(0.04993418409009291), 0: np.float64(0.043934184090092906)} 

err list= [np.float64(0.6272872564998697), np.float64(0.08809499743223828), np.float64(0.22345552270725844), np.float64(0.1019341840900929), np.float64(0.1199341840900929), np.float64(0.04993418409009291), np.float64(0.043934184090092906)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159563275774966), 4: np.float64(0.08226047230486219), 8: np.float64(0.0017652706071234051), 32: np.float64(4.482377629211129e-06), 27: np.float64(4.482377629211129e-06), 82: np.float64(4.482377629211129e-06), 0: np.float64(4.482377629211129e-06)}
err dic= {1: np.float64(0.6939563275774966), 4: np.float64(0.14773952769513782), 8: np.float64(0.23023472939287662), 32: np.float64(0.10199551762237079), 27: np.float64(0.11999551762237079), 82: np.float64(0.04999551762237079), 0: np.float64(0.043995517622370785)} 

err list= [np.float64(0.6939563275774966), np.float64(0.14773952769513782), np.float64(0.23023472939287662), np.float64(0.10199551762237079), np.float64(0.11999551762237079), np.float64(0.04999551762237079), np.float64(0.043995517622370785)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545801139845944), 4: np.float64(0.04507512344184199), 8: np.float64(0.0003435598703037698), 32: np.float64(3.006758150213267e-07), 27: np.float64(3.006758150213267e-07), 82: np.float64(3.006758150213267e-07), 0: np.float64(3.006758150213267e-07)}
err dic= {1: np.float64(0.7325801139845944), 4: np.float64(0.18492487655815804), 8: np.float64(0.23165644012969624), 32: np.float64(0.10199969932418497), 27: np.float64(0.11999969932418497), 82: np.float64(0.04999969932418498), 0: np.float64(0.043999699324184974)} 

err list= [np.float64(0.7325801139845944), np.float64(0.18492487655815804), np.float64(0.23165644012969624), np.float64(0.10199969932418497), np.float64(0.11999969932418497), np.float64(0.04999969932418498), np.float64(0.043999699324184974)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9761795088563877), 4: np.float64(0.023755770125314754), 8: np.float64(6.464308285556709e-05), 32: np.float64(1.9483860536953686e-08), 27: np.float64(1.9483860536953686e-08), 82: np.float64(1.9483860536953686e-08), 0: np.float64(1.9483860536953686e-08)}
err dic= {1: np.float64(0.7541795088563877), 4: np.float64(0.20624422987468527), 8: np.float64(0.23193535691714445), 32: np.float64(0.10199998051613945), 27: np.float64(0.11999998051613946), 82: np.float64(0.049999980516139464), 0: np.float64(0.04399998051613946)} 

err list= [np.float64(0.7541795088563877), np.float64(0.20624422987468527), np.float64(0.23193535691714445), np.float64(0.10199998051613945), np.float64(0.11999998051613946), np.float64(0.049999980516139464), np.float64(0.04399998051613946)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.987814164808579), 4: np.float64(0.012173923965783505), 8: np.float64(1.1906589049099212e-05), 32: np.float64(1.1591470916911442e-09), 27: np.float64(1.1591470916911442e-09), 82: np.float64(1.1591470916911442e-09), 0: np.float64(1.1591470916911442e-09)}
err dic= {1: np.float64(0.765814164808579), 4: np.float64(0.2178260760342165), 8: np.float64(0.23198809341095092), 32: np.float64(0.1019999988408529), 27: np.float64(0.1199999988408529), 82: np.float64(0.04999999884085291), 0: np.float64(0.04399999884085291)} 

err list= [np.float64(0.765814164808579), np.float64(0.2178260760342165), np.float64(0.23198809341095092), np.float64(0.1019999988408529), np.float64(0.1199999988408529), np.float64(0.04999999884085291), np.float64(0.04399999884085291)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855160651335), 4: np.float64(0.006112322432405925), 8: np.float64(2.161251950355805e-06), 32: np.float64(6.262742247156159e-11), 27: np.float64(6.262742247156159e-11), 82: np.float64(6.262742247156159e-11), 0: np.float64(6.262742247156159e-11)}
err dic= {1: np.float64(0.7718855160651336), 4: np.float64(0.2238876775675941), 8: np.float64(0.23199783874804966), 32: np.float64(0.10199999993737258), 27: np.float64(0.11999999993737258), 82: np.float64(0.04999999993737258), 0: np.float64(0.04399999993737257)} 

err list= [np.float64(0.7718855160651336), np.float64(0.2238876775675941), np.float64(0.23199783874804966), np.float64(0.10199999993737258), np.float64(0.11999999993737258), np.float64(0.04999999993737258), np.float64(0.04399999993737257)]
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(0.16449978411132465), 4: np.float64(0.09091593139396462), 6: np.float64(0.08658514804941235), 51: np.float64(0.16449978411132465), 82: np.float64(0.16449978411132465), 41: np.float64(0.16449978411132465), 0: np.float64(0.16449978411132465)}
err dic= {9: np.float64(0.05650021588867535), 4: np.float64(0.15408406860603538), 6: np.float64(0.16941485195058764), 51: np.float64(0.07849978411132466), 82: np.float64(0.12449978411132465), 41: np.float64(0.07149978411132465), 0: np.float64(0.10549978411132466)} 

err list= [np.float64(0.05650021588867535), np.float64(0.15408406860603538), np.float64(0.16941485195058764), np.float64(0.07849978411132466), np.float64(0.12449978411132465), np.float64(0.07149978411132465), np.float64(0.10549978411132466)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.15609846641534053), 4: np.float64(0.1150764229442695), 6: np.float64(0.10443124497902687), 51: np.float64(0.15609846641534053), 82: np.float64(0.15609846641534053), 41: np.float64(0.15609846641534053), 0: np.float64(0.15609846641534053)}
err dic= {9: np.float64(0.06490153358465947), 4: np.float64(0.1299235770557305), 6: np.float64(0.15156875502097314), 51: np.float64(0.07009846641534054), 82: np.float64(0.11609846641534052), 41: np.float64(0.06309846641534053), 0: np.float64(0.09709846641534053)} 

err list= [np.float64(0.06490153358465947), np.float64(0.1299235770557305), np.float64(0.15156875502097314), np.float64(0.07009846641534054), np.float64(0.11609846641534052), np.float64(0.06309846641534053), np.float64(0.09709846641534053)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(0.13624440630647003), 4: np.float64(0.17460403343606842), 6: np.float64(0.14417393503158105), 51: np.float64(0.13624440630647003), 82: np.float64(0.13624440630647003), 41: np.float64(0.13624440630647003), 0: np.float64(0.13624440630647003)}
err dic= {9: np.float64(0.08475559369352997), 4: np.float64(0.07039596656393157), 6: np.float64(0.11182606496841896), 51: np.float64(0.050244406306470035), 82: np.float64(0.09624440630647002), 41: np.float64(0.04324440630647003), 0: np.float64(0.07724440630647003)} 

err list= [np.float64(0.08475559369352997), np.float64(0.07039596656393157), np.float64(0.11182606496841896), np.float64(0.050244406306470035), np.float64(0.09624440630647002), np.float64(0.04324440630647003), np.float64(0.07724440630647003)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(0.07242489108567617), 4: np.float64(0.3902966476287485), 6: np.float64(0.2475788969428681), 51: np.float64(0.07242489108567617), 82: np.float64(0.07242489108567617), 41: np.float64(0.07242489108567617), 0: np.float64(0.07242489108567617)}
err dic= {9: np.float64(0.14857510891432385), 4: np.float64(0.1452966476287485), 6: np.float64(0.008421103057131896), 51: np.float64(0.013575108914323827), 82: np.float64(0.032424891085676165), 41: np.float64(0.020575108914323834), 0: np.float64(0.013424891085676169)} 

