p= 1.5 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(0.3111197284459591), 3: np.float64(0.3034381549809073), 4: np.float64(0.29594624024046845), 59: np.float64(0.022373969083167522), 40: np.float64(0.022373969083167522), 84: np.float64(0.022373969083167522), 0: np.float64(0.022373969083167522)}
err dic= {2: np.float64(0.036119728445959065), 3: np.float64(0.05643815498090732), 4: np.float64(0.04394624024046845), 59: np.float64(0.036626030916832475), 40: np.float64(0.04962603091683247), 84: np.float64(0.037626030916832476), 0: np.float64(0.012626030916832481)} 

err list= [np.float64(0.036119728445959065), np.float64(0.05643815498090732), np.float64(0.04394624024046845), np.float64(0.036626030916832475), np.float64(0.04962603091683247), np.float64(0.037626030916832476), np.float64(0.012626030916832481)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.34788258214643397), 3: np.float64(0.3309161484089747), 4: np.float64(0.31477717740906197), 59: np.float64(0.0016060230088825306), 40: np.float64(0.0016060230088825306), 84: np.float64(0.0016060230088825306), 0: np.float64(0.0016060230088825306)}
err dic= {2: np.float64(0.07288258214643395), 3: np.float64(0.08391614840897471), 4: np.float64(0.06277717740906197), 59: np.float64(0.057393976991117465), 40: np.float64(0.07039397699111746), 84: np.float64(0.058393976991117466), 0: np.float64(0.03339397699111747)} 

err list= [np.float64(0.07288258214643395), np.float64(0.08391614840897471), np.float64(0.06277717740906197), np.float64(0.057393976991117465), np.float64(0.07039397699111746), np.float64(0.058393976991117466), np.float64(0.03339397699111747)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.3671628024547842), 3: np.float64(0.332222642172034), 4: np.float64(0.3006074777560278), 59: np.float64(1.769404288583438e-06), 40: np.float64(1.769404288583438e-06), 84: np.float64(1.769404288583438e-06), 0: np.float64(1.769404288583438e-06)}
err dic= {2: np.float64(0.0921628024547842), 3: np.float64(0.08522264217203401), 4: np.float64(0.048607477756027806), 59: np.float64(0.058998230595711416), 40: np.float64(0.07199823059571141), 84: np.float64(0.05999823059571142), 0: np.float64(0.03499823059571142)} 

err list= [np.float64(0.0921628024547842), np.float64(0.08522264217203401), np.float64(0.048607477756027806), np.float64(0.058998230595711416), np.float64(0.07199823059571141), np.float64(0.05999823059571142), np.float64(0.03499823059571142)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.4192289516096963), 3: np.float64(0.32649583579983554), 4: np.float64(0.2542752125904647), 59: np.float64(7.995892188862396e-16), 40: np.float64(7.995892188862396e-16), 84: np.float64(7.995892188862396e-16), 0: np.float64(7.995892188862396e-16)}
err dic= {2: np.float64(0.1442289516096963), 3: np.float64(0.07949583579983555), 4: np.float64(0.0022752125904647036), 59: np.float64(0.0589999999999992), 40: np.float64(0.07199999999999919), 84: np.float64(0.0599999999999992), 0: np.float64(0.034999999999999205)} 

err list= [np.float64(0.1442289516096963), np.float64(0.07949583579983555), np.float64(0.0022752125904647036), np.float64(0.0589999999999992), np.float64(0.07199999999999919), np.float64(0.0599999999999992), np.float64(0.034999999999999205)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.5064803910556542), 3: np.float64(0.3071958857184985), 4: np.float64(0.18632372322584767), 59: np.float64(2.2449168218638736e-31), 40: np.float64(2.2449168218638736e-31), 84: np.float64(2.2449168218638736e-31), 0: np.float64(2.2449168218638736e-31)}
err dic= {2: np.float64(0.2314803910556542), 3: np.float64(0.06019588571849849), 4: np.float64(0.06567627677415233), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.2314803910556542), np.float64(0.06019588571849849), np.float64(0.06567627677415233), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.5897976636568126), 3: np.float64(0.27860068919627307), 4: np.float64(0.13160164714691439), 59: np.float64(7.106326512143632e-47), 40: np.float64(7.106326512143632e-47), 84: np.float64(7.106326512143632e-47), 0: np.float64(7.106326512143632e-47)}
err dic= {2: np.float64(0.3147976636568126), 3: np.float64(0.03160068919627307), 4: np.float64(0.12039835285308562), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.3147976636568126), np.float64(0.03160068919627307), np.float64(0.12039835285308562), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.6652409557748219), 3: np.float64(0.24472847105479767), 4: np.float64(0.09003057317038048), 59: np.float64(2.445724365094695e-62), 40: np.float64(2.445724365094695e-62), 84: np.float64(2.445724365094695e-62), 0: np.float64(2.445724365094695e-62)}
err dic= {2: np.float64(0.3902409557748219), 3: np.float64(0.002271528945202328), 4: np.float64(0.1619694268296195), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.3902409557748219), np.float64(0.002271528945202328), np.float64(0.1619694268296195), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.7306791292026885), 3: np.float64(0.20934307548219683), 4: np.float64(0.059977795315114234), 59: np.float64(8.811849961991297e-78), 40: np.float64(8.811849961991297e-78), 84: np.float64(8.811849961991297e-78), 0: np.float64(8.811849961991297e-78)}
err dic= {2: np.float64(0.4556791292026885), 3: np.float64(0.03765692451780317), 4: np.float64(0.19202220468488576), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.4556791292026885), np.float64(0.03765692451780317), np.float64(0.19202220468488576), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.5 

learned probs for this beta: {2: np.float64(0.7855970345892754), 3: np.float64(0.17529039214003653), 4: np.float64(0.039112573270687415), 59: np.float64(3.255376173165814e-93), 40: np.float64(3.255376173165814e-93), 84: np.float64(3.255376173165814e-93), 0: np.float64(3.255376173165814e-93)}
err dic= {2: np.float64(0.5105970345892754), 3: np.float64(0.07170960785996347), 4: np.float64(0.2128874267293126), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

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

beta is  1.75 

learned probs for this beta: {2: np.float64(0.8305845643329679), 3: np.float64(0.1443339551132097), 4: np.float64(0.025081480553821995), 59: np.float64(1.2197907024378785e-108), 40: np.float64(1.2197907024378785e-108), 84: np.float64(1.2197907024378785e-108), 0: np.float64(1.2197907024378785e-108)}
err dic= {2: np.float64(0.5555845643329679), 3: np.float64(0.10266604488679029), 4: np.float64(0.226918519446178), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

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

beta is  2 

learned probs for this beta: {2: np.float64(0.8668133321973345), 3: np.float64(0.11731042782619833), 4: np.float64(0.015876239976466765), 59: np.float64(4.608321358227288e-124), 40: np.float64(4.608321358227288e-124), 84: np.float64(4.608321358227288e-124), 0: np.float64(4.608321358227288e-124)}
err dic= {2: np.float64(0.5918133321973345), 3: np.float64(0.12968957217380167), 4: np.float64(0.23612376002353325), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.5918133321973345), np.float64(0.12968957217380167), np.float64(0.23612376002353325), np.float64(0.059), np.float64(0.072), np.float64(0.06), np.float64(0.035)]
results for assortment [2, 3, 4, 59, 40, 84] :

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

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

beta is  0.025 

learned probs for this beta: {3: np.float64(0.3152722208066332), 4: np.float64(0.3074881219398949), 8: np.float64(0.28281852099898697), 74: np.float64(0.023605284063622223), 40: np.float64(0.023605284063622223), 87: np.float64(0.023605284063622223), 0: np.float64(0.023605284063622223)}
err dic= {3: np.float64(0.05627222080663319), 4: np.float64(0.06148812193989489), 8: np.float64(0.02681852099898696), 74: np.float64(0.04239471593637778), 40: np.float64(0.053394715936377776), 87: np.float64(0.023394715936377777), 0: np.float64(0.02539471593637778)} 

err list= [np.float64(0.05627222080663319), np.float64(0.06148812193989489), np.float64(0.02681852099898696), np.float64(0.04239471593637778), np.float64(0.053394715936377776), np.float64(0.023394715936377777), np.float64(0.02539471593637778)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.35998643117293827), 4: np.float64(0.34242968575270005), 8: np.float64(0.2907224217311771), 74: np.float64(0.0017153653357963883), 40: np.float64(0.0017153653357963883), 87: np.float64(0.0017153653357963883), 0: np.float64(0.0017153653357963883)}
err dic= {3: np.float64(0.10098643117293826), 4: np.float64(0.09642968575270006), 8: np.float64(0.03472242173117712), 74: np.float64(0.06428463466420362), 40: np.float64(0.07528463466420361), 87: np.float64(0.04528463466420361), 0: np.float64(0.047284634664203615)} 

err list= [np.float64(0.10098643117293826), np.float64(0.09642968575270006), np.float64(0.03472242173117712), np.float64(0.06428463466420362), np.float64(0.07528463466420361), np.float64(0.04528463466420361), np.float64(0.047284634664203615)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.39125830698258196), 4: np.float64(0.3540251562752403), 8: np.float64(0.25470842029559915), 74: np.float64(2.0291116447963512e-06), 40: np.float64(2.0291116447963512e-06), 87: np.float64(2.0291116447963512e-06), 0: np.float64(2.0291116447963512e-06)}
err dic= {3: np.float64(0.13225830698258195), 4: np.float64(0.10802515627524029), 8: np.float64(0.0012915797044008581), 74: np.float64(0.06599797088835521), 40: np.float64(0.07699797088835521), 87: np.float64(0.0469979708883552), 0: np.float64(0.048997970888355204)} 

