p= 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(0.3416497410198467), 3: np.float64(0.33321437885856936), 4: np.float64(0.32498728653112674), 59: np.float64(3.7148397614246416e-05), 40: np.float64(3.7148397614246416e-05), 84: np.float64(3.7148397614246416e-05), 0: np.float64(3.7148397614246416e-05)}
err dic= {2: np.float64(0.06664974101984666), 3: np.float64(0.08621437885856936), 4: np.float64(0.07298728653112674), 59: np.float64(0.05896285160238575), 40: np.float64(0.07196285160238575), 84: np.float64(0.05996285160238575), 0: np.float64(0.034962851602385756)} 

err list= [np.float64(0.06664974101984666), np.float64(0.08621437885856936), np.float64(0.07298728653112674), np.float64(0.05896285160238575), np.float64(0.07196285160238575), np.float64(0.05996285160238575), np.float64(0.034962851602385756)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.35013186078905256), 3: np.float64(0.3330557284377345), 4: np.float64(0.3168124088884924), 59: np.float64(4.711801271561337e-10), 40: np.float64(4.711801271561337e-10), 84: np.float64(4.711801271561337e-10), 0: np.float64(4.711801271561337e-10)}
err dic= {2: np.float64(0.07513186078905254), 3: np.float64(0.08605572843773451), 4: np.float64(0.06481240888849238), 59: np.float64(0.05899999952881987), 40: np.float64(0.07199999952881987), 84: np.float64(0.05999999952881987), 0: np.float64(0.034999999528819874)} 

err list= [np.float64(0.07513186078905254), np.float64(0.08605572843773451), np.float64(0.06481240888849238), np.float64(0.05899999952881987), np.float64(0.07199999952881987), np.float64(0.05999999952881987), np.float64(0.034999999528819874)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.36716540111092555), 3: np.float64(0.33222499353334733), 4: np.float64(0.30060960535572745), 59: np.float64(7.443810759557951e-20), 40: np.float64(7.443810759557951e-20), 84: np.float64(7.443810759557951e-20), 0: np.float64(7.443810759557951e-20)}
err dic= {2: np.float64(0.09216540111092553), 3: np.float64(0.08522499353334734), 4: np.float64(0.04860960535572745), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.09216540111092553), np.float64(0.08522499353334734), np.float64(0.04860960535572745), 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  0.25 

learned probs for this beta: {2: np.float64(0.41922895160969764), 3: np.float64(0.3264958357998366), 4: np.float64(0.25427521259046554), 59: np.float64(2.8986235958927613e-49), 40: np.float64(2.8986235958927613e-49), 84: np.float64(2.8986235958927613e-49), 0: np.float64(2.8986235958927613e-49)}
err dic= {2: np.float64(0.14422895160969762), 3: np.float64(0.0794958357998366), 4: np.float64(0.0022752125904655363), 59: np.float64(0.059), 40: np.float64(0.072), 84: np.float64(0.06), 0: np.float64(0.035)} 

err list= [np.float64(0.14422895160969762), np.float64(0.0794958357998366), np.float64(0.0022752125904655363), 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  0.5 

learned probs for this beta: {2: np.float64(0.5064803910556542), 3: np.float64(0.3071958857184985), 4: np.float64(0.18632372322584767), 59: np.float64(2.950190370711525e-98), 40: np.float64(2.950190370711525e-98), 84: np.float64(2.950190370711525e-98), 0: np.float64(2.950190370711525e-98)}
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(3.385476771487503e-147), 40: np.float64(3.385476771487503e-147), 84: np.float64(3.385476771487503e-147), 0: np.float64(3.385476771487503e-147)}
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(4.2238363556523133e-196), 40: np.float64(4.2238363556523133e-196), 84: np.float64(4.2238363556523133e-196), 0: np.float64(4.2238363556523133e-196)}
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(5.5168548935249e-245), 40: np.float64(5.5168548935249e-245), 84: np.float64(5.5168548935249e-245), 0: np.float64(5.5168548935249e-245)}
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(7.388402407555756e-294), 40: np.float64(7.388402407555756e-294), 84: np.float64(7.388402407555756e-294), 0: np.float64(7.388402407555756e-294)}
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(0.0), 40: np.float64(0.0), 84: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 40: np.float64(0.0), 84: np.float64(0.0), 0: np.float64(0.0)}
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(0.3478596035770503), 4: np.float64(0.3392709193629437), 8: np.float64(0.31271617892753995), 74: np.float64(3.832453311644184e-05), 40: np.float64(3.832453311644184e-05), 87: np.float64(3.832453311644184e-05), 0: np.float64(3.832453311644184e-05)}
err dic= {3: np.float64(0.0888596035770503), 4: np.float64(0.09327091936294368), 8: np.float64(0.05671617892753994), 74: np.float64(0.06596167546688356), 40: np.float64(0.07696167546688355), 87: np.float64(0.04696167546688356), 0: np.float64(0.04896167546688356)} 

err list= [np.float64(0.0888596035770503), np.float64(0.09327091936294368), np.float64(0.05671617892753994), np.float64(0.06596167546688356), np.float64(0.07696167546688355), np.float64(0.04696167546688356), np.float64(0.04896167546688356)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.3624551654229569), 4: np.float64(0.34477801841259054), 8: np.float64(0.292766814154073), 74: np.float64(5.025949065815151e-10), 40: np.float64(5.025949065815151e-10), 87: np.float64(5.025949065815151e-10), 0: np.float64(5.025949065815151e-10)}
err dic= {3: np.float64(0.10345516542295691), 4: np.float64(0.09877801841259054), 8: np.float64(0.03676681415407301), 74: np.float64(0.06599999949740509), 40: np.float64(0.07699999949740509), 87: np.float64(0.0469999994974051), 0: np.float64(0.0489999994974051)} 