err list= [np.float64(0.14857510891432385), np.float64(0.1452966476287485), np.float64(0.008421103057131896), np.float64(0.013575108914323827), np.float64(0.032424891085676165), np.float64(0.020575108914323834), np.float64(0.013424891085676169)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(0.013706999543609225), 4: np.float64(0.6533417328137932), 6: np.float64(0.278123269468162), 51: np.float64(0.013706999543609225), 82: np.float64(0.013706999543609225), 41: np.float64(0.013706999543609225), 0: np.float64(0.013706999543609225)}
err dic= {9: np.float64(0.20729300045639076), 4: np.float64(0.40834173281379316), 6: np.float64(0.02212326946816201), 51: np.float64(0.07229300045639077), 82: np.float64(0.026293000456390776), 41: np.float64(0.07929300045639077), 0: np.float64(0.04529300045639077)} 

err list= [np.float64(0.20729300045639076), np.float64(0.40834173281379316), np.float64(0.02212326946816201), np.float64(0.07229300045639077), np.float64(0.026293000456390776), np.float64(0.07929300045639077), np.float64(0.04529300045639077)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(0.0016504347549812196), 4: np.float64(0.7731394740070952), 6: np.float64(0.21860835221799996), 51: np.float64(0.0016504347549812196), 82: np.float64(0.0016504347549812196), 41: np.float64(0.0016504347549812196), 0: np.float64(0.0016504347549812196)}
err dic= {9: np.float64(0.21934956524501878), 4: np.float64(0.5281394740070952), 6: np.float64(0.03739164778200005), 51: np.float64(0.08434956524501877), 82: np.float64(0.03834956524501878), 41: np.float64(0.09134956524501878), 0: np.float64(0.057349565245018774)} 

err list= [np.float64(0.21934956524501878), np.float64(0.5281394740070952), np.float64(0.03739164778200005), np.float64(0.08434956524501877), np.float64(0.03834956524501878), np.float64(0.09134956524501878), np.float64(0.057349565245018774)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(0.00021146633542332846), 4: np.float64(0.843327847737953), 6: np.float64(0.1556148205849283), 51: np.float64(0.00021146633542332846), 82: np.float64(0.00021146633542332846), 41: np.float64(0.00021146633542332846), 0: np.float64(0.00021146633542332846)}
err dic= {9: np.float64(0.22078853366457668), 4: np.float64(0.598327847737953), 6: np.float64(0.10038517941507172), 51: np.float64(0.08578853366457666), 82: np.float64(0.03978853366457667), 41: np.float64(0.09278853366457666), 0: np.float64(0.05878853366457667)} 

err list= [np.float64(0.22078853366457668), np.float64(0.598327847737953), np.float64(0.10038517941507172), np.float64(0.08578853366457666), np.float64(0.03978853366457667), np.float64(0.09278853366457666), np.float64(0.05878853366457667)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(3.24638446937738e-05), 4: np.float64(0.8932662459230376), 6: np.float64(0.10657143485349252), 51: np.float64(3.24638446937738e-05), 82: np.float64(3.24638446937738e-05), 41: np.float64(3.24638446937738e-05), 0: np.float64(3.24638446937738e-05)}
err dic= {9: np.float64(0.22096753615530623), 4: np.float64(0.6482662459230376), 6: np.float64(0.14942856514650749), 51: np.float64(0.08596753615530622), 82: np.float64(0.039967536155306224), 41: np.float64(0.09296753615530623), 0: np.float64(0.05896753615530622)} 

err list= [np.float64(0.22096753615530623), np.float64(0.6482662459230376), np.float64(0.14942856514650749), np.float64(0.08596753615530622), np.float64(0.039967536155306224), np.float64(0.09296753615530623), np.float64(0.05896753615530622)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(5.352867144809124e-06), 4: np.float64(0.9288866230042216), 6: np.float64(0.0710866126600542), 51: np.float64(5.352867144809124e-06), 82: np.float64(5.352867144809124e-06), 41: np.float64(5.352867144809124e-06), 0: np.float64(5.352867144809124e-06)}
err dic= {9: np.float64(0.2209946471328552), 4: np.float64(0.6838866230042216), 6: np.float64(0.1849133873399458), 51: np.float64(0.08599464713285518), 82: np.float64(0.03999464713285519), 41: np.float64(0.09299464713285518), 0: np.float64(0.05899464713285519)} 

err list= [np.float64(0.2209946471328552), np.float64(0.6838866230042216), np.float64(0.1849133873399458), np.float64(0.08599464713285518), np.float64(0.03999464713285519), np.float64(0.09299464713285518), np.float64(0.05899464713285519)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(8.394666553929367e-07), 4: np.float64(0.9535464927278381), 6: np.float64(0.04644930993888531), 51: np.float64(8.394666553929367e-07), 82: np.float64(8.394666553929367e-07), 41: np.float64(8.394666553929367e-07), 0: np.float64(8.394666553929367e-07)}
err dic= {9: np.float64(0.22099916053334462), 4: np.float64(0.7085464927278381), 6: np.float64(0.2095506900611147), 51: np.float64(0.0859991605333446), 82: np.float64(0.03999916053334461), 41: np.float64(0.0929991605333446), 0: np.float64(0.058999160533344606)} 

err list= [np.float64(0.22099916053334462), np.float64(0.7085464927278381), np.float64(0.2095506900611147), np.float64(0.0859991605333446), np.float64(0.03999916053334461), np.float64(0.0929991605333446), np.float64(0.058999160533344606)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(1.2089377617087916e-07), 4: np.float64(0.9701394548178333), 6: np.float64(0.029859940713285918), 51: np.float64(1.2089377617087916e-07), 82: np.float64(1.2089377617087916e-07), 41: np.float64(1.2089377617087916e-07), 0: np.float64(1.2089377617087916e-07)}
err dic= {9: np.float64(0.22099987910622382), 4: np.float64(0.7251394548178333), 6: np.float64(0.2261400592867141), 51: np.float64(0.08599987910622382), 82: np.float64(0.03999987910622383), 41: np.float64(0.09299987910622383), 0: np.float64(0.058999879106223826)} 

err list= [np.float64(0.22099987910622382), np.float64(0.7251394548178333), np.float64(0.2261400592867141), np.float64(0.08599987910622382), np.float64(0.03999987910622383), np.float64(0.09299987910622383), np.float64(0.058999879106223826)]
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(0.11434780242142137), 9: np.float64(0.10379513724101894), 6: np.float64(0.11152454512026952), 39: np.float64(0.1675831288043216), 80: np.float64(0.1675831288043216), 68: np.float64(0.1675831288043216), 0: np.float64(0.1675831288043216)}
err dic= {5: np.float64(0.13065219757857863), 9: np.float64(0.12420486275898107), 6: np.float64(0.1464754548797305), 39: np.float64(0.0675831288043216), 80: np.float64(0.1045831288043216), 68: np.float64(0.11158312880432161), 0: np.float64(0.1175831288043216)} 

err list= [np.float64(0.13065219757857863), np.float64(0.12420486275898107), np.float64(0.1464754548797305), np.float64(0.0675831288043216), np.float64(0.1045831288043216), np.float64(0.11158312880432161), np.float64(0.1175831288043216)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.14673123943871477), 9: np.float64(0.12106860127348384), 6: np.float64(0.13957507244756462), 39: np.float64(0.14815627171006102), 80: np.float64(0.14815627171006102), 68: np.float64(0.14815627171006102), 0: np.float64(0.14815627171006102)}
err dic= {5: np.float64(0.09826876056128522), 9: np.float64(0.10693139872651616), 6: np.float64(0.11842492755243539), 39: np.float64(0.04815627171006101), 80: np.float64(0.08515627171006102), 68: np.float64(0.09215627171006102), 0: np.float64(0.09815627171006101)} 