err list= [np.float64(0.13225830698258195), np.float64(0.10802515627524029), np.float64(0.0012915797044008581), np.float64(0.06599797088835521), np.float64(0.07699797088835521), np.float64(0.0469979708883552), np.float64(0.048997970888355204)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.47291907824291723), 4: np.float64(0.368309748464991), 8: np.float64(0.1587711732920866), 74: np.float64(1.1679681922306589e-15), 40: np.float64(1.1679681922306589e-15), 87: np.float64(1.1679681922306589e-15), 0: np.float64(1.1679681922306589e-15)}
err dic= {3: np.float64(0.21391907824291723), 4: np.float64(0.12230974846499099), 8: np.float64(0.09722882670791341), 74: np.float64(0.06599999999999884), 40: np.float64(0.07699999999999883), 87: np.float64(0.046999999999998834), 0: np.float64(0.048999999999998836)} 

err list= [np.float64(0.21391907824291723), np.float64(0.12230974846499099), np.float64(0.09722882670791341), np.float64(0.06599999999999884), np.float64(0.07699999999999883), np.float64(0.046999999999998834), np.float64(0.048999999999998836)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5841457846018505), 4: np.float64(0.3543023281029142), 8: np.float64(0.06155188729523564), 74: np.float64(4.770197967883651e-31), 40: np.float64(4.770197967883651e-31), 87: np.float64(4.770197967883651e-31), 0: np.float64(4.770197967883651e-31)}
err dic= {3: np.float64(0.3251457846018505), 4: np.float64(0.10830232810291418), 8: np.float64(0.19444811270476436), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.3251457846018505), np.float64(0.10830232810291418), np.float64(0.19444811270476436), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.6651469585882833), 4: np.float64(0.31419317589451784), 8: np.float64(0.02065986551719901), 74: np.float64(2.0074120007650777e-46), 40: np.float64(2.0074120007650777e-46), 87: np.float64(2.0074120007650777e-46), 0: np.float64(2.0074120007650777e-46)}
err dic= {3: np.float64(0.4061469585882833), 4: np.float64(0.06819317589451784), 8: np.float64(0.235340134482801), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.4061469585882833), np.float64(0.06819317589451784), np.float64(0.235340134482801), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1 

learned probs for this beta: {3: np.float64(0.7263954957320881), 4: np.float64(0.26722596903937335), 8: np.float64(0.0063785352285387455), 74: np.float64(8.716070596923295e-62), 40: np.float64(8.716070596923295e-62), 87: np.float64(8.716070596923295e-62), 0: np.float64(8.716070596923295e-62)}
err dic= {3: np.float64(0.46739549573208805), 4: np.float64(0.02122596903937335), 8: np.float64(0.24962146477146127), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.46739549573208805), np.float64(0.02122596903937335), np.float64(0.24962146477146127), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.775832220546095), 4: np.float64(0.22227965274514916), 8: np.float64(0.001888126708755253), 74: np.float64(3.887192881212511e-77), 40: np.float64(3.887192881212511e-77), 87: np.float64(3.887192881212511e-77), 0: np.float64(3.887192881212511e-77)}
err dic= {3: np.float64(0.516832220546095), 4: np.float64(0.023720347254850838), 8: np.float64(0.25411187329124474), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.516832220546095), np.float64(0.023720347254850838), np.float64(0.25411187329124474), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.5 

learned probs for this beta: {3: np.float64(0.817126200312965), 4: np.float64(0.18232549993730982), 8: np.float64(0.0005482997497247672), 74: np.float64(1.77166062574803e-92), 40: np.float64(1.77166062574803e-92), 87: np.float64(1.77166062574803e-92), 0: np.float64(1.77166062574803e-92)}
err dic= {3: np.float64(0.558126200312965), 4: np.float64(0.06367450006269018), 8: np.float64(0.25545170025027525), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.558126200312965), np.float64(0.06367450006269018), np.float64(0.25545170025027525), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  1.75 

learned probs for this beta: {3: np.float64(0.851818249643065), 4: np.float64(0.1480238163435311), 8: np.float64(0.00015793401340318878), 74: np.float64(8.21562661513435e-108), 40: np.float64(8.21562661513435e-108), 87: np.float64(8.21562661513435e-108), 0: np.float64(8.21562661513435e-108)}
err dic= {3: np.float64(0.592818249643065), 4: np.float64(0.0979761836564689), 8: np.float64(0.2558420659865968), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

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

beta is  2 

learned probs for this beta: {3: np.float64(0.8807571402411473), 4: np.float64(0.11919751703720469), 8: np.float64(4.534272164780921e-05), 74: np.float64(3.8616334099056576e-123), 40: np.float64(3.8616334099056576e-123), 87: np.float64(3.8616334099056576e-123), 0: np.float64(3.8616334099056576e-123)}
err dic= {3: np.float64(0.6217571402411473), 4: np.float64(0.1268024829627953), 8: np.float64(0.2559546572783522), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.6217571402411473), np.float64(0.1268024829627953), np.float64(0.2559546572783522), np.float64(0.066), np.float64(0.077), np.float64(0.047), np.float64(0.049)]
results for assortment [3, 4, 8, 74, 40, 87] :

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

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

beta is  0.025 

learned probs for this beta: {1: np.float64(0.32156813027054393), 3: np.float64(0.3076269537618288), 9: np.float64(0.2774081701273399), 83: np.float64(0.02334918646007181), 79: np.float64(0.02334918646007181), 70: np.float64(0.02334918646007181), 0: np.float64(0.02334918646007181)}
err dic= {1: np.float64(0.056568130270543915), 3: np.float64(0.0566269537618288), 9: np.float64(0.04240817012733994), 83: np.float64(0.028650813539928186), 79: np.float64(0.0446508135399282), 70: np.float64(0.057650813539928195), 0: np.float64(0.02465081353992819)} 

err list= [np.float64(0.056568130270543915), np.float64(0.0566269537618288), np.float64(0.04240817012733994), np.float64(0.028650813539928186), np.float64(0.0446508135399282), np.float64(0.057650813539928195), np.float64(0.02465081353992819)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3728326096684677), 3: np.float64(0.34177895431465133), 9: np.float64(0.27921915540094067), 83: np.float64(0.0015423201539851677), 79: np.float64(0.0015423201539851677), 70: np.float64(0.0015423201539851677), 0: np.float64(0.0015423201539851677)}
err dic= {1: np.float64(0.1078326096684677), 3: np.float64(0.09077895431465133), 9: np.float64(0.04421915540094068), 83: np.float64(0.05045767984601483), 79: np.float64(0.06645767984601483), 70: np.float64(0.07945767984601483), 0: np.float64(0.046457679846014836)} 

err list= [np.float64(0.1078326096684677), np.float64(0.09077895431465133), np.float64(0.04421915540094068), np.float64(0.05045767984601483), np.float64(0.06645767984601483), np.float64(0.07945767984601483), np.float64(0.046457679846014836)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.4165339197830847), 3: np.float64(0.3504512309718804), 9: np.float64(0.23300823607775034), 83: np.float64(1.6532918212899675e-06), 79: np.float64(1.6532918212899675e-06), 70: np.float64(1.6532918212899675e-06), 0: np.float64(1.6532918212899675e-06)}
err dic= {1: np.float64(0.15153391978308467), 3: np.float64(0.09945123097188041), 9: np.float64(0.0019917639222496453), 83: np.float64(0.05199834670817871), 79: np.float64(0.06799834670817871), 70: np.float64(0.08099834670817871), 0: np.float64(0.047998346708178714)} 

err list= [np.float64(0.15153391978308467), np.float64(0.09945123097188041), np.float64(0.0019917639222496453), np.float64(0.05199834670817871), np.float64(0.06799834670817871), np.float64(0.08099834670817871), np.float64(0.047998346708178714)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5316600100816884), 3: np.float64(0.3473995733591328), 9: np.float64(0.12094041655917513), 83: np.float64(7.479865390406578e-16), 79: np.float64(7.479865390406578e-16), 70: np.float64(7.479865390406578e-16), 0: np.float64(7.479865390406578e-16)}
err dic= {1: np.float64(0.2666600100816884), 3: np.float64(0.0963995733591328), 9: np.float64(0.11405958344082485), 83: np.float64(0.05199999999999925), 79: np.float64(0.06799999999999926), 70: np.float64(0.08099999999999925), 0: np.float64(0.04799999999999925)} 