err list= [np.float64(0.10345516542295691), np.float64(0.09877801841259054), np.float64(0.03676681415407301), np.float64(0.06599999949740509), np.float64(0.07699999949740509), np.float64(0.0469999994974051), np.float64(0.0489999994974051)]
results for assortment [3, 4, 8, 74, 40, 87] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.39126143983898354), 4: np.float64(0.35402799100093785), 8: np.float64(0.25471056916007917), 74: np.float64(8.536384211442546e-20), 40: np.float64(8.536384211442546e-20), 87: np.float64(8.536384211442546e-20), 0: np.float64(8.536384211442546e-20)}
err dic= {3: np.float64(0.13226143983898353), 4: np.float64(0.10802799100093785), 8: np.float64(0.0012894308399208354), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.13226143983898353), np.float64(0.10802799100093785), np.float64(0.0012894308399208354), 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  0.25 

learned probs for this beta: {3: np.float64(0.4729190782429194), 4: np.float64(0.3683097484649926), 8: np.float64(0.15877117329208743), 74: np.float64(4.234049285916718e-49), 40: np.float64(4.234049285916718e-49), 87: np.float64(4.234049285916718e-49), 0: np.float64(4.234049285916718e-49)}
err dic= {3: np.float64(0.2139190782429194), 4: np.float64(0.1223097484649926), 8: np.float64(0.09722882670791258), 74: np.float64(0.066), 40: np.float64(0.077), 87: np.float64(0.047), 0: np.float64(0.049)} 

err list= [np.float64(0.2139190782429194), np.float64(0.1223097484649926), np.float64(0.09722882670791258), 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  0.5 

learned probs for this beta: {3: np.float64(0.5841457846018505), 4: np.float64(0.3543023281029142), 8: np.float64(0.06155188729523564), 74: np.float64(6.268825630498745e-98), 40: np.float64(6.268825630498745e-98), 87: np.float64(6.268825630498745e-98), 0: np.float64(6.268825630498745e-98)}
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(9.563375237236864e-147), 40: np.float64(9.563375237236864e-147), 87: np.float64(9.563375237236864e-147), 0: np.float64(9.563375237236864e-147)}
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(1.5052904730861336e-195), 40: np.float64(1.5052904730861336e-195), 87: np.float64(1.5052904730861336e-195), 0: np.float64(1.5052904730861336e-195)}
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(2.4336636644169822e-244), 40: np.float64(2.4336636644169822e-244), 87: np.float64(2.4336636644169822e-244), 0: np.float64(2.4336636644169822e-244)}
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(4.0209613071901526e-293), 40: np.float64(4.0209613071901526e-293), 87: np.float64(4.0209613071901526e-293), 0: np.float64(4.0209613071901526e-293)}
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(0.0), 40: np.float64(0.0), 87: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 40: np.float64(0.0), 87: np.float64(0.0), 0: np.float64(0.0)}
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(0.35416945378116754), 3: np.float64(0.3390592032760743), 9: np.float64(0.3066457347266652), 83: np.float64(3.14020540232139e-05), 79: np.float64(3.14020540232139e-05), 70: np.float64(3.14020540232139e-05), 0: np.float64(3.14020540232139e-05)}
err dic= {1: np.float64(0.08916945378116753), 3: np.float64(0.0880592032760743), 9: np.float64(0.07164573472666519), 83: np.float64(0.05196859794597678), 79: np.float64(0.06796859794597679), 70: np.float64(0.08096859794597679), 0: np.float64(0.047968597945976785)} 

err list= [np.float64(0.08916945378116753), np.float64(0.0880592032760743), np.float64(0.07164573472666519), np.float64(0.05196859794597678), np.float64(0.06796859794597679), np.float64(0.08096859794597679), np.float64(0.047968597945976785)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.37511270152750253), 3: np.float64(0.3438874311202811), 9: np.float64(0.2809998658870662), 83: np.float64(3.6628760005741786e-10), 79: np.float64(3.6628760005741786e-10), 70: np.float64(3.6628760005741786e-10), 0: np.float64(3.6628760005741786e-10)}
err dic= {1: np.float64(0.11011270152750252), 3: np.float64(0.09288743112028108), 9: np.float64(0.04599986588706623), 83: np.float64(0.0519999996337124), 79: np.float64(0.06799999963371241), 70: np.float64(0.0809999996337124), 0: np.float64(0.047999999633712404)} 

err list= [np.float64(0.11011270152750252), np.float64(0.09288743112028108), np.float64(0.04599986588706623), np.float64(0.0519999996337124), np.float64(0.06799999963371241), np.float64(0.0809999996337124), np.float64(0.047999999633712404)]
results for assortment [1, 3, 9, 83, 79, 70] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.41653659914613067), 3: np.float64(0.35045352839142585), 9: np.float64(0.2330098724624441), 83: np.float64(4.9008644399286846e-20), 79: np.float64(4.9008644399286846e-20), 70: np.float64(4.9008644399286846e-20), 0: np.float64(4.9008644399286846e-20)}
err dic= {1: np.float64(0.15153659914613066), 3: np.float64(0.09945352839142585), 9: np.float64(0.001990127537555897), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.15153659914613066), np.float64(0.09945352839142585), np.float64(0.001990127537555897), 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  0.25 