err list= [np.float64(0.09826876056128522), np.float64(0.10693139872651616), np.float64(0.11842492755243539), np.float64(0.04815627171006101), np.float64(0.08515627171006102), np.float64(0.09215627171006102), np.float64(0.09815627171006101)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.21880038954368802), 9: np.float64(0.149845258847401), 6: np.float64(0.19797877953997253), 39: np.float64(0.1083438930172374), 80: np.float64(0.1083438930172374), 68: np.float64(0.1083438930172374), 0: np.float64(0.1083438930172374)}
err dic= {5: np.float64(0.026199610456311972), 9: np.float64(0.07815474115259902), 6: np.float64(0.060021220460027475), 39: np.float64(0.008343893017237397), 80: np.float64(0.0453438930172374), 68: np.float64(0.0523438930172374), 0: np.float64(0.0583438930172374)} 

err list= [np.float64(0.026199610456311972), np.float64(0.07815474115259902), np.float64(0.060021220460027475), np.float64(0.008343893017237397), np.float64(0.0453438930172374), np.float64(0.0523438930172374), np.float64(0.0583438930172374)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.40616914469582405), 9: np.float64(0.1629038091899281), 6: np.float64(0.3163248479485509), 39: np.float64(0.028650549541422557), 80: np.float64(0.028650549541422557), 68: np.float64(0.028650549541422557), 0: np.float64(0.028650549541422557)}
err dic= {5: np.float64(0.16116914469582405), 9: np.float64(0.0650961908100719), 6: np.float64(0.05832484794855092), 39: np.float64(0.07134945045857745), 80: np.float64(0.034349450458577444), 68: np.float64(0.027349450458577444), 0: np.float64(0.021349450458577446)} 

err list= [np.float64(0.16116914469582405), np.float64(0.0650961908100719), np.float64(0.05832484794855092), np.float64(0.07134945045857745), np.float64(0.034349450458577444), np.float64(0.027349450458577444), np.float64(0.021349450458577446)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5615961673416582), 9: np.float64(0.09077656334815212), 6: np.float64(0.3406252938698224), 39: np.float64(0.0017504938600896064), 80: np.float64(0.0017504938600896064), 68: np.float64(0.0017504938600896064), 0: np.float64(0.0017504938600896064)}
err dic= {5: np.float64(0.3165961673416582), 9: np.float64(0.13722343665184789), 6: np.float64(0.08262529386982237), 39: np.float64(0.0982495061399104), 80: np.float64(0.06124950613991039), 68: np.float64(0.05424950613991039), 0: np.float64(0.04824950613991039)} 

err list= [np.float64(0.3165961673416582), np.float64(0.13722343665184789), np.float64(0.08262529386982237), np.float64(0.0982495061399104), np.float64(0.06124950613991039), np.float64(0.05424950613991039), np.float64(0.04824950613991039)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6514857939610517), 9: np.float64(0.04014977179785385), 6: np.float64(0.30774009865312624), 39: np.float64(0.0001560838969905853), 80: np.float64(0.0001560838969905853), 68: np.float64(0.0001560838969905853), 0: np.float64(0.0001560838969905853)}
err dic= {5: np.float64(0.40648579396105167), 9: np.float64(0.18785022820214614), 6: np.float64(0.04974009865312623), 39: np.float64(0.09984391610300943), 80: np.float64(0.06284391610300942), 68: np.float64(0.055843916103009414), 0: np.float64(0.049843916103009415)} 

err list= [np.float64(0.40648579396105167), np.float64(0.18785022820214614), np.float64(0.04974009865312623), np.float64(0.09984391610300943), np.float64(0.06284391610300942), np.float64(0.055843916103009414), np.float64(0.049843916103009415)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7190542750278802), 9: np.float64(0.01635577201320525), 6: np.float64(0.2645252848691934), 39: np.float64(1.6167022430167505e-05), 80: np.float64(1.6167022430167505e-05), 68: np.float64(1.6167022430167505e-05), 0: np.float64(1.6167022430167505e-05)}
err dic= {5: np.float64(0.4740542750278802), 9: np.float64(0.21164422798679475), 6: np.float64(0.006525284869193404), 39: np.float64(0.09998383297756984), 80: np.float64(0.06298383297756983), 68: np.float64(0.055983832977569835), 0: np.float64(0.049983832977569836)} 

err list= [np.float64(0.4740542750278802), np.float64(0.21164422798679475), np.float64(0.006525284869193404), np.float64(0.09998383297756984), np.float64(0.06298383297756983), np.float64(0.055983832977569835), np.float64(0.049983832977569836)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723517437070595), 9: np.float64(0.00635904525354752), 6: np.float64(0.22128247943540452), 39: np.float64(1.6829009972776493e-06), 80: np.float64(1.6829009972776493e-06), 68: np.float64(1.6829009972776493e-06), 0: np.float64(1.6829009972776493e-06)}
err dic= {5: np.float64(0.5273517437070595), 9: np.float64(0.22164095474645248), 6: np.float64(0.036717520564595485), 39: np.float64(0.09999831709900273), 80: np.float64(0.06299831709900272), 68: np.float64(0.05599831709900272), 0: np.float64(0.04999831709900272)} 

err list= [np.float64(0.5273517437070595), np.float64(0.22164095474645248), np.float64(0.036717520564595485), np.float64(0.09999831709900273), np.float64(0.06299831709900272), np.float64(0.05599831709900272), np.float64(0.04999831709900272)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.8156051626306513), 9: np.float64(0.0024080389846926876), 6: np.float64(0.18198611055566355), 39: np.float64(1.7195724798028442e-07), 80: np.float64(1.7195724798028442e-07), 68: np.float64(1.7195724798028442e-07), 0: np.float64(1.7195724798028442e-07)}
err dic= {5: np.float64(0.5706051626306513), 9: np.float64(0.22559196101530732), 6: np.float64(0.07601388944433646), 39: np.float64(0.09999982804275202), 80: np.float64(0.06299982804275202), 68: np.float64(0.05599982804275202), 0: np.float64(0.04999982804275202)} 

err list= [np.float64(0.5706051626306513), np.float64(0.22559196101530732), np.float64(0.07601388944433646), np.float64(0.09999982804275202), np.float64(0.06299982804275202), np.float64(0.05599982804275202), np.float64(0.04999982804275202)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511868464478995), 9: np.float64(0.0008989931364884126), 6: np.float64(0.1479140949204), 39: np.float64(1.6373802854229294e-08), 80: np.float64(1.6373802854229294e-08), 68: np.float64(1.6373802854229294e-08), 0: np.float64(1.6373802854229294e-08)}
err dic= {5: np.float64(0.6061868464478996), 9: np.float64(0.2271010068635116), 6: np.float64(0.1100859050796), 39: np.float64(0.09999998362619715), 80: np.float64(0.06299998362619715), 68: np.float64(0.055999983626197146), 0: np.float64(0.04999998362619715)} 

err list= [np.float64(0.6061868464478996), np.float64(0.2271010068635116), np.float64(0.1100859050796), np.float64(0.09999998362619715), np.float64(0.06299998362619715), np.float64(0.055999983626197146), np.float64(0.04999998362619715)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036356108911), 9: np.float64(0.0003331497510648564), 6: np.float64(0.11916320891626717), 39: np.float64(1.4304441904184042e-09), 80: np.float64(1.4304441904184042e-09), 68: np.float64(1.4304441904184042e-09), 0: np.float64(1.4304441904184042e-09)}
err dic= {5: np.float64(0.6355036356108911), 9: np.float64(0.22766685024893515), 6: np.float64(0.13883679108373284), 39: np.float64(0.09999999856955581), 80: np.float64(0.0629999985695558), 68: np.float64(0.05599999856955581), 0: np.float64(0.04999999856955581)} 