err list= [np.float64(0.2666600100816884), np.float64(0.0963995733591328), np.float64(0.11405958344082485), np.float64(0.05199999999999925), np.float64(0.06799999999999926), np.float64(0.08099999999999925), np.float64(0.04799999999999925)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6768077271813894), 3: np.float64(0.29176229833973133), 9: np.float64(0.03142997447887963), 83: np.float64(1.8351079091465536e-31), 79: np.float64(1.8351079091465536e-31), 70: np.float64(1.8351079091465536e-31), 0: np.float64(1.8351079091465536e-31)}
err dic= {1: np.float64(0.41180772718138936), 3: np.float64(0.04076229833973133), 9: np.float64(0.20357002552112036), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.41180772718138936), np.float64(0.04076229833973133), np.float64(0.20357002552112036), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.774105702190221), 3: np.float64(0.2191786384934047), 9: np.float64(0.006715659316374057), 83: np.float64(4.401538145486818e-47), 79: np.float64(4.401538145486818e-47), 70: np.float64(4.401538145486818e-47), 0: np.float64(4.401538145486818e-47)}
err dic= {1: np.float64(0.509105702190221), 3: np.float64(0.031821361506595314), 9: np.float64(0.22828434068362594), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.509105702190221), np.float64(0.031821361506595314), np.float64(0.22828434068362594), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8431197129536219), 3: np.float64(0.1555712984978225), 9: np.float64(0.0013089885485560214), 83: np.float64(1.0757224859979457e-62), 79: np.float64(1.0757224859979457e-62), 70: np.float64(1.0757224859979457e-62), 0: np.float64(1.0757224859979457e-62)}
err dic= {1: np.float64(0.5781197129536219), 3: np.float64(0.0954287015021775), 9: np.float64(0.23369101145144397), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.5781197129536219), np.float64(0.0954287015021775), np.float64(0.23369101145144397), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8931967343909478), 3: np.float64(0.10655825341124762), 9: np.float64(0.0002450121978041865), 83: np.float64(2.6911430312012507e-78), 79: np.float64(2.6911430312012507e-78), 70: np.float64(2.6911430312012507e-78), 0: np.float64(2.6911430312012507e-78)}
err dic= {1: np.float64(0.6281967343909478), 3: np.float64(0.14444174658875236), 9: np.float64(0.2347549878021958), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.6281967343909478), np.float64(0.14444174658875236), np.float64(0.2347549878021958), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9288707240606471), 3: np.float64(0.07108431987050234), 9: np.float64(4.495606885052531e-05), 83: np.float64(6.854188237713304e-94), 79: np.float64(6.854188237713304e-94), 70: np.float64(6.854188237713304e-94), 0: np.float64(6.854188237713304e-94)}
err dic= {1: np.float64(0.6638707240606471), 3: np.float64(0.17991568012949766), 9: np.float64(0.23495504393114947), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.6638707240606471), np.float64(0.17991568012949766), np.float64(0.23495504393114947), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535429244147727), 3: np.float64(0.04644892580560327), 9: np.float64(8.149779623627911e-06), 83: np.float64(1.7667705322078477e-109), 79: np.float64(1.7667705322078477e-109), 70: np.float64(1.7667705322078477e-109), 0: np.float64(1.7667705322078477e-109)}
err dic= {1: np.float64(0.6885429244147727), 3: np.float64(0.20455107419439672), 9: np.float64(0.23499185022037636), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

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

beta is  2 

learned probs for this beta: {1: np.float64(0.9701386587635774), 3: np.float64(0.029859876603523985), 9: np.float64(1.4646328981753289e-06), 83: np.float64(4.5887538903881763e-125), 79: np.float64(4.5887538903881763e-125), 70: np.float64(4.5887538903881763e-125), 0: np.float64(4.5887538903881763e-125)}
err dic= {1: np.float64(0.7051386587635774), 3: np.float64(0.221140123396476), 9: np.float64(0.2349985353671018), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.7051386587635774), np.float64(0.221140123396476), np.float64(0.2349985353671018), np.float64(0.052), np.float64(0.068), np.float64(0.081), np.float64(0.048)]
results for assortment [1, 3, 9, 83, 79, 70] :

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

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

beta is  0.025 

learned probs for this beta: {1: np.float64(0.3233399819165702), 4: np.float64(0.30339010398725375), 8: np.float64(0.2789852243052027), 32: np.float64(0.023571172447743313), 27: np.float64(0.023571172447743313), 82: np.float64(0.023571172447743313), 0: np.float64(0.023571172447743313)}
err dic= {1: np.float64(0.1013399819165702), 4: np.float64(0.07339010398725374), 8: np.float64(0.04698522430520266), 32: np.float64(0.07842882755225668), 27: np.float64(0.09642882755225668), 82: np.float64(0.02642882755225669), 0: np.float64(0.020428827552256685)} 

err list= [np.float64(0.1013399819165702), np.float64(0.07339010398725374), np.float64(0.04698522430520266), np.float64(0.07842882755225668), np.float64(0.09642882755225668), np.float64(0.02642882755225669), np.float64(0.020428827552256685)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3774385921799621), 4: np.float64(0.333413418316826), 8: np.float64(0.2829078607013938), 32: np.float64(0.0015600322004546135), 27: np.float64(0.0015600322004546135), 82: np.float64(0.0015600322004546135), 0: np.float64(0.0015600322004546135)}
err dic= {1: np.float64(0.15543859217996212), 4: np.float64(0.10341341831682602), 8: np.float64(0.050907860701393776), 32: np.float64(0.10043996779954538), 27: np.float64(0.11843996779954538), 82: np.float64(0.04843996779954539), 0: np.float64(0.04243996779954538)} 

err list= [np.float64(0.15543859217996212), np.float64(0.10341341831682602), np.float64(0.050907860701393776), np.float64(0.10043996779954538), np.float64(0.11843996779954538), np.float64(0.04843996779954539), np.float64(0.04243996779954538)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.4267382633120569), 4: np.float64(0.3337233626372936), 8: np.float64(0.23953159645130365), 32: np.float64(1.694399836579802e-06), 27: np.float64(1.694399836579802e-06), 82: np.float64(1.694399836579802e-06), 0: np.float64(1.694399836579802e-06)}
err dic= {1: np.float64(0.20473826331205688), 4: np.float64(0.10372336263729356), 8: np.float64(0.007531596451303635), 32: np.float64(0.10199830560016342), 27: np.float64(0.11999830560016342), 82: np.float64(0.049998305600163426), 0: np.float64(0.04399830560016342)} 

err list= [np.float64(0.20473826331205688), np.float64(0.10372336263729356), np.float64(0.007531596451303635), np.float64(0.10199830560016342), np.float64(0.11999830560016342), np.float64(0.049998305600163426), np.float64(0.04399830560016342)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5619787294115641), 4: np.float64(0.3074614303185374), 8: np.float64(0.1305598402698944), 32: np.float64(8.059034225263658e-16), 27: np.float64(8.059034225263658e-16), 82: np.float64(8.059034225263658e-16), 0: np.float64(8.059034225263658e-16)}
err dic= {1: np.float64(0.33997872941156415), 4: np.float64(0.07746143031853739), 8: np.float64(0.10144015973010562), 32: np.float64(0.10199999999999919), 27: np.float64(0.11999999999999919), 82: np.float64(0.0499999999999992), 0: np.float64(0.04399999999999919)} 

err list= [np.float64(0.33997872941156415), np.float64(0.07746143031853739), np.float64(0.10144015973010562), np.float64(0.10199999999999919), np.float64(0.11999999999999919), np.float64(0.0499999999999992), np.float64(0.04399999999999919)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.7383008689607047), 4: np.float64(0.22465672961378827), 8: np.float64(0.03704240142550746), 32: np.float64(2.169489160664685e-31), 27: np.float64(2.169489160664685e-31), 82: np.float64(2.169489160664685e-31), 0: np.float64(2.169489160664685e-31)}
err dic= {1: np.float64(0.5163008689607047), 4: np.float64(0.00534327038621174), 8: np.float64(0.19495759857449255), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.5163008689607047), np.float64(0.00534327038621174), np.float64(0.19495759857449255), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.8494867469393008), 4: np.float64(0.14196251324014011), 8: np.float64(0.008550739820558834), 32: np.float64(5.62540230738158e-47), 27: np.float64(5.62540230738158e-47), 82: np.float64(5.62540230738158e-47), 0: np.float64(5.62540230738158e-47)}
err dic= {1: np.float64(0.6274867469393008), 4: np.float64(0.0880374867598599), 8: np.float64(0.22344926017944117), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.6274867469393008), np.float64(0.0880374867598599), np.float64(0.22344926017944117), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1 

learned probs for this beta: {1: np.float64(0.9159711584829692), 4: np.float64(0.08226343877516215), 8: np.float64(0.0017654027418688649), 32: np.float64(1.4540633691169907e-62), 27: np.float64(1.4540633691169907e-62), 82: np.float64(1.4540633691169907e-62), 0: np.float64(1.4540633691169907e-62)}
err dic= {1: np.float64(0.6939711584829692), 4: np.float64(0.14773656122483786), 8: np.float64(0.23023459725813114), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.6939711584829692), np.float64(0.14773656122483786), np.float64(0.23023459725813114), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.9545811653267549), 4: np.float64(0.045075272089623815), 8: np.float64(0.00034356258362130363), 32: np.float64(3.777357461477852e-78), 27: np.float64(3.777357461477852e-78), 82: np.float64(3.777357461477852e-78), 0: np.float64(3.777357461477852e-78)}
err dic= {1: np.float64(0.7325811653267549), 4: np.float64(0.1849247279103762), 8: np.float64(0.2316564374163787), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7325811653267549), np.float64(0.1849247279103762), np.float64(0.2316564374163787), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.976179579565728), 4: np.float64(0.023755777298822976), 8: np.float64(6.464313544905663e-05), 32: np.float64(9.859486947722335e-94), 27: np.float64(9.859486947722335e-94), 82: np.float64(9.859486947722335e-94), 0: np.float64(9.859486947722335e-94)}
err dic= {1: np.float64(0.754179579565728), 4: np.float64(0.20624422270117704), 8: np.float64(0.23193535686455097), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.754179579565728), np.float64(0.20624422270117704), np.float64(0.23193535686455097), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9878141691253702), 4: np.float64(0.012173924284659167), 8: np.float64(1.1906589970439095e-05), 32: np.float64(2.581537106272949e-109), 27: np.float64(2.581537106272949e-109), 82: np.float64(2.581537106272949e-109), 0: np.float64(2.581537106272949e-109)}
err dic= {1: np.float64(0.7658141691253703), 4: np.float64(0.21782607571534085), 8: np.float64(0.23198809341002957), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7658141691253703), np.float64(0.21782607571534085), np.float64(0.23198809341002957), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  2 

learned probs for this beta: {1: np.float64(0.9938855163026799), 4: np.float64(0.00611232244535478), 8: np.float64(2.1612519648732226e-06), 32: np.float64(6.771577420280493e-125), 27: np.float64(6.771577420280493e-125), 82: np.float64(6.771577420280493e-125), 0: np.float64(6.771577420280493e-125)}
err dic= {1: np.float64(0.7718855163026799), 4: np.float64(0.22388767755464523), 8: np.float64(0.23199783874803515), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.7718855163026799), np.float64(0.22388767755464523), np.float64(0.23199783874803515), np.float64(0.102), np.float64(0.12), np.float64(0.05), np.float64(0.044)]
results for assortment [1, 4, 8, 32, 27, 82] :