learned probs for this beta: {1: np.float64(0.53166001008169), 3: np.float64(0.3473995733591339), 9: np.float64(0.12094041655917559), 83: np.float64(1.130344964769752e-49), 79: np.float64(1.130344964769752e-49), 70: np.float64(1.130344964769752e-49), 0: np.float64(1.130344964769752e-49)}
err dic= {1: np.float64(0.26666001008168994), 3: np.float64(0.0963995733591339), 9: np.float64(0.1140595834408244), 83: np.float64(0.052), 79: np.float64(0.068), 70: np.float64(0.081), 0: np.float64(0.048)} 

err list= [np.float64(0.26666001008168994), np.float64(0.0963995733591339), np.float64(0.1140595834408244), 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  0.5 

learned probs for this beta: {1: np.float64(0.6768077271813894), 3: np.float64(0.29176229833973133), 9: np.float64(0.03142997447887963), 83: np.float64(4.1907914631411214e-99), 79: np.float64(4.1907914631411214e-99), 70: np.float64(4.1907914631411214e-99), 0: np.float64(4.1907914631411214e-99)}
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(1.5189942690373687e-148), 79: np.float64(1.5189942690373687e-148), 70: np.float64(1.5189942690373687e-148), 0: np.float64(1.5189942690373687e-148)}
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(5.61008102855678e-198), 79: np.float64(5.61008102855678e-198), 70: np.float64(5.61008102855678e-198), 0: np.float64(5.61008102855678e-198)}
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(2.120913173201311e-247), 79: np.float64(2.120913173201311e-247), 70: np.float64(2.120913173201311e-247), 0: np.float64(2.120913173201311e-247)}
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(8.163179721183582e-297), 79: np.float64(8.163179721183582e-297), 70: np.float64(8.163179721183582e-297), 0: np.float64(8.163179721183582e-297)}
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(0.0), 79: np.float64(0.0), 70: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 79: np.float64(0.0), 70: np.float64(0.0), 0: np.float64(0.0)}
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(0.35637593274340384), 4: np.float64(0.33487631880292706), 8: np.float64(0.3086214730821277), 32: np.float64(3.156884288540751e-05), 27: np.float64(3.156884288540751e-05), 82: np.float64(3.156884288540751e-05), 0: np.float64(3.156884288540751e-05)}
err dic= {1: np.float64(0.13437593274340384), 4: np.float64(0.10487631880292705), 8: np.float64(0.07662147308212766), 32: np.float64(0.10196843115711458), 27: np.float64(0.11996843115711459), 82: np.float64(0.04996843115711459), 0: np.float64(0.04396843115711459)} 

err list= [np.float64(0.13437593274340384), np.float64(0.10487631880292705), np.float64(0.07662147308212766), np.float64(0.10196843115711458), np.float64(0.11996843115711459), np.float64(0.04996843115711459), np.float64(0.04396843115711459)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.3797664732526993), 4: np.float64(0.33550574409928413), 8: np.float64(0.2847277811664003), 32: np.float64(3.7040410694710336e-10), 27: np.float64(3.7040410694710336e-10), 82: np.float64(3.7040410694710336e-10), 0: np.float64(3.7040410694710336e-10)}
err dic= {1: np.float64(0.1577664732526993), 4: np.float64(0.10550574409928412), 8: np.float64(0.052727781166400284), 32: np.float64(0.10199999962959588), 27: np.float64(0.11999999962959589), 82: np.float64(0.04999999962959589), 0: np.float64(0.04399999962959589)} 

err list= [np.float64(0.1577664732526993), np.float64(0.10550574409928412), np.float64(0.052727781166400284), np.float64(0.10199999962959588), np.float64(0.11999999962959589), np.float64(0.04999999962959589), np.float64(0.04399999962959589)]
results for assortment [1, 4, 8, 32, 27, 82] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.42674105797228107), 4: np.float64(0.33372563169505487), 8: np.float64(0.2395333103326645), 32: np.float64(5.022720795480278e-20), 27: np.float64(5.022720795480278e-20), 82: np.float64(5.022720795480278e-20), 0: np.float64(5.022720795480278e-20)}
err dic= {1: np.float64(0.20474105797228107), 4: np.float64(0.10372563169505486), 8: np.float64(0.007533310332664495), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.20474105797228107), np.float64(0.10372563169505486), np.float64(0.007533310332664495), 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  0.25 

learned probs for this beta: {1: np.float64(0.5619787294115659), 4: np.float64(0.30746143031853845), 8: np.float64(0.13055984026989492), 32: np.float64(1.217868007239461e-49), 27: np.float64(1.217868007239461e-49), 82: np.float64(1.217868007239461e-49), 0: np.float64(1.217868007239461e-49)}
err dic= {1: np.float64(0.3399787294115659), 4: np.float64(0.07746143031853844), 8: np.float64(0.10144015973010509), 32: np.float64(0.102), 27: np.float64(0.12), 82: np.float64(0.05), 0: np.float64(0.044)} 

err list= [np.float64(0.3399787294115659), np.float64(0.07746143031853844), np.float64(0.10144015973010509), 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  0.5 