err list= [np.float64(0.6355036356108911), np.float64(0.22766685024893515), np.float64(0.13883679108373284), np.float64(0.09999999856955581), np.float64(0.0629999985695558), np.float64(0.05599999856955581), np.float64(0.04999999856955581)]
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(0.09442661240330383), 3: np.float64(0.10150269518386676), 8: np.float64(0.08993749207293047), 15: np.float64(0.17853330008497434), 78: np.float64(0.17853330008497434), 97: np.float64(0.17853330008497434), 0: np.float64(0.17853330008497434)}
err dic= {6: np.float64(0.12657338759669617), 3: np.float64(0.13349730481613323), 8: np.float64(0.14806250792706951), 15: np.float64(0.005533300084974352), 78: np.float64(0.12253330008497434), 97: np.float64(0.13953330008497433), 0: np.float64(0.14053330008497433)} 

err list= [np.float64(0.12657338759669617), np.float64(0.13349730481613323), np.float64(0.14806250792706951), np.float64(0.005533300084974352), np.float64(0.12253330008497434), np.float64(0.13953330008497433), np.float64(0.14053330008497433)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.114425502045447), 3: np.float64(0.1320275952380989), 8: np.float64(0.10385647431634283), 15: np.float64(0.16242260710002807), 78: np.float64(0.16242260710002807), 97: np.float64(0.16242260710002807), 0: np.float64(0.16242260710002807)}
err dic= {6: np.float64(0.106574497954553), 3: np.float64(0.10297240476190109), 8: np.float64(0.13414352568365717), 15: np.float64(0.010577392899971921), 78: np.float64(0.10642260710002807), 97: np.float64(0.12342260710002806), 0: np.float64(0.12442260710002806)} 

err list= [np.float64(0.106574497954553), np.float64(0.10297240476190109), np.float64(0.13414352568365717), np.float64(0.010577392899971921), np.float64(0.10642260710002807), np.float64(0.12342260710002806), np.float64(0.12442260710002806)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.15627592960102088), 3: np.float64(0.2066172392694051), 8: np.float64(0.1290220980033822), 15: np.float64(0.1270211832815494), 78: np.float64(0.1270211832815494), 97: np.float64(0.1270211832815494), 0: np.float64(0.1270211832815494)}
err dic= {6: np.float64(0.06472407039897912), 3: np.float64(0.028382760730594897), 8: np.float64(0.10897790199661778), 15: np.float64(0.04597881671845058), 78: np.float64(0.07102118328154941), 97: np.float64(0.0880211832815494), 0: np.float64(0.0890211832815494)} 

err list= [np.float64(0.06472407039897912), np.float64(0.028382760730594897), np.float64(0.10897790199661778), np.float64(0.04597881671845058), np.float64(0.07102118328154941), np.float64(0.0880211832815494), np.float64(0.0890211832815494)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.23624326722702996), 3: np.float64(0.449403276752534), 8: np.float64(0.1483072690259399), 15: np.float64(0.041511546748624076), 78: np.float64(0.041511546748624076), 97: np.float64(0.041511546748624076), 0: np.float64(0.041511546748624076)}
err dic= {6: np.float64(0.015243267227029955), 3: np.float64(0.214403276752534), 8: np.float64(0.08969273097406008), 15: np.float64(0.13148845325137593), 78: np.float64(0.014488453251375925), 97: np.float64(0.002511546748624076), 0: np.float64(0.0035115467486240767)} 

err list= [np.float64(0.015243267227029955), np.float64(0.214403276752534), np.float64(0.08969273097406008), np.float64(0.13148845325137593), np.float64(0.014488453251375925), np.float64(0.002511546748624076), np.float64(0.0035115467486240767)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.20797407169340953), 3: np.float64(0.6970209595791879), 8: np.float64(0.08240540476500452), 15: np.float64(0.0031498909905995592), 78: np.float64(0.0031498909905995592), 97: np.float64(0.0031498909905995592), 0: np.float64(0.0031498909905995592)}
err dic= {6: np.float64(0.013025928306590467), 3: np.float64(0.4620209595791879), 8: np.float64(0.15559459523499547), 15: np.float64(0.16985010900940042), 78: np.float64(0.052850109009400445), 97: np.float64(0.035850109009400444), 0: np.float64(0.03485010900940044)} 

err list= [np.float64(0.013025928306590467), np.float64(0.4620209595791879), np.float64(0.15559459523499547), np.float64(0.16985010900940042), np.float64(0.052850109009400445), np.float64(0.035850109009400444), np.float64(0.03485010900940044)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13650717703375861), 3: np.float64(0.8292311522685146), 8: np.float64(0.033160679986040026), 15: np.float64(0.00027524767792212203), 78: np.float64(0.00027524767792212203), 97: np.float64(0.00027524767792212203), 0: np.float64(0.00027524767792212203)}
err dic= {6: np.float64(0.08449282296624139), 3: np.float64(0.5942311522685146), 8: np.float64(0.20483932001395996), 15: np.float64(0.17272475232207787), 78: np.float64(0.05572475232207788), 97: np.float64(0.03872475232207788), 0: np.float64(0.03772475232207788)} 

err list= [np.float64(0.08449282296624139), np.float64(0.5942311522685146), np.float64(0.20483932001395996), np.float64(0.17272475232207787), np.float64(0.05572475232207788), np.float64(0.03872475232207788), np.float64(0.03772475232207788)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.0806460114385459), 3: np.float64(0.9073954028797347), 8: np.float64(0.011835386634318495), 15: np.float64(3.079976184986902e-05), 78: np.float64(3.079976184986902e-05), 97: np.float64(3.079976184986902e-05), 0: np.float64(3.079976184986902e-05)}
err dic= {6: np.float64(0.1403539885614541), 3: np.float64(0.6723954028797348), 8: np.float64(0.2261646133656815), 15: np.float64(0.17296920023815013), 78: np.float64(0.055969200238150135), 97: np.float64(0.038969200238150134), 0: np.float64(0.03796920023815013)} 

err list= [np.float64(0.1403539885614541), np.float64(0.6723954028797348), np.float64(0.2261646133656815), np.float64(0.17296920023815013), np.float64(0.055969200238150135), np.float64(0.038969200238150134), np.float64(0.03796920023815013)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.044646762172778465), 3: np.float64(0.9514032837085055), 8: np.float64(0.003936012952233576), 15: np.float64(3.485291620740743e-06), 78: np.float64(3.485291620740743e-06), 97: np.float64(3.485291620740743e-06), 0: np.float64(3.485291620740743e-06)}
err dic= {6: np.float64(0.17635323782722154), 3: np.float64(0.7164032837085055), 8: np.float64(0.2340639870477664), 15: np.float64(0.17299651470837923), 78: np.float64(0.05599651470837926), 97: np.float64(0.03899651470837926), 0: np.float64(0.03799651470837926)} 

err list= [np.float64(0.17635323782722154), np.float64(0.7164032837085055), np.float64(0.2340639870477664), np.float64(0.17299651470837923), np.float64(0.05599651470837926), np.float64(0.03899651470837926), np.float64(0.03799651470837926)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023649878990142176), 3: np.float64(0.9750980590180705), 8: np.float64(0.0012505453081045528), 15: np.float64(3.791709207732022e-07), 78: np.float64(3.791709207732022e-07), 97: np.float64(3.791709207732022e-07), 0: np.float64(3.791709207732022e-07)}
err dic= {6: np.float64(0.19735012100985783), 3: np.float64(0.7400980590180705), 8: np.float64(0.23674945469189543), 15: np.float64(0.17299962082907921), 78: np.float64(0.05599962082907923), 97: np.float64(0.03899962082907923), 0: np.float64(0.03799962082907923)} 