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

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

beta is  0.025 

learned probs for this beta: {9: np.float64(0.0414465292241289), 4: np.float64(0.40504313205488296), 6: np.float64(0.3877242218244729), 51: np.float64(0.0414465292241289), 82: np.float64(0.0414465292241289), 41: np.float64(0.0414465292241289), 0: np.float64(0.0414465292241289)}
err dic= {9: np.float64(0.1795534707758711), 4: np.float64(0.16004313205488296), 6: np.float64(0.1317242218244729), 51: np.float64(0.044553470775871094), 82: np.float64(0.001446529224128898), 41: np.float64(0.0515534707758711), 0: np.float64(0.017553470775871098)} 

err list= [np.float64(0.1795534707758711), np.float64(0.16004313205488296), np.float64(0.1317242218244729), np.float64(0.044553470775871094), np.float64(0.001446529224128898), np.float64(0.0515534707758711), np.float64(0.017553470775871098)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(0.0023832653771216003), 4: np.float64(0.5146535474886547), 6: np.float64(0.4734301256257376), 51: np.float64(0.0023832653771216003), 82: np.float64(0.0023832653771216003), 41: np.float64(0.0023832653771216003), 0: np.float64(0.0023832653771216003)}
err dic= {9: np.float64(0.2186167346228784), 4: np.float64(0.26965354748865467), 6: np.float64(0.2174301256257376), 51: np.float64(0.08361673462287839), 82: np.float64(0.0376167346228784), 41: np.float64(0.09061673462287839), 0: np.float64(0.0566167346228784)} 

err list= [np.float64(0.2186167346228784), np.float64(0.26965354748865467), np.float64(0.2174301256257376), np.float64(0.08361673462287839), np.float64(0.0376167346228784), np.float64(0.09061673462287839), np.float64(0.0566167346228784)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(2.2259267913947885e-06), 4: np.float64(0.5415706344662076), 6: np.float64(0.45841823589983566), 51: np.float64(2.2259267913947885e-06), 82: np.float64(2.2259267913947885e-06), 41: np.float64(2.2259267913947885e-06), 0: np.float64(2.2259267913947885e-06)}
err dic= {9: np.float64(0.2209977740732086), 4: np.float64(0.29657063446620757), 6: np.float64(0.20241823589983565), 51: np.float64(0.0859977740732086), 82: np.float64(0.039997774073208606), 41: np.float64(0.09299777407320861), 0: np.float64(0.0589977740732086)} 

err list= [np.float64(0.2209977740732086), np.float64(0.29657063446620757), np.float64(0.20241823589983565), np.float64(0.0859977740732086), np.float64(0.039997774073208606), np.float64(0.09299777407320861), np.float64(0.0589977740732086)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.25 

learned probs for this beta: {9: np.float64(1.3054118565053581e-15), 4: np.float64(0.6027772381334299), 6: np.float64(0.3972227618665631), 51: np.float64(1.3054118565053581e-15), 82: np.float64(1.3054118565053581e-15), 41: np.float64(1.3054118565053581e-15), 0: np.float64(1.3054118565053581e-15)}
err dic= {9: np.float64(0.2209999999999987), 4: np.float64(0.3577772381334299), 6: np.float64(0.14122276186656307), 51: np.float64(0.08599999999999869), 82: np.float64(0.039999999999998696), 41: np.float64(0.0929999999999987), 0: np.float64(0.05899999999999869)} 

err list= [np.float64(0.2209999999999987), np.float64(0.3577772381334299), np.float64(0.14122276186656307), np.float64(0.08599999999999869), np.float64(0.039999999999998696), np.float64(0.0929999999999987), np.float64(0.05899999999999869)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.5 

learned probs for this beta: {9: np.float64(5.850348307845487e-31), 4: np.float64(0.6976973366279521), 6: np.float64(0.3023026633720482), 51: np.float64(5.850348307845487e-31), 82: np.float64(5.850348307845487e-31), 41: np.float64(5.850348307845487e-31), 0: np.float64(5.850348307845487e-31)}
err dic= {9: np.float64(0.221), 4: np.float64(0.4526973366279521), 6: np.float64(0.04630266337204819), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.4526973366279521), np.float64(0.04630266337204819), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.75 

learned probs for this beta: {9: np.float64(2.7199972320547255e-46), 4: np.float64(0.7790173173345053), 6: np.float64(0.22098268266549476), 51: np.float64(2.7199972320547255e-46), 82: np.float64(2.7199972320547255e-46), 41: np.float64(2.7199972320547255e-46), 0: np.float64(2.7199972320547255e-46)}
err dic= {9: np.float64(0.221), 4: np.float64(0.5340173173345053), 6: np.float64(0.03501731733450525), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.5340173173345053), np.float64(0.03501731733450525), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1 

learned probs for this beta: {9: np.float64(1.2779530542899327e-61), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(1.2779530542899327e-61), 82: np.float64(1.2779530542899327e-61), 41: np.float64(1.2779530542899327e-61), 0: np.float64(1.2779530542899327e-61)}
err dic= {9: np.float64(0.221), 4: np.float64(0.5991518039744367), 6: np.float64(0.10015180397443652), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.5991518039744367), np.float64(0.10015180397443652), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.25 

learned probs for this beta: {9: np.float64(6.060754742397765e-77), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(6.060754742397765e-77), 82: np.float64(6.060754742397765e-77), 41: np.float64(6.060754742397765e-77), 0: np.float64(6.060754742397765e-77)}
err dic= {9: np.float64(0.221), 4: np.float64(0.6484014727128832), 6: np.float64(0.14940147271288337), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.6484014727128832), np.float64(0.14940147271288337), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.5 

learned probs for this beta: {9: np.float64(2.902432377348091e-92), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(2.902432377348091e-92), 82: np.float64(2.902432377348091e-92), 41: np.float64(2.902432377348091e-92), 0: np.float64(2.902432377348091e-92)}
err dic= {9: np.float64(0.221), 4: np.float64(0.6839099851249452), 6: np.float64(0.18490998512494472), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.6839099851249452), np.float64(0.18490998512494472), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  1.75 

learned probs for this beta: {9: np.float64(1.4013753249337562e-107), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(1.4013753249337562e-107), 82: np.float64(1.4013753249337562e-107), 41: np.float64(1.4013753249337562e-107), 0: np.float64(1.4013753249337562e-107)}
err dic= {9: np.float64(0.221), 4: np.float64(0.7085502818108356), 6: np.float64(0.20955028181083563), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.7085502818108356), np.float64(0.20955028181083563), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  2 

learned probs for this beta: {9: np.float64(6.806868333380587e-123), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(6.806868333380587e-123), 82: np.float64(6.806868333380587e-123), 41: np.float64(6.806868333380587e-123), 0: np.float64(6.806868333380587e-123)}
err dic= {9: np.float64(0.221), 4: np.float64(0.7251400142429856), 6: np.float64(0.22614001424298566), 51: np.float64(0.086), 82: np.float64(0.04), 41: np.float64(0.093), 0: np.float64(0.059)} 

err list= [np.float64(0.221), np.float64(0.7251400142429856), np.float64(0.22614001424298566), np.float64(0.086), np.float64(0.04), np.float64(0.093), np.float64(0.059)]
results for assortment [9, 4, 6, 51, 82, 41] :

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

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

beta is  0.025 

learned probs for this beta: {5: np.float64(0.3122804781963041), 9: np.float64(0.28566898493116966), 6: np.float64(0.30457024571780295), 39: np.float64(0.02437007278868012), 80: np.float64(0.02437007278868012), 68: np.float64(0.02437007278868012), 0: np.float64(0.02437007278868012)}
err dic= {5: np.float64(0.06728047819630412), 9: np.float64(0.05766898493116965), 6: np.float64(0.04657024571780294), 39: np.float64(0.07562992721131989), 80: np.float64(0.03862992721131988), 68: np.float64(0.03162992721131988), 0: np.float64(0.025629927211319882)} 

err list= [np.float64(0.06728047819630412), np.float64(0.05766898493116965), np.float64(0.04657024571780294), np.float64(0.07562992721131989), np.float64(0.03862992721131988), np.float64(0.03162992721131988), np.float64(0.025629927211319882)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.3556367115652194), 9: np.float64(0.2983297110013204), 6: np.float64(0.33829210447351), 39: np.float64(0.001935368239987582), 80: np.float64(0.001935368239987582), 68: np.float64(0.001935368239987582), 0: np.float64(0.001935368239987582)}
err dic= {5: np.float64(0.11063671156521943), 9: np.float64(0.07032971100132038), 6: np.float64(0.08029210447350998), 39: np.float64(0.09806463176001243), 80: np.float64(0.061064631760012415), 68: np.float64(0.054064631760012416), 0: np.float64(0.04806463176001242)} 

