p= 0.15 num clusters= 6
linkage completed in  10.669620990753174
silhouette_score of the clusters -0.08218945357074746
sampled assortment [2, 3, 4, 59, 40, 84] number: 0
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 7: 1, 8: 0, 27: 1, 100: 1} [8, 1, 2, 3, 7, 27, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 11: 0, 12: 0, 21: 0} [1, 3, 5, 6, 7, 9, 10, 11, 12, 21]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 2, 6: 1, 8: 2, 9: 0, 13: 3, 21: 7, 26: 7} [9, 4, 6, 5, 8, 1, 2, 13, 21, 26]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 6: 1, 7: 1, 100: 0} [100, 1, 3, 4, 6, 7]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 22: 2, 28: 5} [2, 1, 3, 6, 10, 11, 22, 28]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 3, 5: 0, 6: 2, 7: 1, 10: 0, 11: 5, 12: 5, 13: 8, 14: 0, 16: 8, 18: 8, 20: 6, 25: 9, 33: 9} [3, 5, 10, 14, 7, 6, 4, 11, 12, 20, 1, 13, 16, 18, 25, 33]
#  Learning probs for MM model, A = [2, 3, 4, 59, 40, 84]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 12: 1, 13: 1, 100: 1} [8, 1, 2, 3, 5, 7, 12, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 4: 0, 5: 0, 6: 0, 10: 0, 14: 0, 15: 0} [1, 4, 5, 6, 10, 14, 15]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 4, 4: 1, 5: 3, 6: 1, 7: 4, 8: 2, 9: 0, 14: 4} [9, 4, 6, 8, 1, 2, 5, 3, 7, 14]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 6: 1, 7: 1, 12: 1, 13: 1, 100: 0} [100, 1, 3, 5, 6, 7, 12, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 17: 3} [2, 1, 3, 6, 10, 11, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 8, 3: 0, 4: 2, 5: 0, 6: 2, 7: 0, 9: 6, 10: 0, 11: 4, 12: 5, 14: 1, 16: 8, 18: 8, 19: 8, 21: 6, 28: 13, 33: 11} [3, 5, 7, 10, 14, 4, 6, 11, 12, 9, 21, 1, 16, 18, 19, 33, 28]
empirical probabilities from test set: {2: 0.254, 3: 0.259, 4: 0.25, 59: 0.061, 40: 0.065, 84: 0.054, 0: 0.057}
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.13376198806021086), 3: np.float64(0.12365213115298164), 4: np.float64(0.12968742032434002), 59: np.float64(0.15322461511561697), 40: np.float64(0.15322461511561697), 84: np.float64(0.15322461511561697), 0: np.float64(0.15322461511561697)}
err dic= {2: np.float64(0.12023801193978914), 3: np.float64(0.13534786884701838), 4: np.float64(0.12031257967565998), 59: np.float64(0.09222461511561697), 40: np.float64(0.08822461511561697), 84: np.float64(0.09922461511561698), 0: np.float64(0.09622461511561697)} 

err list= [np.float64(0.12023801193978914), np.float64(0.13534786884701838), np.float64(0.12031257967565998), np.float64(0.09222461511561697), np.float64(0.08822461511561697), np.float64(0.09922461511561698), np.float64(0.09622461511561697)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.14854975841401014), 3: np.float64(0.15203771050624126), 4: np.float64(0.14590228990240903), 59: np.float64(0.1383775602943349), 40: np.float64(0.1383775602943349), 84: np.float64(0.1383775602943349), 0: np.float64(0.1383775602943349)}
err dic= {2: np.float64(0.10545024158598987), 3: np.float64(0.10696228949375874), 4: np.float64(0.10409771009759097), 59: np.float64(0.0773775602943349), 40: np.float64(0.0733775602943349), 84: np.float64(0.08437756029433491), 0: np.float64(0.0813775602943349)} 

err list= [np.float64(0.10545024158598987), np.float64(0.10696228949375874), np.float64(0.10409771009759097), np.float64(0.0773775602943349), np.float64(0.0733775602943349), np.float64(0.08437756029433491), np.float64(0.0813775602943349)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.18154833297024353), 3: np.float64(0.21882219081945836), 4: np.float64(0.19357267548951246), 59: np.float64(0.10151420018019654), 40: np.float64(0.10151420018019654), 84: np.float64(0.10151420018019654), 0: np.float64(0.10151420018019654)}
err dic= {2: np.float64(0.07245166702975647), 3: np.float64(0.040177809180541646), 4: np.float64(0.05642732451048754), 59: np.float64(0.04051420018019654), 40: np.float64(0.036514200180196535), 84: np.float64(0.04751420018019654), 0: np.float64(0.044514200180196535)} 