err list= [np.float64(0.19735012100985783), np.float64(0.7400980590180705), np.float64(0.23674945469189543), np.float64(0.17299962082907921), np.float64(0.05599962082907923), np.float64(0.03899962082907923), np.float64(0.03799962082907923)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.012148810369171113), 3: np.float64(0.9874655535173129), 8: np.float64(0.0003854855503131166), 15: np.float64(3.76408006314034e-08), 78: np.float64(3.76408006314034e-08), 97: np.float64(3.76408006314034e-08), 0: np.float64(3.76408006314034e-08)}
err dic= {6: np.float64(0.20885118963082888), 3: np.float64(0.7524655535173129), 8: np.float64(0.23761451444968687), 15: np.float64(0.17299996235919934), 78: np.float64(0.05599996235919937), 97: np.float64(0.03899996235919937), 0: np.float64(0.03799996235919937)} 

err list= [np.float64(0.20885118963082888), np.float64(0.7524655535173129), np.float64(0.23761451444968687), np.float64(0.17299996235919934), np.float64(0.05599996235919937), np.float64(0.03899996235919937), np.float64(0.03799996235919937)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.0061065102541364765), 3: np.float64(0.9937770587332426), 8: np.float64(0.00011641749873188503), 15: np.float64(3.3784721444430164e-09), 78: np.float64(3.3784721444430164e-09), 97: np.float64(3.3784721444430164e-09), 0: np.float64(3.3784721444430164e-09)}
err dic= {6: np.float64(0.21489348974586353), 3: np.float64(0.7587770587332426), 8: np.float64(0.2378835825012681), 15: np.float64(0.17299999662152785), 78: np.float64(0.05599999662152785), 97: np.float64(0.03899999662152785), 0: np.float64(0.03799999662152785)} 

err list= [np.float64(0.21489348974586353), np.float64(0.7587770587332426), np.float64(0.2378835825012681), np.float64(0.17299999662152785), np.float64(0.05599999662152785), np.float64(0.03899999662152785), np.float64(0.03799999662152785)]
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(0.10360895320028879), 2: np.float64(0.11958057249904591), 4: np.float64(0.11394700666957033), 95: np.float64(0.1880524492978388), 11: np.float64(0.09870611973757369), 22: np.float64(0.1880524492978388), 0: np.float64(0.1880524492978388)}
err dic= {8: np.float64(0.1313910467997112), 2: np.float64(0.0824194275009541), 4: np.float64(0.08305299333042968), 95: np.float64(0.14605244929783878), 11: np.float64(0.06729388026242632), 22: np.float64(0.05105244929783878), 0: np.float64(0.1670524492978388)} 

err list= [np.float64(0.1313910467997112), np.float64(0.0824194275009541), np.float64(0.08305299333042968), np.float64(0.14605244929783878), np.float64(0.06729388026242632), np.float64(0.05105244929783878), np.float64(0.1670524492978388)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.11989186427953825), 2: np.float64(0.15913455921654668), 4: np.float64(0.14465913858214138), 95: np.float64(0.1558147804868202), 11: np.float64(0.10887009646132141), 22: np.float64(0.1558147804868202), 0: np.float64(0.1558147804868202)}
err dic= {8: np.float64(0.11510813572046173), 2: np.float64(0.042865440783453335), 4: np.float64(0.052340861417858625), 95: np.float64(0.1138147804868202), 11: np.float64(0.0571299035386786), 22: np.float64(0.0188147804868202), 0: np.float64(0.13481478048682022)} 

err list= [np.float64(0.11510813572046173), np.float64(0.042865440783453335), np.float64(0.052340861417858625), np.float64(0.1138147804868202), np.float64(0.0571299035386786), np.float64(0.0188147804868202), np.float64(0.13481478048682022)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.1429592948377441), 2: np.float64(0.2480028012286626), 4: np.float64(0.20602380350258126), 95: np.float64(0.09497122994929777), 11: np.float64(0.11810041058312963), 22: np.float64(0.09497122994929777), 0: np.float64(0.09497122994929777)}
err dic= {8: np.float64(0.09204070516225588), 2: np.float64(0.0460028012286626), 4: np.float64(0.009023803502581251), 95: np.float64(0.05297122994929777), 11: np.float64(0.04789958941687038), 22: np.float64(0.04202877005070224), 0: np.float64(0.07397122994929776)} 

err list= [np.float64(0.09204070516225588), np.float64(0.0460028012286626), np.float64(0.009023803502581251), np.float64(0.05297122994929777), np.float64(0.04789958941687038), np.float64(0.04202877005070224), np.float64(0.07397122994929776)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.12504228216350755), 2: np.float64(0.46242344172280736), 4: np.float64(0.299327070116105), 95: np.float64(0.01181688013516262), 11: np.float64(0.07775656559208322), 22: np.float64(0.01181688013516262), 0: np.float64(0.01181688013516262)}
err dic= {8: np.float64(0.10995771783649244), 2: np.float64(0.26042344172280735), 4: np.float64(0.10232707011610498), 95: np.float64(0.030183119864837384), 11: np.float64(0.0882434344079168), 22: np.float64(0.12518311986483738), 0: np.float64(0.00918311986483738)} 

err list= [np.float64(0.10995771783649244), np.float64(0.26042344172280735), np.float64(0.10232707011610498), np.float64(0.030183119864837384), np.float64(0.0882434344079168), np.float64(0.12518311986483738), np.float64(0.00918311986483738)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04699863440338483), 2: np.float64(0.6536749451763441), 4: np.float64(0.28028573136712276), 95: np.float64(0.00043983871573968596), 11: np.float64(0.017721172905922792), 22: np.float64(0.00043983871573968596), 0: np.float64(0.00043983871573968596)}
err dic= {8: np.float64(0.18800136559661515), 2: np.float64(0.45167494517634404), 4: np.float64(0.08328573136712275), 95: np.float64(0.041560161284260315), 11: np.float64(0.14827882709407722), 22: np.float64(0.13656016128426032), 0: np.float64(0.020560161284260317)} 

err list= [np.float64(0.18800136559661515), np.float64(0.45167494517634404), np.float64(0.08328573136712275), np.float64(0.041560161284260315), np.float64(0.14827882709407722), np.float64(0.13656016128426032), np.float64(0.020560161284260317)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013534607060031064), 2: np.float64(0.7668013458367896), 4: np.float64(0.21653211325555236), 95: np.float64(2.36390642659828e-05), 11: np.float64(0.0030610166548247224), 22: np.float64(2.36390642659828e-05), 0: np.float64(2.36390642659828e-05)}
err dic= {8: np.float64(0.22146539293996892), 2: np.float64(0.5648013458367895), 4: np.float64(0.019532113255552347), 95: np.float64(0.04197636093573402), 11: np.float64(0.1629389833451753), 22: np.float64(0.13697636093573404), 0: np.float64(0.020976360935734017)} 

err list= [np.float64(0.22146539293996892), np.float64(0.5648013458367895), np.float64(0.019532113255552347), np.float64(0.04197636093573402), np.float64(0.1629389833451753), np.float64(0.13697636093573404), np.float64(0.020976360935734017)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034775183652280455), 2: np.float64(0.8410299285432017), 4: np.float64(0.15501547730777326), 95: np.float64(1.2393683624098616e-06), 11: np.float64(0.0004733576787099921), 22: np.float64(1.2393683624098616e-06), 0: np.float64(1.2393683624098616e-06)}
err dic= {8: np.float64(0.23152248163477193), 2: np.float64(0.6390299285432017), 4: np.float64(0.041984522692226744), 95: np.float64(0.04199876063163759), 11: np.float64(0.16552664232129002), 22: np.float64(0.1369987606316376), 0: np.float64(0.02099876063163759)} 