err list= [np.float64(0.11063671156521943), np.float64(0.07032971100132038), np.float64(0.08029210447350998), np.float64(0.09806463176001243), np.float64(0.061064631760012415), np.float64(0.054064631760012416), np.float64(0.04806463176001242)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.3834550352285498), 9: np.float64(0.26957017101036784), 6: np.float64(0.3469644640090889), 39: np.float64(2.5824379985383504e-06), 80: np.float64(2.5824379985383504e-06), 68: np.float64(2.5824379985383504e-06), 0: np.float64(2.5824379985383504e-06)}
err dic= {5: np.float64(0.1384550352285498), 9: np.float64(0.041570171010367835), 6: np.float64(0.08896446400908892), 39: np.float64(0.09999741756200146), 80: np.float64(0.06299741756200146), 68: np.float64(0.05599741756200146), 0: np.float64(0.04999741756200146)} 

err list= [np.float64(0.1384550352285498), np.float64(0.041570171010367835), np.float64(0.08896446400908892), np.float64(0.09999741756200146), np.float64(0.06299741756200146), np.float64(0.05599741756200146), np.float64(0.04999741756200146)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.25 

learned probs for this beta: {5: np.float64(0.45682980227176534), 9: np.float64(0.18739078998861994), 6: np.float64(0.355779407739606), 39: np.float64(2.0281425002555e-15), 80: np.float64(2.0281425002555e-15), 68: np.float64(2.0281425002555e-15), 0: np.float64(2.0281425002555e-15)}
err dic= {5: np.float64(0.21182980227176534), 9: np.float64(0.04060921001138007), 6: np.float64(0.09777940773960597), 39: np.float64(0.09999999999999798), 80: np.float64(0.06299999999999797), 68: np.float64(0.055999999999997975), 0: np.float64(0.04999999999999798)} 

err list= [np.float64(0.21182980227176534), np.float64(0.04060921001138007), np.float64(0.09777940773960597), np.float64(0.09999999999999798), np.float64(0.06299999999999797), np.float64(0.055999999999997975), np.float64(0.04999999999999798)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.5 

learned probs for this beta: {5: np.float64(0.5654187560796601), 9: np.float64(0.09163743278144765), 6: np.float64(0.3429438111388928), 39: np.float64(1.5286183655853976e-30), 80: np.float64(1.5286183655853976e-30), 68: np.float64(1.5286183655853976e-30), 0: np.float64(1.5286183655853976e-30)}
err dic= {5: np.float64(0.3204187560796601), 9: np.float64(0.13636256721855236), 6: np.float64(0.08494381113889277), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.3204187560796601), np.float64(0.13636256721855236), np.float64(0.08494381113889277), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.75 

learned probs for this beta: {5: np.float64(0.6518852874465689), 9: np.float64(0.04018590653971), 6: np.float64(0.30792880601372125), 39: np.float64(1.2245915393270361e-45), 80: np.float64(1.2245915393270361e-45), 68: np.float64(1.2245915393270361e-45), 0: np.float64(1.2245915393270361e-45)}
err dic= {5: np.float64(0.40688528744656893), 9: np.float64(0.18781409346029002), 6: np.float64(0.04992880601372124), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.40688528744656893), np.float64(0.18781409346029002), np.float64(0.04992880601372124), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1 

learned probs for this beta: {5: np.float64(0.7191002954879085), 9: np.float64(0.016357489661781185), 6: np.float64(0.26454221485031076), 39: np.float64(1.0142228350539648e-60), 80: np.float64(1.0142228350539648e-60), 68: np.float64(1.0142228350539648e-60), 0: np.float64(1.0142228350539648e-60)}
err dic= {5: np.float64(0.47410029548790855), 9: np.float64(0.21164251033821882), 6: np.float64(0.006542214850310757), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.47410029548790855), np.float64(0.21164251033821882), np.float64(0.006542214850310757), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.25 

learned probs for this beta: {5: np.float64(0.7723569153432931), 9: np.float64(0.006359123522713147), 6: np.float64(0.22128396113399326), 39: np.float64(8.594945268975069e-76), 80: np.float64(8.594945268975069e-76), 68: np.float64(8.594945268975069e-76), 0: np.float64(8.594945268975069e-76)}
err dic= {5: np.float64(0.5273569153432931), 9: np.float64(0.22164087647728686), 6: np.float64(0.036716038866006745), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.5273569153432931), np.float64(0.22164087647728686), np.float64(0.036716038866006745), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.5 

learned probs for this beta: {5: np.float64(0.8156057222377775), 9: np.float64(0.002408042341331115), 6: np.float64(0.18198623542089104), 39: np.float64(7.406101916552074e-91), 80: np.float64(7.406101916552074e-91), 68: np.float64(7.406101916552074e-91), 0: np.float64(7.406101916552074e-91)}
err dic= {5: np.float64(0.5706057222377775), 9: np.float64(0.2255919576586689), 6: np.float64(0.07601376457910897), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.5706057222377775), np.float64(0.2255919576586689), np.float64(0.07601376457910897), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  1.75 

learned probs for this beta: {5: np.float64(0.8511869021360521), 9: np.float64(0.0008989932663974902), 6: np.float64(0.14791410459754986), 39: np.float64(6.464621934716856e-106), 80: np.float64(6.464621934716856e-106), 68: np.float64(6.464621934716856e-106), 0: np.float64(6.464621934716856e-106)}
err dic= {5: np.float64(0.6061869021360521), 9: np.float64(0.2271010067336025), 6: np.float64(0.11008589540245015), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

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

beta is  2 

learned probs for this beta: {5: np.float64(0.8805036406466493), 9: np.float64(0.00033314975556754796), 6: np.float64(0.11916320959778291), 39: np.float64(5.7017698242071855e-121), 80: np.float64(5.7017698242071855e-121), 68: np.float64(5.7017698242071855e-121), 0: np.float64(5.7017698242071855e-121)}
err dic= {5: np.float64(0.6355036406466493), 9: np.float64(0.22766685024443245), 6: np.float64(0.13883679040221708), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.6355036406466493), np.float64(0.22766685024443245), np.float64(0.13883679040221708), np.float64(0.1), np.float64(0.063), np.float64(0.056), np.float64(0.05)]
results for assortment [5, 9, 6, 39, 80, 68] :

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

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

beta is  0.025 

learned probs for this beta: {6: np.float64(0.29846061930227274), 3: np.float64(0.31813956697649043), 8: np.float64(0.28543344121266245), 15: np.float64(0.024491593127143593), 78: np.float64(0.024491593127143593), 97: np.float64(0.024491593127143593), 0: np.float64(0.024491593127143593)}
err dic= {6: np.float64(0.07746061930227274), 3: np.float64(0.08313956697649044), 8: np.float64(0.047433441212662464), 15: np.float64(0.14850840687285638), 78: np.float64(0.03150840687285641), 97: np.float64(0.014508406872856407), 0: np.float64(0.013508406872856406)} 

err list= [np.float64(0.07746061930227274), np.float64(0.08313956697649044), np.float64(0.047433441212662464), np.float64(0.14850840687285638), np.float64(0.03150840687285641), np.float64(0.014508406872856407), np.float64(0.013508406872856406)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.3259149786695292), 3: np.float64(0.3690832008417285), 8: np.float64(0.29846417780121925), 15: np.float64(0.0016344106718808938), 78: np.float64(0.0016344106718808938), 97: np.float64(0.0016344106718808938), 0: np.float64(0.0016344106718808938)}
err dic= {6: np.float64(0.10491497866952917), 3: np.float64(0.13408320084172853), 8: np.float64(0.060464177801219265), 15: np.float64(0.1713655893281191), 78: np.float64(0.05436558932811911), 97: np.float64(0.037365589328119106), 0: np.float64(0.036365589328119105)} 

err list= [np.float64(0.10491497866952917), np.float64(0.13408320084172853), np.float64(0.060464177801219265), np.float64(0.1713655893281191), np.float64(0.05436558932811911), np.float64(0.037365589328119106), np.float64(0.036365589328119105)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.32067310215786327), 3: np.float64(0.4106038068722724), 8: np.float64(0.26871558510976684), 15: np.float64(1.8764650245021469e-06), 78: np.float64(1.8764650245021469e-06), 97: np.float64(1.8764650245021469e-06), 0: np.float64(1.8764650245021469e-06)}
err dic= {6: np.float64(0.09967310215786326), 3: np.float64(0.1756038068722724), 8: np.float64(0.030715585109766852), 15: np.float64(0.17299812353497548), 78: np.float64(0.0559981235349755), 97: np.float64(0.0389981235349755), 0: np.float64(0.037998123534975496)} 

err list= [np.float64(0.09967310215786326), np.float64(0.1756038068722724), np.float64(0.030715585109766852), np.float64(0.17299812353497548), np.float64(0.0559981235349755), np.float64(0.0389981235349755), np.float64(0.037998123534975496)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.25 

learned probs for this beta: {6: np.float64(0.2875137926500762), 3: np.float64(0.528988846555889), 8: np.float64(0.1834973607940296), 15: np.float64(1.1222444216473187e-15), 78: np.float64(1.1222444216473187e-15), 97: np.float64(1.1222444216473187e-15), 0: np.float64(1.1222444216473187e-15)}
err dic= {6: np.float64(0.0665137926500762), 3: np.float64(0.29398884655588897), 8: np.float64(0.0545026392059704), 15: np.float64(0.17299999999999888), 78: np.float64(0.05599999999999888), 97: np.float64(0.038999999999998876), 0: np.float64(0.037999999999998875)} 