learned probs for this beta: {1: np.float64(0.7383008689607047), 4: np.float64(0.22465672961378827), 8: np.float64(0.03704240142550746), 32: np.float64(4.954409824389608e-99), 27: np.float64(4.954409824389608e-99), 82: np.float64(4.954409824389608e-99), 0: np.float64(4.954409824389608e-99)}
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(1.941356313066127e-148), 27: np.float64(1.941356313066127e-148), 82: np.float64(1.941356313066127e-148), 0: np.float64(1.941356313066127e-148)}
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(7.583194948123604e-198), 27: np.float64(7.583194948123604e-198), 82: np.float64(7.583194948123604e-198), 0: np.float64(7.583194948123604e-198)}
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(2.976968190487651e-247), 27: np.float64(2.976968190487651e-247), 82: np.float64(2.976968190487651e-247), 0: np.float64(2.976968190487651e-247)}
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(1.1742421001815454e-296), 27: np.float64(1.1742421001815454e-296), 82: np.float64(1.1742421001815454e-296), 0: np.float64(1.1742421001815454e-296)}
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(0.0), 27: np.float64(0.0), 82: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 27: np.float64(0.0), 82: np.float64(0.0), 0: np.float64(0.0)}
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(3.5737250120836525e-05), 4: np.float64(0.5103242473035078), 6: np.float64(0.489497066445888), 51: np.float64(3.5737250120836525e-05), 82: np.float64(3.5737250120836525e-05), 41: np.float64(3.5737250120836525e-05), 0: np.float64(3.5737250120836525e-05)}
err dic= {9: np.float64(0.22096426274987915), 4: np.float64(0.2653242473035078), 6: np.float64(0.23349706644588797), 51: np.float64(0.08596426274987916), 82: np.float64(0.039964262749879166), 41: np.float64(0.09296426274987916), 0: np.float64(0.05896426274987916)} 

err list= [np.float64(0.22096426274987915), np.float64(0.2653242473035078), np.float64(0.23349706644588797), np.float64(0.08596426274987916), np.float64(0.039964262749879166), np.float64(0.09296426274987916), np.float64(0.05896426274987916)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.05 

learned probs for this beta: {9: np.float64(3.8987001315060684e-10), 4: np.float64(0.5208220544682736), 6: np.float64(0.47917794358237653), 51: np.float64(3.8987001315060684e-10), 82: np.float64(3.8987001315060684e-10), 41: np.float64(3.8987001315060684e-10), 0: np.float64(3.8987001315060684e-10)}
err dic= {9: np.float64(0.22099999961012998), 4: np.float64(0.27582205446827357), 6: np.float64(0.22317794358237653), 51: np.float64(0.08599999961012998), 82: np.float64(0.03999999961012999), 41: np.float64(0.09299999961012999), 0: np.float64(0.058999999610129986)} 

err list= [np.float64(0.22099999961012998), np.float64(0.27582205446827357), np.float64(0.22317794358237653), np.float64(0.08599999961012998), np.float64(0.03999999961012999), np.float64(0.09299999961012999), np.float64(0.058999999610129986)]
results for assortment [9, 4, 6, 51, 82, 41] :

beta is  0.1 

learned probs for this beta: {9: np.float64(4.6483717878516514e-20), 4: np.float64(0.5415766082762583), 6: np.float64(0.45842339172374186), 51: np.float64(4.6483717878516514e-20), 82: np.float64(4.6483717878516514e-20), 41: np.float64(4.6483717878516514e-20), 0: np.float64(4.6483717878516514e-20)}
err dic= {9: np.float64(0.221), 4: np.float64(0.2965766082762583), 6: np.float64(0.20242339172374185), 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(0.2965766082762583), np.float64(0.20242339172374185), 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  0.25 

learned probs for this beta: {9: np.float64(8.223507692520892e-50), 4: np.float64(0.6027772381334338), 6: np.float64(0.3972227618665658), 51: np.float64(8.223507692520892e-50), 82: np.float64(8.223507692520892e-50), 41: np.float64(8.223507692520892e-50), 0: np.float64(8.223507692520892e-50)}
err dic= {9: np.float64(0.221), 4: np.float64(0.35777723813343376), 6: np.float64(0.1412227618665658), 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(0.35777723813343376), np.float64(0.1412227618665658), 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  0.5 

learned probs for this beta: {9: np.float64(2.3216717843347606e-99), 4: np.float64(0.6976973366279521), 6: np.float64(0.3023026633720482), 51: np.float64(2.3216717843347606e-99), 82: np.float64(2.3216717843347606e-99), 41: np.float64(2.3216717843347606e-99), 0: np.float64(2.3216717843347606e-99)}
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(6.799815238928727e-149), 4: np.float64(0.7790173173345053), 6: np.float64(0.22098268266549476), 51: np.float64(6.799815238928727e-149), 82: np.float64(6.799815238928727e-149), 41: np.float64(6.799815238928727e-149), 0: np.float64(6.799815238928727e-149)}
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(2.0125797598170073e-198), 4: np.float64(0.8441518039744367), 6: np.float64(0.1558481960255635), 51: np.float64(2.0125797598170073e-198), 82: np.float64(2.0125797598170073e-198), 41: np.float64(2.0125797598170073e-198), 0: np.float64(2.0125797598170073e-198)}
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(6.0127681864860745e-248), 4: np.float64(0.8934014727128832), 6: np.float64(0.10659852728711663), 51: np.float64(6.0127681864860745e-248), 82: np.float64(6.0127681864860745e-248), 41: np.float64(6.0127681864860745e-248), 0: np.float64(6.0127681864860745e-248)}
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(1.8139253524131678e-297), 4: np.float64(0.9289099851249452), 6: np.float64(0.07109001487505527), 51: np.float64(1.8139253524131678e-297), 82: np.float64(1.8139253524131678e-297), 41: np.float64(1.8139253524131678e-297), 0: np.float64(1.8139253524131678e-297)}
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(0.0), 4: np.float64(0.9535502818108356), 6: np.float64(0.046449718189164366), 51: np.float64(0.0), 82: np.float64(0.0), 41: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 4: np.float64(0.9701400142429856), 6: np.float64(0.029859985757014335), 51: np.float64(0.0), 82: np.float64(0.0), 41: np.float64(0.0), 0: np.float64(0.0)}
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(0.345788735245964), 9: np.float64(0.3167724170546524), 6: np.float64(0.33725118095312945), 39: np.float64(4.69166865634571e-05), 80: np.float64(4.69166865634571e-05), 68: np.float64(4.69166865634571e-05), 0: np.float64(4.69166865634571e-05)}
err dic= {5: np.float64(0.10078873524596399), 9: np.float64(0.08877241705465241), 6: np.float64(0.07925118095312944), 39: np.float64(0.09995308331343655), 80: np.float64(0.06295308331343655), 68: np.float64(0.05595308331343654), 0: np.float64(0.04995308331343654)} 