err list= [np.float64(0.23152248163477193), np.float64(0.6390299285432017), np.float64(0.041984522692226744), np.float64(0.04199876063163759), np.float64(0.16552664232129002), np.float64(0.1369987606316376), np.float64(0.02099876063163759)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467387239491243), 2: np.float64(0.8926351225528917), 4: np.float64(0.10644829406433381), 95: np.float64(6.361468321536103e-08), 11: np.float64(6.96538147762298e-05), 22: np.float64(6.361468321536103e-08), 0: np.float64(6.361468321536103e-08)}
err dic= {8: np.float64(0.23415326127605085), 2: np.float64(0.6906351225528917), 4: np.float64(0.0905517059356662), 95: np.float64(0.04199993638531679), 11: np.float64(0.1659303461852238), 22: np.float64(0.1369999363853168), 0: np.float64(0.020999936385316786)} 

err list= [np.float64(0.23415326127605085), np.float64(0.6906351225528917), np.float64(0.0905517059356662), np.float64(0.04199993638531679), np.float64(0.1659303461852238), np.float64(0.1369999363853168), np.float64(0.020999936385316786)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066373596367662), 2: np.float64(0.9287259605835172), 4: np.float64(0.07106336837218331), 95: np.float64(3.184308632105614e-09), 11: np.float64(9.997755408646783e-06), 22: np.float64(3.184308632105614e-09), 0: np.float64(3.184308632105614e-09)}
err dic= {8: np.float64(0.23479933626403632), 2: np.float64(0.7267259605835172), 4: np.float64(0.1259366316278167), 95: np.float64(0.04199999681569137), 11: np.float64(0.16599000224459137), 22: np.float64(0.1369999968156914), 0: np.float64(0.02099999681569137)} 

err list= [np.float64(0.23479933626403632), np.float64(0.7267259605835172), np.float64(0.1259366316278167), np.float64(0.04199999681569137), np.float64(0.16599000224459137), np.float64(0.1369999968156914), np.float64(0.02099999681569137)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.6823878665399245e-05), 2: np.float64(0.953506729795835), 4: np.float64(0.046445031590646293), 95: np.float64(1.4794257711360477e-10), 11: np.float64(1.4142910246354873e-06), 22: np.float64(1.4794257711360477e-10), 0: np.float64(1.4794257711360477e-10)}
err dic= {8: np.float64(0.2349531761213346), 2: np.float64(0.7515067297958349), 4: np.float64(0.15055496840935373), 95: np.float64(0.04199999985205743), 11: np.float64(0.16599858570897538), 22: np.float64(0.13699999985205744), 0: np.float64(0.020999999852057423)} 

err list= [np.float64(0.2349531761213346), np.float64(0.7515067297958349), np.float64(0.15055496840935373), np.float64(0.04199999985205743), np.float64(0.16599858570897538), np.float64(0.13699999985205744), np.float64(0.020999999852057423)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.0815608600876456e-05), 2: np.float64(0.9701298210381897), 4: np.float64(0.029859165225122414), 95: np.float64(6.280363926807124e-12), 11: np.float64(1.9810924548166526e-07), 22: np.float64(6.280363926807124e-12), 0: np.float64(6.280363926807124e-12)}
err dic= {8: np.float64(0.2349891843913991), 2: np.float64(0.7681298210381897), 4: np.float64(0.1671408347748776), 95: np.float64(0.04199999999371964), 11: np.float64(0.16599980189075453), 22: np.float64(0.13699999999371965), 0: np.float64(0.020999999993719636)} 

err list= [np.float64(0.2349891843913991), np.float64(0.7681298210381897), np.float64(0.1671408347748776), np.float64(0.04199999999371964), np.float64(0.16599980189075453), np.float64(0.13699999999371965), np.float64(0.020999999993719636)]
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(0.12249495546883347), 3: np.float64(0.11672869220588042), 9: np.float64(0.10129199985586373), 100: np.float64(0.09425026828310548), 22: np.float64(0.18841136139543715), 58: np.float64(0.18841136139543715), 0: np.float64(0.18841136139543715)}
err dic= {1: np.float64(0.09550504453116652), 3: np.float64(0.06427130779411958), 9: np.float64(0.09570800014413627), 100: np.float64(0.12774973171689452), 22: np.float64(0.07541136139543715), 58: np.float64(0.14741136139543715), 0: np.float64(0.16041136139543716)} 

err list= [np.float64(0.09550504453116652), np.float64(0.06427130779411958), np.float64(0.09570800014413627), np.float64(0.12774973171689452), np.float64(0.07541136139543715), np.float64(0.14741136139543715), np.float64(0.16041136139543716)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.1665528940920995), 3: np.float64(0.15143286638169423), 9: np.float64(0.11449323470772506), 100: np.float64(0.09920532553530907), 22: np.float64(0.1561052264277276), 58: np.float64(0.1561052264277276), 0: np.float64(0.1561052264277276)}
err dic= {1: np.float64(0.0514471059079005), 3: np.float64(0.029567133618305763), 9: np.float64(0.08250676529227495), 100: np.float64(0.12279467446469093), 22: np.float64(0.043105226427727586), 58: np.float64(0.11510522642772758), 0: np.float64(0.1281052264277276)} 

err list= [np.float64(0.0514471059079005), np.float64(0.029567133618305763), np.float64(0.08250676529227495), np.float64(0.12279467446469093), np.float64(0.043105226427727586), np.float64(0.11510522642772758), np.float64(0.1281052264277276)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.2678283099377845), 3: np.float64(0.22272908644496603), 9: np.float64(0.12948586354853914), 100: np.float64(0.09745113570508317), 22: np.float64(0.09416853478787948), 58: np.float64(0.09416853478787948), 0: np.float64(0.09416853478787948)}
err dic= {1: np.float64(0.049828309937784504), 3: np.float64(0.041729086444966035), 9: np.float64(0.06751413645146087), 100: np.float64(0.12454886429491684), 22: np.float64(0.01883146521212052), 58: np.float64(0.05316853478787948), 0: np.float64(0.06616853478787948)} 

err list= [np.float64(0.049828309937784504), np.float64(0.041729086444966035), np.float64(0.06751413645146087), np.float64(0.12454886429491684), np.float64(0.01883146521212052), np.float64(0.05316853478787948), np.float64(0.06616853478787948)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5052804209153131), 3: np.float64(0.3287017655912385), 9: np.float64(0.08993387649666508), 100: np.float64(0.04403076943254476), 22: np.float64(0.010684389188076794), 58: np.float64(0.010684389188076794), 0: np.float64(0.010684389188076794)}
err dic= {1: np.float64(0.28728042091531314), 3: np.float64(0.1477017655912385), 9: np.float64(0.10706612350333493), 100: np.float64(0.17796923056745523), 22: np.float64(0.10231561081192321), 58: np.float64(0.03031561081192321), 0: np.float64(0.017315610811923204)} 

err list= [np.float64(0.28728042091531314), np.float64(0.1477017655912385), np.float64(0.10706612350333493), np.float64(0.17796923056745523), np.float64(0.10231561081192321), np.float64(0.03031561081192321), np.float64(0.017315610811923204)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6809133504276427), 3: np.float64(0.2937932389742398), 9: np.float64(0.0198550175644565), 100: np.float64(0.004532908910253419), 22: np.float64(0.00030182804113344623), 58: np.float64(0.00030182804113344623), 0: np.float64(0.00030182804113344623)}
err dic= {1: np.float64(0.4629133504276427), 3: np.float64(0.11279323897423982), 9: np.float64(0.1771449824355435), 100: np.float64(0.21746709108974657), 22: np.float64(0.11269817195886656), 58: np.float64(0.040698171958866554), 0: np.float64(0.027698171958866553)} 