err list= [np.float64(0.0665137926500762), np.float64(0.29398884655588897), np.float64(0.0545026392059704), np.float64(0.17299999999999888), np.float64(0.05599999999999888), np.float64(0.038999999999998876), np.float64(0.037999999999998875)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.5 

learned probs for this beta: {6: np.float64(0.21136722905274474), 3: np.float64(0.7045769546695909), 8: np.float64(0.08405581627766473), 15: np.float64(4.9971247581273215e-31), 78: np.float64(4.9971247581273215e-31), 97: np.float64(4.9971247581273215e-31), 0: np.float64(4.9971247581273215e-31)}
err dic= {6: np.float64(0.00963277094725526), 3: np.float64(0.46957695466959093), 8: np.float64(0.15394418372233526), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.00963277094725526), np.float64(0.46957695466959093), np.float64(0.15394418372233526), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.75 

learned probs for this beta: {6: np.float64(0.13673323328089826), 3: np.float64(0.8300378726980453), 8: np.float64(0.033228894021056346), 15: np.float64(2.2356470675820252e-46), 78: np.float64(2.2356470675820252e-46), 97: np.float64(2.2356470675820252e-46), 0: np.float64(2.2356470675820252e-46)}
err dic= {6: np.float64(0.08426676671910174), 3: np.float64(0.5950378726980453), 8: np.float64(0.20477110597894366), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.08426676671910174), np.float64(0.5950378726980453), np.float64(0.20477110597894366), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1 

learned probs for this beta: {6: np.float64(0.0806651538227525), 3: np.float64(0.9074958368084762), 8: np.float64(0.011839009368771462), 15: np.float64(9.921667426414478e-62), 78: np.float64(9.921667426414478e-62), 97: np.float64(9.921667426414478e-62), 0: np.float64(9.921667426414478e-62)}
err dic= {6: np.float64(0.1403348461772475), 3: np.float64(0.6724958368084762), 8: np.float64(0.22616099063122852), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.1403348461772475), np.float64(0.6724958368084762), np.float64(0.22616099063122852), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.25 

learned probs for this beta: {6: np.float64(0.04464840069712358), 3: np.float64(0.9514153882278131), 8: np.float64(0.00393621107506327), 15: np.float64(4.37373881869069e-77), 78: np.float64(4.37373881869069e-77), 97: np.float64(4.37373881869069e-77), 0: np.float64(4.37373881869069e-77)}
err dic= {6: np.float64(0.17635159930287642), 3: np.float64(0.7164153882278131), 8: np.float64(0.23406378892493673), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.17635159930287642), np.float64(0.7164153882278131), np.float64(0.23406378892493673), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.5 

learned probs for this beta: {6: np.float64(0.023650013524335572), 3: np.float64(0.975099430792984), 8: np.float64(0.0012505556826808662), 15: np.float64(1.918400064999713e-92), 78: np.float64(1.918400064999713e-92), 97: np.float64(1.918400064999713e-92), 0: np.float64(1.918400064999713e-92)}
err dic= {6: np.float64(0.19734998647566443), 3: np.float64(0.740099430792984), 8: np.float64(0.23674944431731912), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.19734998647566443), np.float64(0.740099430792984), np.float64(0.23674944431731912), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  1.75 

learned probs for this beta: {6: np.float64(0.012148820459890007), 3: np.float64(0.9874656934961611), 8: np.float64(0.0003854860439483042), 15: np.float64(8.38277266009707e-108), 78: np.float64(8.38277266009707e-108), 97: np.float64(8.38277266009707e-108), 0: np.float64(8.38277266009707e-108)}
err dic= {6: np.float64(0.20885117954010998), 3: np.float64(0.7524656934961611), 8: np.float64(0.23761451395605168), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.20885117954010998), np.float64(0.7524656934961611), np.float64(0.23761451395605168), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  2 

learned probs for this beta: {6: np.float64(0.00610651094060876), 3: np.float64(0.9937770715394815), 8: np.float64(0.00011641751990945703), 15: np.float64(3.6529534324980925e-123), 78: np.float64(3.6529534324980925e-123), 97: np.float64(3.6529534324980925e-123), 0: np.float64(3.6529534324980925e-123)}
err dic= {6: np.float64(0.21489348905939124), 3: np.float64(0.7587770715394815), 8: np.float64(0.23788358248009053), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.21489348905939124), np.float64(0.7587770715394815), np.float64(0.23788358248009053), np.float64(0.173), np.float64(0.056), np.float64(0.039), np.float64(0.038)]
results for assortment [6, 3, 8, 15, 78, 97] :

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

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

beta is  0.025 

learned probs for this beta: {8: np.float64(0.22710092491879882), 2: np.float64(0.2588659992354154), 4: np.float64(0.24745916666451956), 95: np.float64(0.01652463745574016), 11: np.float64(0.21699999681404403), 22: np.float64(0.01652463745574016), 0: np.float64(0.01652463745574016)}
err dic= {8: np.float64(0.007899075081201162), 2: np.float64(0.05686599923541541), 4: np.float64(0.05045916666451955), 95: np.float64(0.025475362544259843), 11: np.float64(0.05099999681404402), 22: np.float64(0.12047536254425985), 0: np.float64(0.004475362544259842)} 

err list= [np.float64(0.007899075081201162), np.float64(0.05686599923541541), np.float64(0.05045916666451955), np.float64(0.025475362544259843), np.float64(0.05099999681404402), np.float64(0.12047536254425985), np.float64(0.004475362544259842)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.2265442643767802), 2: np.float64(0.2936334987984021), 4: np.float64(0.26857925564976476), 95: np.float64(0.0014618644304647552), 11: np.float64(0.20685738788365857), 22: np.float64(0.0014618644304647552), 0: np.float64(0.0014618644304647552)}
err dic= {8: np.float64(0.008455735623219773), 2: np.float64(0.0916334987984021), 4: np.float64(0.07157925564976475), 95: np.float64(0.04053813556953525), 11: np.float64(0.04085738788365856), 22: np.float64(0.13553813556953526), 0: np.float64(0.019538135569535247)} 

err list= [np.float64(0.008455735623219773), np.float64(0.0916334987984021), np.float64(0.07157925564976475), np.float64(0.04053813556953525), np.float64(0.04085738788365856), np.float64(0.13553813556953526), np.float64(0.019538135569535247)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.20339798491527555), 2: np.float64(0.34129421969550894), 4: np.float64(0.28601169161660267), 95: np.float64(1.8398267483657162e-06), 11: np.float64(0.16929058429236854), 22: np.float64(1.8398267483657162e-06), 0: np.float64(1.8398267483657162e-06)}
err dic= {8: np.float64(0.03160201508472443), 2: np.float64(0.13929421969550893), 4: np.float64(0.08901169161660266), 95: np.float64(0.041998160173251635), 11: np.float64(0.0032905842923685313), 22: np.float64(0.13699816017325164), 0: np.float64(0.020998160173251637)} 

err list= [np.float64(0.03160201508472443), np.float64(0.13929421969550893), np.float64(0.08901169161660266), np.float64(0.041998160173251635), np.float64(0.0032905842923685313), np.float64(0.13699816017325164), np.float64(0.020998160173251637)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.13082576069904342), 2: np.float64(0.47752044770785945), 4: np.float64(0.3100295164258381), 95: np.float64(1.10880561537201e-15), 11: np.float64(0.0816242751672549), 22: np.float64(1.10880561537201e-15), 0: np.float64(1.10880561537201e-15)}
err dic= {8: np.float64(0.10417423930095657), 2: np.float64(0.27552044770785944), 4: np.float64(0.11302951642583808), 95: np.float64(0.04199999999999889), 11: np.float64(0.08437572483274511), 22: np.float64(0.1369999999999989), 0: np.float64(0.02099999999999889)} 

err list= [np.float64(0.10417423930095657), np.float64(0.27552044770785944), np.float64(0.11302951642583808), np.float64(0.04199999999999889), np.float64(0.08437572483274511), np.float64(0.1369999999999989), np.float64(0.02099999999999889)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.5 

learned probs for this beta: {8: np.float64(0.04709325965882175), 2: np.float64(0.6544667084443634), 4: np.float64(0.2806804187885039), 95: np.float64(4.6180536399275935e-31), 11: np.float64(0.017759613108311294), 22: np.float64(4.6180536399275935e-31), 0: np.float64(4.6180536399275935e-31)}
err dic= {8: np.float64(0.18790674034117824), 2: np.float64(0.4524667084443634), 4: np.float64(0.08368041878850391), 95: np.float64(0.042), 11: np.float64(0.14824038689168872), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.18790674034117824), np.float64(0.4524667084443634), np.float64(0.08368041878850391), np.float64(0.042), np.float64(0.14824038689168872), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.75 

learned probs for this beta: {8: np.float64(0.013536549016638746), 2: np.float64(0.7668515971786537), 4: np.float64(0.2165503665695186), 95: np.float64(1.891620693004808e-46), 11: np.float64(0.003061487235188769), 22: np.float64(1.891620693004808e-46), 0: np.float64(1.891620693004808e-46)}
err dic= {8: np.float64(0.22146345098336123), 2: np.float64(0.5648515971786536), 4: np.float64(0.019550366569518585), 95: np.float64(0.042), 11: np.float64(0.16293851276481125), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.22146345098336123), np.float64(0.5648515971786536), np.float64(0.019550366569518585), np.float64(0.042), np.float64(0.16293851276481125), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1 