err list= [np.float64(0.10078873524596399), np.float64(0.08877241705465241), np.float64(0.07925118095312944), np.float64(0.09995308331343655), np.float64(0.06295308331343655), np.float64(0.05595308331343654), np.float64(0.04995308331343654)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.05 

learned probs for this beta: {5: np.float64(0.35839737606932476), 9: np.float64(0.3006844913524342), 6: np.float64(0.3409181297809897), 39: np.float64(6.99312818651888e-10), 80: np.float64(6.99312818651888e-10), 68: np.float64(6.99312818651888e-10), 0: np.float64(6.99312818651888e-10)}
err dic= {5: np.float64(0.11339737606932476), 9: np.float64(0.07268449135243418), 6: np.float64(0.08291812978098967), 39: np.float64(0.09999999930068719), 80: np.float64(0.06299999930068718), 68: np.float64(0.055999999300687185), 0: np.float64(0.04999999930068719)} 

err list= [np.float64(0.11339737606932476), np.float64(0.07268449135243418), np.float64(0.08291812978098967), np.float64(0.09999999930068719), np.float64(0.06299999930068718), np.float64(0.055999999300687185), np.float64(0.04999999930068719)]
results for assortment [5, 9, 6, 39, 80, 68] :

beta is  0.1 

learned probs for this beta: {5: np.float64(0.3834589591641221), 9: np.float64(0.26957302630305796), 6: np.float64(0.3469680145328206), 39: np.float64(1.5418756089696805e-19), 80: np.float64(1.5418756089696805e-19), 68: np.float64(1.5418756089696805e-19), 0: np.float64(1.5418756089696805e-19)}
err dic= {5: np.float64(0.1384589591641221), 9: np.float64(0.04157302630305795), 6: np.float64(0.0889680145328206), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.1384589591641221), np.float64(0.04157302630305795), np.float64(0.0889680145328206), 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  0.25 

learned probs for this beta: {5: np.float64(0.4568298022717689), 9: np.float64(0.18739078998862158), 6: np.float64(0.35577940773960876), 39: np.float64(1.7637256503263924e-48), 80: np.float64(1.7637256503263924e-48), 68: np.float64(1.7637256503263924e-48), 0: np.float64(1.7637256503263924e-48)}
err dic= {5: np.float64(0.2118298022717689), 9: np.float64(0.04060921001137843), 6: np.float64(0.09777940773960875), 39: np.float64(0.1), 80: np.float64(0.063), 68: np.float64(0.056), 0: np.float64(0.05)} 

err list= [np.float64(0.2118298022717689), np.float64(0.04060921001137843), np.float64(0.09777940773960875), 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  0.5 

learned probs for this beta: {5: np.float64(0.5654187560796601), 9: np.float64(0.09163743278144765), 6: np.float64(0.3429438111388928), 39: np.float64(1.1560169537378858e-96), 80: np.float64(1.1560169537378858e-96), 68: np.float64(1.1560169537378858e-96), 0: np.float64(1.1560169537378858e-96)}
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(8.05357949621734e-145), 80: np.float64(8.05357949621734e-145), 68: np.float64(8.05357949621734e-145), 0: np.float64(8.05357949621734e-145)}
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(5.800476142222826e-193), 80: np.float64(5.800476142222826e-193), 68: np.float64(5.800476142222826e-193), 0: np.float64(5.800476142222826e-193)}
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(4.2747029519784595e-241), 80: np.float64(4.2747029519784595e-241), 68: np.float64(4.2747029519784595e-241), 0: np.float64(4.2747029519784595e-241)}
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(3.203207516087633e-289), 80: np.float64(3.203207516087633e-289), 68: np.float64(3.203207516087633e-289), 0: np.float64(3.203207516087633e-289)}
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(0.0), 80: np.float64(0.0), 68: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 80: np.float64(0.0), 68: np.float64(0.0), 0: np.float64(0.0)}
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(0.3309308264620943), 3: np.float64(0.3522094269696874), 8: np.float64(0.3167307430792024), 15: np.float64(3.225087225400696e-05), 78: np.float64(3.225087225400696e-05), 97: np.float64(3.225087225400696e-05), 0: np.float64(3.225087225400696e-05)}
err dic= {6: np.float64(0.10993082646209432), 3: np.float64(0.11720942696968739), 8: np.float64(0.07873074307920241), 15: np.float64(0.17296774912774598), 78: np.float64(0.05596774912774599), 97: np.float64(0.03896774912774599), 0: np.float64(0.03796774912774599)} 

err list= [np.float64(0.10993082646209432), np.float64(0.11720942696968739), np.float64(0.07873074307920241), np.float64(0.17296774912774598), np.float64(0.05596774912774599), np.float64(0.03896774912774599), np.float64(0.03796774912774599)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.05 