err list= [np.float64(0.4629133504276427), np.float64(0.11279323897423982), np.float64(0.1771449824355435), np.float64(0.21746709108974657), np.float64(0.11269817195886656), np.float64(0.040698171958866554), np.float64(0.027698171958866553)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.776364084415), 3: np.float64(0.2200035765078477), 9: np.float64(0.0032515064746979367), 100: np.float64(0.0003451927438374205), 22: np.float64(1.1879952869462605e-05), 58: np.float64(1.1879952869462605e-05), 0: np.float64(1.1879952869462605e-05)}
err dic= {1: np.float64(0.5583640844150001), 3: np.float64(0.03900357650784769), 9: np.float64(0.19374849352530207), 100: np.float64(0.22165480725616257), 22: np.float64(0.11298812004713055), 58: np.float64(0.04098812004713054), 0: np.float64(0.027988120047130537)} 

err list= [np.float64(0.5583640844150001), np.float64(0.03900357650784769), np.float64(0.19374849352530207), np.float64(0.22165480725616257), np.float64(0.11298812004713055), np.float64(0.04098812004713054), np.float64(0.027988120047130537)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437482606999024), 3: np.float64(0.15573962830098678), 9: np.float64(0.00048644417556270575), 100: np.float64(2.4260561994592236e-05), 22: np.float64(4.687538510238809e-07), 58: np.float64(4.687538510238809e-07), 0: np.float64(4.687538510238809e-07)}
err dic= {1: np.float64(0.6257482606999024), 3: np.float64(0.025260371699013212), 9: np.float64(0.1965135558244373), 100: np.float64(0.22197573943800541), 22: np.float64(0.11299953124614898), 58: np.float64(0.040999531246148975), 0: np.float64(0.027999531246148977)} 

err list= [np.float64(0.6257482606999024), np.float64(0.025260371699013212), np.float64(0.1965135558244373), np.float64(0.22197573943800541), np.float64(0.11299953124614898), np.float64(0.040999531246148975), np.float64(0.027999531246148977)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933411880709233), 3: np.float64(0.10658665345378887), 9: np.float64(7.044584558605561e-05), 100: np.float64(1.6573243354876441e-06), 22: np.float64(1.8435121979130086e-08), 58: np.float64(1.8435121979130086e-08), 0: np.float64(1.8435121979130086e-08)}
err dic= {1: np.float64(0.6753411880709234), 3: np.float64(0.07441334654621112), 9: np.float64(0.19692955415441396), 100: np.float64(0.2219983426756645), 22: np.float64(0.11299998156487802), 58: np.float64(0.040999981564878024), 0: np.float64(0.027999981564878023)} 

err list= [np.float64(0.6753411880709234), np.float64(0.07441334654621112), np.float64(0.19692955415441396), np.float64(0.2219983426756645), np.float64(0.11299998156487802), np.float64(0.040999981564878024), np.float64(0.027999981564878023)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011160889787), 3: np.float64(0.07108872771652017), 9: np.float64(1.004248369487257e-05), 100: np.float64(1.1156967618619916e-07), 22: np.float64(7.137095905013718e-10), 58: np.float64(7.137095905013718e-10), 0: np.float64(7.137095905013718e-10)}
err dic= {1: np.float64(0.7109011160889788), 3: np.float64(0.10991127228347983), 9: np.float64(0.19698995751630513), 100: np.float64(0.2219998884303238), 22: np.float64(0.11299999928629041), 58: np.float64(0.04099999928629041), 0: np.float64(0.02799999928629041)} 

err list= [np.float64(0.7109011160889788), np.float64(0.10991127228347983), np.float64(0.19698995751630513), np.float64(0.2219998884303238), np.float64(0.11299999928629041), np.float64(0.04099999928629041), np.float64(0.02799999928629041)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489960816278), 3: np.float64(0.04644957969159889), 9: np.float64(1.4167151794952274e-06), 100: np.float64(7.434334676834773e-09), 22: np.float64(2.5752736977847213e-11), 58: np.float64(2.5752736977847213e-11), 0: np.float64(2.5752736977847213e-11)}
err dic= {1: np.float64(0.7355489960816278), 3: np.float64(0.13455042030840111), 9: np.float64(0.1969985832848205), 100: np.float64(0.22199999256566533), 22: np.float64(0.11299999997424727), 58: np.float64(0.04099999997424726), 0: np.float64(0.027999999974247264)} 

err list= [np.float64(0.7355489960816278), np.float64(0.13455042030840111), np.float64(0.1969985832848205), np.float64(0.22199999256566533), np.float64(0.11299999997424727), np.float64(0.04099999997424726), np.float64(0.027999999974247264)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303233342), 3: np.float64(0.02985997094546106), 9: np.float64(1.9823727026598624e-07), 100: np.float64(4.913822077169616e-10), 22: np.float64(8.505047401517469e-13), 58: np.float64(8.505047401517469e-13), 0: np.float64(8.505047401517469e-13)}
err dic= {1: np.float64(0.7521398303233342), 3: np.float64(0.15114002905453894), 9: np.float64(0.19699980176272974), 100: np.float64(0.2219999995086178), 22: np.float64(0.1129999999991495), 58: np.float64(0.040999999999149495), 0: np.float64(0.027999999999149497)} 

err list= [np.float64(0.7521398303233342), np.float64(0.15114002905453894), np.float64(0.19699980176272974), np.float64(0.2219999995086178), np.float64(0.1129999999991495), np.float64(0.040999999999149495), np.float64(0.027999999999149497)]
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(0.09272142123592478), 6: np.float64(0.09506867518970859), 8: np.float64(0.09043212118875178), 16: np.float64(0.18044444559640332), 83: np.float64(0.18044444559640332), 70: np.float64(0.18044444559640332), 0: np.float64(0.18044444559640332)}
err dic= {7: np.float64(0.11427857876407521), 6: np.float64(0.15093132481029142), 8: np.float64(0.15856787881124823), 16: np.float64(0.03244444559640333), 83: np.float64(0.13244444559640334), 70: np.float64(0.12244444559640333), 0: np.float64(0.13644444559640334)} 

err list= [np.float64(0.11427857876407521), np.float64(0.15093132481029142), np.float64(0.15856787881124823), np.float64(0.03244444559640333), np.float64(0.13244444559640334), np.float64(0.12244444559640333), np.float64(0.13644444559640334)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.11070848107212237), 6: np.float64(0.11638462627481437), 8: np.float64(0.1053091647375831), 16: np.float64(0.16689943197886978), 83: np.float64(0.16689943197886978), 70: np.float64(0.16689943197886978), 0: np.float64(0.16689943197886978)}
err dic= {7: np.float64(0.09629151892787761), 6: np.float64(0.1296153737251856), 8: np.float64(0.14369083526241688), 16: np.float64(0.018899431978869785), 83: np.float64(0.11889943197886978), 70: np.float64(0.10889943197886978), 0: np.float64(0.12289943197886978)} 

err list= [np.float64(0.09629151892787761), np.float64(0.1296153737251856), np.float64(0.14369083526241688), np.float64(0.018899431978869785), np.float64(0.11889943197886978), np.float64(0.10889943197886978), np.float64(0.12289943197886978)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.14872702831655282), 6: np.float64(0.16436878642726754), 8: np.float64(0.13457378029411055), 16: np.float64(0.13808260124051863), 83: np.float64(0.13808260124051863), 70: np.float64(0.13808260124051863), 0: np.float64(0.13808260124051863)}
err dic= {7: np.float64(0.05827297168344717), 6: np.float64(0.08163121357273245), 8: np.float64(0.11442621970588945), 16: np.float64(0.00991739875948136), 83: np.float64(0.09008260124051863), 70: np.float64(0.08008260124051864), 0: np.float64(0.09408260124051863)} 