learned probs for this beta: {8: np.float64(0.0034775536988864626), 2: np.float64(0.8410328325211592), 4: np.float64(0.15501625097215452), 95: np.float64(7.792176760863947e-62), 11: np.float64(0.00047336280779999217), 22: np.float64(7.792176760863947e-62), 0: np.float64(7.792176760863947e-62)}
err dic= {8: np.float64(0.23152244630111352), 2: np.float64(0.6390328325211592), 4: np.float64(0.04198374902784549), 95: np.float64(0.042), 11: np.float64(0.1655266371922), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23152244630111352), np.float64(0.6390328325211592), np.float64(0.04198374902784549), np.float64(0.042), np.float64(0.1655266371922), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.25 

learned probs for this beta: {8: np.float64(0.0008467393110206104), 2: np.float64(0.8926352815932924), 4: np.float64(0.10644832522985162), 95: np.float64(3.2498172739972907e-77), 11: np.float64(6.965386583462914e-05), 22: np.float64(3.2498172739972907e-77), 0: np.float64(3.2498172739972907e-77)}
err dic= {8: np.float64(0.23415326068897938), 2: np.float64(0.6906352815932923), 4: np.float64(0.09055167477014839), 95: np.float64(0.042), 11: np.float64(0.16593034613416538), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23415326068897938), np.float64(0.6906352815932923), np.float64(0.09055167477014839), np.float64(0.042), np.float64(0.16593034613416538), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.5 

learned probs for this beta: {8: np.float64(0.00020066374506286724), 2: np.float64(0.9287259689199104), 4: np.float64(0.07106336957914271), 95: np.float64(1.3715043718086033e-92), 11: np.float64(9.99775588346969e-06), 22: np.float64(1.3715043718086033e-92), 0: np.float64(1.3715043718086033e-92)}
err dic= {8: np.float64(0.23479933625493712), 2: np.float64(0.7267259689199104), 4: np.float64(0.1259366304208573), 95: np.float64(0.042), 11: np.float64(0.16599000224411653), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23479933625493712), np.float64(0.7267259689199104), np.float64(0.1259366304208573), np.float64(0.042), np.float64(0.16599000224411653), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  1.75 

learned probs for this beta: {8: np.float64(4.682387879268542e-05), 2: np.float64(0.9535067301964254), 4: np.float64(0.04644503163375219), 95: np.float64(5.841010645387081e-108), 11: np.float64(1.414291028627564e-06), 22: np.float64(5.841010645387081e-108), 0: np.float64(5.841010645387081e-108)}
err dic= {8: np.float64(0.2349531761212073), 2: np.float64(0.7515067301964253), 4: np.float64(0.15055496836624782), 95: np.float64(0.042), 11: np.float64(0.16599858570897139), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.2349531761212073), np.float64(0.7515067301964253), np.float64(0.15055496836624782), np.float64(0.042), np.float64(0.16599858570897139), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  2 

learned probs for this beta: {8: np.float64(1.0815608602475049e-05), 2: np.float64(0.9701298210556255), 4: np.float64(0.02985916522652595), 95: np.float64(2.5033621691158992e-123), 11: np.float64(1.9810924551184603e-07), 22: np.float64(2.5033621691158992e-123), 0: np.float64(2.5033621691158992e-123)}
err dic= {8: np.float64(0.23498918439139752), 2: np.float64(0.7681298210556256), 4: np.float64(0.16714083477347405), 95: np.float64(0.042), 11: np.float64(0.1659998018907545), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.23498918439139752), np.float64(0.7681298210556256), np.float64(0.16714083477347405), np.float64(0.042), np.float64(0.1659998018907545), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

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

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

beta is  0.025 

learned probs for this beta: {1: np.float64(0.26488528574158837), 3: np.float64(0.25323344276348003), 9: np.float64(0.22317286264359212), 100: np.float64(0.20888340073805658), 22: np.float64(0.016608336037760518), 58: np.float64(0.016608336037760518), 0: np.float64(0.016608336037760518)}
err dic= {1: np.float64(0.04688528574158837), 3: np.float64(0.07223344276348004), 9: np.float64(0.026172862643592115), 100: np.float64(0.013116599261943418), 22: np.float64(0.09639166396223948), 58: np.float64(0.024391663962239483), 0: np.float64(0.011391663962239482)} 

err list= [np.float64(0.04688528574158837), np.float64(0.07223344276348004), np.float64(0.026172862643592115), np.float64(0.013116599261943418), np.float64(0.09639166396223948), np.float64(0.024391663962239483), np.float64(0.011391663962239482)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3062000451733673), 3: np.float64(0.28016185183696457), 9: np.float64(0.21815619243698967), 100: np.float64(0.1910829698895634), 22: np.float64(0.0014663135543716904), 58: np.float64(0.0014663135543716904), 0: np.float64(0.0014663135543716904)}
err dic= {1: np.float64(0.0882000451733673), 3: np.float64(0.09916185183696458), 9: np.float64(0.021156192436989657), 100: np.float64(0.030917030110436616), 22: np.float64(0.11153368644562832), 58: np.float64(0.03953368644562831), 0: np.float64(0.02653368644562831)} 

err list= [np.float64(0.0882000451733673), np.float64(0.09916185183696458), np.float64(0.021156192436989657), np.float64(0.030917030110436616), np.float64(0.11153368644562832), np.float64(0.03953368644562831), np.float64(0.02653368644562831)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.36559260004103755), 3: np.float64(0.30672981777763), 9: np.float64(0.18580515164421915), 100: np.float64(0.1418669403919846), 22: np.float64(1.8300483763416442e-06), 58: np.float64(1.8300483763416442e-06), 0: np.float64(1.8300483763416442e-06)}
err dic= {1: np.float64(0.14759260004103755), 3: np.float64(0.12572981777762998), 9: np.float64(0.011194848355780856), 100: np.float64(0.0801330596080154), 22: np.float64(0.11299816995162366), 58: np.float64(0.04099816995162366), 0: np.float64(0.027998169951623658)} 

err list= [np.float64(0.14759260004103755), np.float64(0.12572981777762998), np.float64(0.011194848355780856), np.float64(0.0801330596080154), np.float64(0.11299816995162366), np.float64(0.04099816995162366), np.float64(0.027998169951623658)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5199273620382416), 3: np.float64(0.33916654873196556), 9: np.float64(0.09438635240642447), 100: np.float64(0.046519736823364674), 22: np.float64(1.0064925535313943e-15), 58: np.float64(1.0064925535313943e-15), 0: np.float64(1.0064925535313943e-15)}
err dic= {1: np.float64(0.30192736203824166), 3: np.float64(0.15816654873196556), 9: np.float64(0.10261364759357554), 100: np.float64(0.17548026317663534), 22: np.float64(0.11299999999999899), 58: np.float64(0.040999999999998996), 0: np.float64(0.027999999999998994)} 

err list= [np.float64(0.30192736203824166), np.float64(0.15816654873196556), np.float64(0.10261364759357554), np.float64(0.17548026317663534), np.float64(0.11299999999999899), np.float64(0.040999999999998996), np.float64(0.027999999999998994)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6814823849754578), 3: np.float64(0.29408206868659303), 9: np.float64(0.019892551348217543), 100: np.float64(0.004542994989732106), 22: np.float64(3.158622230366253e-31), 58: np.float64(3.158622230366253e-31), 0: np.float64(3.158622230366253e-31)}
err dic= {1: np.float64(0.4634823849754578), 3: np.float64(0.11308206868659304), 9: np.float64(0.17710744865178246), 100: np.float64(0.2174570050102679), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.4634823849754578), np.float64(0.11308206868659304), np.float64(0.17710744865178246), np.float64(0.2174570050102679), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.776389841292173), 3: np.float64(0.22001307711622542), 9: np.float64(0.003251848726695263), 100: np.float64(0.00034523286490644345), 22: np.float64(9.513232140010762e-47), 58: np.float64(9.513232140010762e-47), 0: np.float64(9.513232140010762e-47)}
err dic= {1: np.float64(0.5583898412921731), 3: np.float64(0.039013077116225425), 9: np.float64(0.19374815127330475), 100: np.float64(0.22165476713509355), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.5583898412921731), np.float64(0.039013077116225425), np.float64(0.19374815127330475), np.float64(0.22165476713509355), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1 

learned probs for this beta: {1: np.float64(0.8437493664948656), 3: np.float64(0.15573992576810317), 9: np.float64(0.00048644702219156026), 100: np.float64(2.426071484012091e-05), 22: np.float64(2.947499119011448e-62), 58: np.float64(2.947499119011448e-62), 0: np.float64(2.947499119011448e-62)}
err dic= {1: np.float64(0.6257493664948657), 3: np.float64(0.02526007423189683), 9: np.float64(0.19651355297780845), 100: np.float64(0.22197573928515987), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.6257493664948657), np.float64(0.02526007423189683), np.float64(0.19651355297780845), np.float64(0.22197573928515987), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.8933412342571281), 3: np.float64(0.10658666255059607), 9: np.float64(7.044586739699485e-05), 100: np.float64(1.6573248786188935e-06), 22: np.float64(9.417866619641752e-78), 58: np.float64(9.417866619641752e-78), 0: np.float64(9.417866619641752e-78)}
err dic= {1: np.float64(0.6753412342571281), 3: np.float64(0.07441333744940393), 9: np.float64(0.19692955413260302), 100: np.float64(0.2219983426751214), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.6753412342571281), np.float64(0.07441333744940393), np.float64(0.19692955413260302), np.float64(0.2219983426751214), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.5 

learned probs for this beta: {1: np.float64(0.9289011179586114), 3: np.float64(0.07108872798785826), 9: np.float64(1.00424838519458e-05), 100: np.float64(1.1156967800869512e-07), 22: np.float64(3.0740005759158465e-93), 58: np.float64(3.0740005759158465e-93), 0: np.float64(3.0740005759158465e-93)}
err dic= {1: np.float64(0.7109011179586114), 3: np.float64(0.10991127201214174), 9: np.float64(0.19698995751614806), 100: np.float64(0.221999888430322), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.7109011179586114), np.float64(0.10991127201214174), np.float64(0.19698995751614806), np.float64(0.221999888430322), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  1.75 

learned probs for this beta: {1: np.float64(0.9535489961513725), 3: np.float64(0.04644957969911168), 9: np.float64(1.416715180521834e-06), 100: np.float64(7.434334682403295e-09), 22: np.float64(1.0167594870851722e-108), 58: np.float64(1.0167594870851722e-108), 0: np.float64(1.0167594870851722e-108)}
err dic= {1: np.float64(0.7355489961513725), 3: np.float64(0.13455042030088832), 9: np.float64(0.19699858328481948), 100: np.float64(0.22199999256566533), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