learned probs for this beta: {6: np.float64(0.3280678610229729), 3: np.float64(0.37148018215513695), 8: np.float64(0.30045195527127794), 15: np.float64(3.8765314261215394e-10), 78: np.float64(3.8765314261215394e-10), 97: np.float64(3.8765314261215394e-10), 0: np.float64(3.8765314261215394e-10)}
err dic= {6: np.float64(0.10706786102297292), 3: np.float64(0.13648018215513696), 8: np.float64(0.06245195527127795), 15: np.float64(0.17299999961234686), 78: np.float64(0.055999999612346855), 97: np.float64(0.038999999612346854), 0: np.float64(0.03799999961234685)} 

err list= [np.float64(0.10706786102297292), np.float64(0.13648018215513696), np.float64(0.06245195527127795), np.float64(0.17299999961234686), np.float64(0.055999999612346855), np.float64(0.038999999612346854), np.float64(0.03799999961234685)]
results for assortment [6, 3, 8, 15, 78, 97] :

beta is  0.1 

learned probs for this beta: {6: np.float64(0.3206755332526871), 3: np.float64(0.4106068102581274), 8: np.float64(0.26871765648918594), 15: np.float64(5.562415903851098e-20), 78: np.float64(5.562415903851098e-20), 97: np.float64(5.562415903851098e-20), 0: np.float64(5.562415903851098e-20)}
err dic= {6: np.float64(0.0996755332526871), 3: np.float64(0.1756068102581274), 8: np.float64(0.03071765648918595), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.0996755332526871), np.float64(0.1756068102581274), np.float64(0.03071765648918595), 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  0.25 

learned probs for this beta: {6: np.float64(0.2875137926500776), 3: np.float64(0.5289888465558913), 8: np.float64(0.1834973607940305), 15: np.float64(1.6959173261018183e-49), 78: np.float64(1.6959173261018183e-49), 97: np.float64(1.6959173261018183e-49), 0: np.float64(1.6959173261018183e-49)}
err dic= {6: np.float64(0.06651379265007759), 3: np.float64(0.2939888465558913), 8: np.float64(0.05450263920596948), 15: np.float64(0.173), 78: np.float64(0.056), 97: np.float64(0.039), 0: np.float64(0.038)} 

err list= [np.float64(0.06651379265007759), np.float64(0.2939888465558913), np.float64(0.05450263920596948), 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  0.5 

learned probs for this beta: {6: np.float64(0.21136722905274474), 3: np.float64(0.7045769546695909), 8: np.float64(0.08405581627766473), 15: np.float64(1.1411812718059997e-98), 78: np.float64(1.1411812718059997e-98), 97: np.float64(1.1411812718059997e-98), 0: np.float64(1.1411812718059997e-98)}
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(7.715337163962481e-148), 78: np.float64(7.715337163962481e-148), 97: np.float64(7.715337163962481e-148), 0: np.float64(7.715337163962481e-148)}
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(5.174323203715567e-197), 78: np.float64(5.174323203715567e-197), 97: np.float64(5.174323203715567e-197), 0: np.float64(5.174323203715567e-197)}
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(3.4469815127449133e-246), 78: np.float64(3.4469815127449133e-246), 97: np.float64(3.4469815127449133e-246), 0: np.float64(3.4469815127449133e-246)}
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(2.284770123697025e-295), 78: np.float64(2.284770123697025e-295), 97: np.float64(2.284770123697025e-295), 0: np.float64(2.284770123697025e-295)}
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(0.0), 78: np.float64(0.0), 97: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 78: np.float64(0.0), 97: np.float64(0.0), 0: np.float64(0.0)}
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(0.2390295636434467), 2: np.float64(0.2721594429405534), 4: np.float64(0.2602394307546519), 95: np.float64(3.6640386823328504e-05), 11: np.float64(0.2284616415008777), 22: np.float64(3.6640386823328504e-05), 0: np.float64(3.6640386823328504e-05)}
err dic= {8: np.float64(0.004029563643446726), 2: np.float64(0.07015944294055337), 4: np.float64(0.06323943075465188), 95: np.float64(0.041963359613176675), 11: np.float64(0.062461641500877685), 22: np.float64(0.13696335961317668), 0: np.float64(0.020963359613176673)} 

err list= [np.float64(0.004029563643446726), np.float64(0.07015944294055337), np.float64(0.06323943075465188), np.float64(0.041963359613176675), np.float64(0.062461641500877685), np.float64(0.13696335961317668), np.float64(0.020963359613176673)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.05 

learned probs for this beta: {8: np.float64(0.22755533708526682), 2: np.float64(0.2949057346369167), 4: np.float64(0.26975195523881307), 95: np.float64(5.314012299871053e-10), 11: np.float64(0.2077869714447997), 22: np.float64(5.314012299871053e-10), 0: np.float64(5.314012299871053e-10)}
err dic= {8: np.float64(0.007444662914733169), 2: np.float64(0.0929057346369167), 4: np.float64(0.07275195523881306), 95: np.float64(0.041999999468598774), 11: np.float64(0.0417869714447997), 22: np.float64(0.13699999946859878), 0: np.float64(0.020999999468598773)} 

err list= [np.float64(0.007444662914733169), np.float64(0.0929057346369167), np.float64(0.07275195523881306), np.float64(0.041999999468598774), np.float64(0.0417869714447997), np.float64(0.13699999946859878), np.float64(0.020999999468598773)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.1 

learned probs for this beta: {8: np.float64(0.20339914463855893), 2: np.float64(0.34129604465345215), 4: np.float64(0.28601324767576086), 95: np.float64(1.0984915592057456e-19), 11: np.float64(0.1692915630322288), 22: np.float64(1.0984915592057456e-19), 0: np.float64(1.0984915592057456e-19)}
err dic= {8: np.float64(0.031600855361441055), 2: np.float64(0.13929604465345213), 4: np.float64(0.08901324767576085), 95: np.float64(0.042), 11: np.float64(0.0032915630322288003), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.031600855361441055), np.float64(0.13929604465345213), np.float64(0.08901324767576085), np.float64(0.042), np.float64(0.0032915630322288003), np.float64(0.137), np.float64(0.021)]
results for assortment [8, 2, 4, 95, 11, 22] :