err list= [np.float64(0.05827297168344717), np.float64(0.08163121357273245), np.float64(0.11442621970588945), np.float64(0.00991739875948136), np.float64(0.09008260124051863), np.float64(0.08008260124051864), np.float64(0.09408260124051863)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.24048640210070507), 6: np.float64(0.30879065266509326), 8: np.float64(0.18729099827405382), 16: np.float64(0.06585798674003653), 83: np.float64(0.06585798674003653), 70: np.float64(0.06585798674003653), 0: np.float64(0.06585798674003653)}
err dic= {7: np.float64(0.03348640210070508), 6: np.float64(0.06279065266509326), 8: np.float64(0.06170900172594618), 16: np.float64(0.08214201325996347), 83: np.float64(0.017857986740036524), 70: np.float64(0.007857986740036522), 0: np.float64(0.021857986740036528)} 

err list= [np.float64(0.03348640210070508), np.float64(0.06279065266509326), np.float64(0.06170900172594618), np.float64(0.08214201325996347), np.float64(0.017857986740036524), np.float64(0.007857986740036522), np.float64(0.021857986740036528)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.2937089530657019), 6: np.float64(0.4842441983144882), 8: np.float64(0.1781434850664469), 16: np.float64(0.010975840888340456), 83: np.float64(0.010975840888340456), 70: np.float64(0.010975840888340456), 0: np.float64(0.010975840888340456)}
err dic= {7: np.float64(0.0867089530657019), 6: np.float64(0.23824419831448818), 8: np.float64(0.0708565149335531), 16: np.float64(0.13702415911165955), 83: np.float64(0.037024159111659544), 70: np.float64(0.047024159111659546), 0: np.float64(0.03302415911165954)} 

err list= [np.float64(0.0867089530657019), np.float64(0.23824419831448818), np.float64(0.0708565149335531), np.float64(0.13702415911165955), np.float64(0.037024159111659544), np.float64(0.047024159111659546), np.float64(0.03302415911165954)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.2770952122429821), 6: np.float64(0.5866105689216876), 8: np.float64(0.13089051018825748), 16: np.float64(0.0013509271617688171), 83: np.float64(0.0013509271617688171), 70: np.float64(0.0013509271617688171), 0: np.float64(0.0013509271617688171)}
err dic= {7: np.float64(0.07009521224298212), 6: np.float64(0.3406105689216876), 8: np.float64(0.11810948981174252), 16: np.float64(0.14664907283823117), 83: np.float64(0.046649072838231186), 70: np.float64(0.05664907283823119), 0: np.float64(0.04264907283823118)} 

err list= [np.float64(0.07009521224298212), np.float64(0.3406105689216876), np.float64(0.11810948981174252), np.float64(0.14664907283823117), np.float64(0.046649072838231186), np.float64(0.05664907283823119), np.float64(0.04264907283823118)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24448074021779445), 6: np.float64(0.6645675535422474), 8: np.float64(0.08993943808850278), 16: np.float64(0.0002530670378635691), 83: np.float64(0.0002530670378635691), 70: np.float64(0.0002530670378635691), 0: np.float64(0.0002530670378635691)}
err dic= {7: np.float64(0.03748074021779446), 6: np.float64(0.4185675535422474), 8: np.float64(0.1590605619114972), 16: np.float64(0.14774693296213642), 83: np.float64(0.04774693296213643), 70: np.float64(0.057746932962136434), 0: np.float64(0.04374693296213643)} 

err list= [np.float64(0.03748074021779446), np.float64(0.4185675535422474), np.float64(0.1590605619114972), np.float64(0.14774693296213642), np.float64(0.04774693296213643), np.float64(0.057746932962136434), np.float64(0.04374693296213643)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20929650241385328), 6: np.float64(0.7305165732215874), 8: np.float64(0.0599644519076292), 16: np.float64(5.56181142326551e-05), 83: np.float64(5.56181142326551e-05), 70: np.float64(5.56181142326551e-05), 0: np.float64(5.56181142326551e-05)}
err dic= {7: np.float64(0.002296502413853291), 6: np.float64(0.48451657322158737), 8: np.float64(0.1890355480923708), 16: np.float64(0.14794438188576733), 83: np.float64(0.04794438188576734), 70: np.float64(0.057944381885767345), 0: np.float64(0.04394438188576734)} 

err list= [np.float64(0.002296502413853291), np.float64(0.48451657322158737), np.float64(0.1890355480923708), np.float64(0.14794438188576733), np.float64(0.04794438188576734), np.float64(0.057944381885767345), np.float64(0.04394438188576734)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17528181034734447), 6: np.float64(0.7855585736627626), 8: np.float64(0.03911065841390964), 16: np.float64(1.2239393995858489e-05), 83: np.float64(1.2239393995858489e-05), 70: np.float64(1.2239393995858489e-05), 0: np.float64(1.2239393995858489e-05)}
err dic= {7: np.float64(0.03171818965265552), 6: np.float64(0.5395585736627626), 8: np.float64(0.20988934158609035), 16: np.float64(0.14798776060600413), 83: np.float64(0.04798776060600414), 70: np.float64(0.05798776060600414), 0: np.float64(0.043987760606004137)} 

err list= [np.float64(0.03171818965265552), np.float64(0.5395585736627626), np.float64(0.20988934158609035), np.float64(0.14798776060600413), np.float64(0.04798776060600414), np.float64(0.05798776060600414), np.float64(0.043987760606004137)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.14433251060910438), 6: np.float64(0.8305762517857773), 8: np.float64(0.02508122953664728), 16: np.float64(2.502017117692311e-06), 83: np.float64(2.502017117692311e-06), 70: np.float64(2.502017117692311e-06), 0: np.float64(2.502017117692311e-06)}
err dic= {7: np.float64(0.06266748939089561), 6: np.float64(0.5845762517857773), 8: np.float64(0.22391877046335273), 16: np.float64(0.1479974979828823), 83: np.float64(0.04799749798288231), 70: np.float64(0.05799749798288231), 0: np.float64(0.04399749798288231)} 

err list= [np.float64(0.06266748939089561), np.float64(0.5845762517857773), np.float64(0.22391877046335273), np.float64(0.1479974979828823), np.float64(0.04799749798288231), np.float64(0.05799749798288231), np.float64(0.04399749798288231)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11731020855495641), 6: np.float64(0.8668117119898271), 8: np.float64(0.015876210301331125), 16: np.float64(4.6728847125733434e-07), 83: np.float64(4.6728847125733434e-07), 70: np.float64(4.6728847125733434e-07), 0: np.float64(4.6728847125733434e-07)}
err dic= {7: np.float64(0.08968979144504358), 6: np.float64(0.6208117119898271), 8: np.float64(0.23312378969866887), 16: np.float64(0.14799953271152874), 83: np.float64(0.04799953271152874), 70: np.float64(0.057999532711528745), 0: np.float64(0.04399953271152874)} 

err list= [np.float64(0.08968979144504358), np.float64(0.6208117119898271), np.float64(0.23312378969866887), np.float64(0.14799953271152874), np.float64(0.04799953271152874), np.float64(0.057999532711528745), np.float64(0.04399953271152874)]
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= [0.12107937 0.11333936 0.10072603 0.08581959 0.08722443 0.09224444
 0.09768088 0.10285695 0.10855724 0.1144037  0.12012834]
mean_std= [0.         0.00774001 0.01892434 0.03058109 0.02749649 0.02749637
 0.02872929 0.03016194 0.03268955 0.0356283  0.03849277]
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