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

beta is  2 

learned probs for this beta: {1: np.float64(0.9701398303256955), 3: np.float64(0.029859970945651217), 9: np.float64(1.9823727027203242e-07), 100: np.float64(4.913822077323317e-10), 22: np.float64(3.3901242385422172e-124), 58: np.float64(3.3901242385422172e-124), 0: np.float64(3.3901242385422172e-124)}
err dic= {1: np.float64(0.7521398303256955), 3: np.float64(0.15114002905434878), 9: np.float64(0.19699980176272974), 100: np.float64(0.2219999995086178), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.7521398303256955), np.float64(0.15114002905434878), np.float64(0.19699980176272974), np.float64(0.2219999995086178), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

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

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

beta is  0.025 

learned probs for this beta: {7: np.float64(0.29933673407635136), 6: np.float64(0.30691447957688306), 8: np.float64(0.29194608377885445), 16: np.float64(0.02545067564197786), 83: np.float64(0.02545067564197786), 70: np.float64(0.02545067564197786), 0: np.float64(0.02545067564197786)}
err dic= {7: np.float64(0.09233673407635137), 6: np.float64(0.06091447957688306), 8: np.float64(0.04294608377885445), 16: np.float64(0.12254932435802213), 83: np.float64(0.022549324358022142), 70: np.float64(0.032549324358022144), 0: np.float64(0.01854932435802214)} 

err list= [np.float64(0.09233673407635137), np.float64(0.06091447957688306), np.float64(0.04294608377885445), np.float64(0.12254932435802213), np.float64(0.022549324358022142), np.float64(0.032549324358022144), np.float64(0.01854932435802214)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.33077624081457463), 6: np.float64(0.3477355013362776), 8: np.float64(0.3146440931885574), 16: np.float64(0.0017110411651477923), 83: np.float64(0.0017110411651477923), 70: np.float64(0.0017110411651477923), 0: np.float64(0.0017110411651477923)}
err dic= {7: np.float64(0.12377624081457464), 6: np.float64(0.10173550133627762), 8: np.float64(0.0656440931885574), 16: np.float64(0.1462889588348522), 83: np.float64(0.046288958834852206), 70: np.float64(0.05628895883485221), 0: np.float64(0.0422889588348522)} 

err list= [np.float64(0.12377624081457464), np.float64(0.10173550133627762), np.float64(0.0656440931885574), np.float64(0.1462889588348522), np.float64(0.046288958834852206), np.float64(0.05628895883485221), np.float64(0.0422889588348522)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.3322222418352864), 6: np.float64(0.36716236001425334), 8: np.float64(0.30060711551635877), 16: np.float64(2.070658525464765e-06), 83: np.float64(2.070658525464765e-06), 70: np.float64(2.070658525464765e-06), 0: np.float64(2.070658525464765e-06)}
err dic= {7: np.float64(0.12522224183528644), 6: np.float64(0.12116236001425335), 8: np.float64(0.05160711551635877), 16: np.float64(0.14799792934147452), 83: np.float64(0.04799792934147454), 70: np.float64(0.05799792934147454), 0: np.float64(0.043997929341474534)} 

err list= [np.float64(0.12522224183528644), np.float64(0.12116236001425335), np.float64(0.05160711551635877), np.float64(0.14799792934147452), np.float64(0.04799792934147454), np.float64(0.05799792934147454), np.float64(0.043997929341474534)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.32649583579983443), 6: np.float64(0.4192289516096948), 8: np.float64(0.25427521259046393), 16: np.float64(1.536520996358413e-15), 83: np.float64(1.536520996358413e-15), 70: np.float64(1.536520996358413e-15), 0: np.float64(1.536520996358413e-15)}
err dic= {7: np.float64(0.11949583579983444), 6: np.float64(0.17322895160969481), 8: np.float64(0.005275212590463929), 16: np.float64(0.14799999999999847), 83: np.float64(0.04799999999999847), 70: np.float64(0.05799999999999847), 0: np.float64(0.043999999999998464)} 

err list= [np.float64(0.11949583579983444), np.float64(0.17322895160969481), np.float64(0.005275212590463929), np.float64(0.14799999999999847), np.float64(0.04799999999999847), np.float64(0.05799999999999847), np.float64(0.043999999999998464)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.30719588571849854), 6: np.float64(0.5064803910556542), 8: np.float64(0.1863237232258477), 16: np.float64(1.130394358122328e-30), 83: np.float64(1.130394358122328e-30), 70: np.float64(1.130394358122328e-30), 0: np.float64(1.130394358122328e-30)}
err dic= {7: np.float64(0.10019588571849855), 6: np.float64(0.26048039105565424), 8: np.float64(0.0626762767741523), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.10019588571849855), np.float64(0.26048039105565424), np.float64(0.0626762767741523), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.27860068919627307), 6: np.float64(0.5897976636568125), 8: np.float64(0.13160164714691433), 16: np.float64(9.259864055594299e-46), 83: np.float64(9.259864055594299e-46), 70: np.float64(9.259864055594299e-46), 0: np.float64(9.259864055594299e-46)}
err dic= {7: np.float64(0.07160068919627308), 6: np.float64(0.3437976636568125), 8: np.float64(0.11739835285308567), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.07160068919627308), np.float64(0.3437976636568125), np.float64(0.11739835285308567), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1 

learned probs for this beta: {7: np.float64(0.24472847105479775), 6: np.float64(0.6652409557748219), 8: np.float64(0.09003057317038048), 16: np.float64(7.921837993142807e-61), 83: np.float64(7.921837993142807e-61), 70: np.float64(7.921837993142807e-61), 0: np.float64(7.921837993142807e-61)}
err dic= {7: np.float64(0.03772847105479776), 6: np.float64(0.4192409557748219), 8: np.float64(0.1589694268296195), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.03772847105479776), np.float64(0.4192409557748219), np.float64(0.1589694268296195), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.20934307548219694), 6: np.float64(0.7306791292026886), 8: np.float64(0.05997779531511427), 16: np.float64(6.944005439255368e-76), 83: np.float64(6.944005439255368e-76), 70: np.float64(6.944005439255368e-76), 0: np.float64(6.944005439255368e-76)}
err dic= {7: np.float64(0.002343075482196949), 6: np.float64(0.48467912920268863), 8: np.float64(0.18902220468488573), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.002343075482196949), np.float64(0.48467912920268863), np.float64(0.18902220468488573), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.5 

learned probs for this beta: {7: np.float64(0.17529039214003667), 6: np.float64(0.7855970345892757), 8: np.float64(0.03911257327068745), 16: np.float64(6.186170340448698e-91), 83: np.float64(6.186170340448698e-91), 70: np.float64(6.186170340448698e-91), 0: np.float64(6.186170340448698e-91)}
err dic= {7: np.float64(0.031709607859963324), 6: np.float64(0.5395970345892757), 8: np.float64(0.20988742672931254), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.031709607859963324), np.float64(0.5395970345892757), np.float64(0.20988742672931254), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  1.75 

learned probs for this beta: {7: np.float64(0.1443339551132098), 6: np.float64(0.8305845643329679), 8: np.float64(0.025081480553822005), 16: np.float64(5.571015323454254e-106), 83: np.float64(5.571015323454254e-106), 70: np.float64(5.571015323454254e-106), 0: np.float64(5.571015323454254e-106)}
err dic= {7: np.float64(0.0626660448867902), 6: np.float64(0.5845845643329679), 8: np.float64(0.223918519446178), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.0626660448867902), np.float64(0.5845845643329679), np.float64(0.223918519446178), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  2 

learned probs for this beta: {7: np.float64(0.11731042782619833), 6: np.float64(0.8668133321973345), 8: np.float64(0.01587623997646676), 16: np.float64(5.052350570357873e-121), 83: np.float64(5.052350570357873e-121), 70: np.float64(5.052350570357873e-121), 0: np.float64(5.052350570357873e-121)}
err dic= {7: np.float64(0.08968957217380166), 6: np.float64(0.6208133321973345), 8: np.float64(0.23312376002353324), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.08968957217380166), np.float64(0.6208133321973345), np.float64(0.23312376002353324), np.float64(0.148), np.float64(0.048), np.float64(0.058), np.float64(0.044)]
results for assortment [7, 6, 8, 16, 83, 70] :

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

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

mean_err= [0.05605637 0.06962188 0.07479475 0.07738178 0.08251549 0.08854378
 0.09454649 0.10012183 0.10612724 0.11221693 0.11814042]
mean_std= [0.         0.01356551 0.013274   0.01233805 0.01507323 0.01926231
 0.02311333 0.02617324 0.02995736 0.03378547 0.03726346]
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