beta is  0.25 

learned probs for this beta: {8: np.float64(0.1308257606990439), 2: np.float64(0.4775204477078609), 4: np.float64(0.31002951642583915), 95: np.float64(9.642463016337387e-49), 11: np.float64(0.0816242751672552), 22: np.float64(9.642463016337387e-49), 0: np.float64(9.642463016337387e-49)}
err dic= {8: np.float64(0.1041742393009561), 2: np.float64(0.2755204477078609), 4: np.float64(0.11302951642583914), 95: np.float64(0.042), 11: np.float64(0.0843757248327448), 22: np.float64(0.137), 0: np.float64(0.021)} 

err list= [np.float64(0.1041742393009561), np.float64(0.2755204477078609), np.float64(0.11302951642583914), np.float64(0.042), np.float64(0.0843757248327448), np.float64(0.137), np.float64(0.021)]
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(3.492400995053338e-97), 11: np.float64(0.017759613108311294), 22: np.float64(3.492400995053338e-97), 0: np.float64(3.492400995053338e-97)}
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(1.244032572377223e-145), 11: np.float64(0.003061487235188769), 22: np.float64(1.244032572377223e-145), 0: np.float64(1.244032572377223e-145)}
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(4.4564501838463896e-194), 11: np.float64(0.00047336280779999217), 22: np.float64(4.4564501838463896e-194), 0: np.float64(4.4564501838463896e-194)}
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(1.616299238657444e-242), 11: np.float64(6.965386583462914e-05), 22: np.float64(1.616299238657444e-242), 0: np.float64(1.616299238657444e-242)}
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(5.931883143959805e-291), 11: np.float64(9.99775588346969e-06), 22: np.float64(5.931883143959805e-291), 0: np.float64(5.931883143959805e-291)}
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(0.0), 11: np.float64(1.414291028627564e-06), 22: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 11: np.float64(1.9810924551184603e-07), 22: np.float64(0.0), 0: np.float64(0.0)}
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(0.2784754812268456), 3: np.float64(0.2663005205760023), 9: np.float64(0.23501888357405087), 100: np.float64(0.22009487746444742), 22: np.float64(3.674571955122194e-05), 58: np.float64(3.674571955122194e-05), 0: np.float64(3.674571955122194e-05)}
err dic= {1: np.float64(0.06047548122684562), 3: np.float64(0.08530052057600229), 9: np.float64(0.038018883574050866), 100: np.float64(0.0019051225355525836), 22: np.float64(0.11296325428044877), 58: np.float64(0.04096325428044878), 0: np.float64(0.02796325428044878)} 

err list= [np.float64(0.06047548122684562), np.float64(0.08530052057600229), np.float64(0.038018883574050866), np.float64(0.0019051225355525836), np.float64(0.11296325428044877), np.float64(0.04096325428044878), np.float64(0.02796325428044878)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.30752170062240985), 3: np.float64(0.28138067983007176), 9: np.float64(0.21914068975158305), 100: np.float64(0.1919569281969077), 22: np.float64(5.330092327025098e-10), 58: np.float64(5.330092327025098e-10), 0: np.float64(5.330092327025098e-10)}
err dic= {1: np.float64(0.08952170062240986), 3: np.float64(0.10038067983007176), 9: np.float64(0.022140689751583037), 100: np.float64(0.03004307180309229), 22: np.float64(0.11299999946699077), 58: np.float64(0.04099999946699077), 0: np.float64(0.027999999466990767)} 

err list= [np.float64(0.08952170062240986), np.float64(0.10038067983007176), np.float64(0.022140689751583037), np.float64(0.03004307180309229), np.float64(0.11299999946699077), np.float64(0.04099999946699077), np.float64(0.027999999466990767)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3655945243325265), 3: np.float64(0.30673146153013786), 9: np.float64(0.18580622910229905), 100: np.float64(0.14186778503503683), 22: np.float64(1.0926532408255075e-19), 58: np.float64(1.0926532408255075e-19), 0: np.float64(1.0926532408255075e-19)}
err dic= {1: np.float64(0.14759452433252648), 3: np.float64(0.12573146153013787), 9: np.float64(0.011193770897700961), 100: np.float64(0.08013221496496317), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.14759452433252648), np.float64(0.12573146153013787), np.float64(0.011193770897700961), np.float64(0.08013221496496317), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
results for assortment [1, 3, 9, 100, 22, 58] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.5199273620382431), 3: np.float64(0.33916654873196656), 9: np.float64(0.09438635240642483), 100: np.float64(0.04651973682336486), 22: np.float64(8.752721928080565e-49), 58: np.float64(8.752721928080565e-49), 0: np.float64(8.752721928080565e-49)}
err dic= {1: np.float64(0.3019273620382431), 3: np.float64(0.15816654873196656), 9: np.float64(0.10261364759357518), 100: np.float64(0.17548026317663515), 22: np.float64(0.113), 58: np.float64(0.041), 0: np.float64(0.028)} 

err list= [np.float64(0.3019273620382431), np.float64(0.15816654873196656), np.float64(0.10261364759357518), np.float64(0.17548026317663515), np.float64(0.113), np.float64(0.041), np.float64(0.028)]
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(2.3887066457941033e-97), 58: np.float64(2.3887066457941033e-97), 0: np.float64(2.3887066457941033e-97)}
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(6.2564184746572675e-146), 58: np.float64(6.2564184746572675e-146), 0: np.float64(6.2564184746572675e-146)}
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(1.6857141969337542e-194), 58: np.float64(1.6857141969337542e-194), 0: np.float64(1.6857141969337542e-194)}
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(4.683983548521507e-243), 58: np.float64(4.683983548521507e-243), 0: np.float64(4.683983548521507e-243)}
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(1.3295336548400467e-291), 58: np.float64(1.3295336548400467e-291), 0: np.float64(1.3295336548400467e-291)}
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(0.0), 58: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 58: np.float64(0.0), 0: np.float64(0.0)}
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(0.33321998895702487), 6: np.float64(0.34165549313862076), 8: np.float64(0.3249927581157579), 16: np.float64(3.2939947149081093e-05), 83: np.float64(3.2939947149081093e-05), 70: np.float64(3.2939947149081093e-05), 0: np.float64(3.2939947149081093e-05)}
err dic= {7: np.float64(0.12621998895702488), 6: np.float64(0.09565549313862076), 8: np.float64(0.0759927581157579), 16: np.float64(0.1479670600528509), 83: np.float64(0.04796706005285092), 70: np.float64(0.05796706005285092), 0: np.float64(0.04396706005285091)} 

err list= [np.float64(0.12621998895702488), np.float64(0.09565549313862076), np.float64(0.0759927581157579), np.float64(0.1479670600528509), np.float64(0.04796706005285092), np.float64(0.05796706005285092), np.float64(0.04396706005285091)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.3330557285254626), 6: np.float64(0.3501318608812785), 8: np.float64(0.31681240897194185), 16: np.float64(4.053293095023739e-10), 83: np.float64(4.053293095023739e-10), 70: np.float64(4.053293095023739e-10), 0: np.float64(4.053293095023739e-10)}
err dic= {7: np.float64(0.12605572852546262), 6: np.float64(0.10413186088127852), 8: np.float64(0.06781240897194185), 16: np.float64(0.1479999995946707), 83: np.float64(0.04799999959467069), 70: np.float64(0.05799999959467069), 0: np.float64(0.043999999594670686)} 

err list= [np.float64(0.12605572852546262), np.float64(0.10413186088127852), np.float64(0.06781240897194185), np.float64(0.1479999995946707), np.float64(0.04799999959467069), np.float64(0.05799999959467069), np.float64(0.043999999594670686)]
results for assortment [7, 6, 8, 16, 83, 70] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.33222499353334733), 6: np.float64(0.3671654011109256), 8: np.float64(0.30060960535572745), 16: np.float64(6.138062580487352e-20), 83: np.float64(6.138062580487352e-20), 70: np.float64(6.138062580487352e-20), 0: np.float64(6.138062580487352e-20)}
err dic= {7: np.float64(0.12522499353334735), 6: np.float64(0.12116540111092561), 8: np.float64(0.05160960535572745), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.12522499353334735), np.float64(0.12116540111092561), np.float64(0.05160960535572745), 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  0.25 

learned probs for this beta: {7: np.float64(0.3264958357998365), 6: np.float64(0.4192289516096974), 8: np.float64(0.2542752125904655), 16: np.float64(2.321965277241866e-49), 83: np.float64(2.321965277241866e-49), 70: np.float64(2.321965277241866e-49), 0: np.float64(2.321965277241866e-49)}
err dic= {7: np.float64(0.1194958357998365), 6: np.float64(0.17322895160969742), 8: np.float64(0.005275212590465483), 16: np.float64(0.148), 83: np.float64(0.048), 70: np.float64(0.058), 0: np.float64(0.044)} 

err list= [np.float64(0.1194958357998365), np.float64(0.17322895160969742), np.float64(0.005275212590465483), 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  0.5 

learned probs for this beta: {7: np.float64(0.30719588571849854), 6: np.float64(0.5064803910556542), 8: np.float64(0.1863237232258477), 16: np.float64(2.5814542035324097e-98), 83: np.float64(2.5814542035324097e-98), 70: np.float64(2.5814542035324097e-98), 0: np.float64(2.5814542035324097e-98)}
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(3.195628429787736e-147), 83: np.float64(3.195628429787736e-147), 70: np.float64(3.195628429787736e-147), 0: np.float64(3.195628429787736e-147)}
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(4.131377154899004e-196), 83: np.float64(4.131377154899004e-196), 70: np.float64(4.131377154899004e-196), 0: np.float64(4.131377154899004e-196)}
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(5.472630937912007e-245), 83: np.float64(5.472630937912007e-245), 70: np.float64(5.472630937912007e-245), 0: np.float64(5.472630937912007e-245)}
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(7.367585850222518e-294), 83: np.float64(7.367585850222518e-294), 70: np.float64(7.367585850222518e-294), 0: np.float64(7.367585850222518e-294)}
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(0.0), 83: np.float64(0.0), 70: np.float64(0.0), 0: np.float64(0.0)}
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(0.0), 83: np.float64(0.0), 70: np.float64(0.0), 0: np.float64(0.0)}
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= [0.08510521 0.08512403 0.08513031 0.08513345 0.08871683 0.09371157
 0.09897601 0.10399766 0.10957243 0.1153176  0.12095921]
mean_std= [0.00000000e+00 1.88225953e-05 1.77462222e-05 1.63009794e-05
 7.16678250e-03 1.29436947e-02 1.76037344e-02 2.11583014e-02
 2.54274770e-02 2.96473280e-02 3.34265628e-02]
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