err list= [np.float64(0.07245166702975647), np.float64(0.040177809180541646), np.float64(0.05642732451048754), np.float64(0.04051420018019654), np.float64(0.036514200180196535), np.float64(0.04751420018019654), np.float64(0.044514200180196535)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.2190023826368386), 3: np.float64(0.3361400713026014), 4: np.float64(0.35345777021607905), 59: np.float64(0.022849943961120278), 40: np.float64(0.022849943961120278), 84: np.float64(0.022849943961120278), 0: np.float64(0.022849943961120278)}
err dic= {2: np.float64(0.0349976173631614), 3: np.float64(0.07714007130260137), 4: np.float64(0.10345777021607905), 59: np.float64(0.03815005603887972), 40: np.float64(0.042150056038879724), 84: np.float64(0.03115005603887972), 0: np.float64(0.034150056038879724)} 

err list= [np.float64(0.0349976173631614), np.float64(0.07714007130260137), np.float64(0.10345777021607905), np.float64(0.03815005603887972), np.float64(0.042150056038879724), np.float64(0.03115005603887972), np.float64(0.034150056038879724)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.22722174793090522), 3: np.float64(0.34315227079495875), 4: np.float64(0.42737101767878094), 59: np.float64(0.000563740898838779), 40: np.float64(0.000563740898838779), 84: np.float64(0.000563740898838779), 0: np.float64(0.000563740898838779)}
err dic= {2: np.float64(0.026778252069094788), 3: np.float64(0.08415227079495874), 4: np.float64(0.17737101767878094), 59: np.float64(0.06043625910116122), 40: np.float64(0.06443625910116123), 84: np.float64(0.05343625910116122), 0: np.float64(0.05643625910116122)} 

err list= [np.float64(0.026778252069094788), np.float64(0.08415227079495874), np.float64(0.17737101767878094), np.float64(0.06043625910116122), np.float64(0.06443625910116123), np.float64(0.05343625910116122), np.float64(0.05643625910116122)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.24509221130650835), 3: np.float64(0.32147287010800607), 4: np.float64(0.4334172504389788), 59: np.float64(4.4170366266821045e-06), 40: np.float64(4.4170366266821045e-06), 84: np.float64(4.4170366266821045e-06), 0: np.float64(4.4170366266821045e-06)}
err dic= {2: np.float64(0.008907788693491653), 3: np.float64(0.06247287010800606), 4: np.float64(0.18341725043897877), 59: np.float64(0.06099558296337332), 40: np.float64(0.06499558296337332), 84: np.float64(0.05399558296337332), 0: np.float64(0.05699558296337332)} 

err list= [np.float64(0.008907788693491653), np.float64(0.06247287010800606), np.float64(0.18341725043897877), np.float64(0.06099558296337332), np.float64(0.06499558296337332), np.float64(0.05399558296337332), np.float64(0.05699558296337332)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1 

learned probs for this beta: {2: np.float64(0.2619309023546286), 3: np.float64(0.3024126655847009), 4: np.float64(0.4356563045675334), 59: np.float64(3.187328425949353e-08), 40: np.float64(3.187328425949353e-08), 84: np.float64(3.187328425949353e-08), 0: np.float64(3.187328425949353e-08)}
err dic= {2: np.float64(0.007930902354628622), 3: np.float64(0.043412665584700916), 4: np.float64(0.1856563045675334), 59: np.float64(0.06099996812671574), 40: np.float64(0.06499996812671574), 84: np.float64(0.05399996812671574), 0: np.float64(0.05699996812671574)} 

err list= [np.float64(0.007930902354628622), np.float64(0.043412665584700916), np.float64(0.1856563045675334), np.float64(0.06099996812671574), np.float64(0.06499996812671574), np.float64(0.05399996812671574), np.float64(0.05699996812671574)]
results for assortment [2, 3, 4, 59, 40, 84] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.27672151898085934), 3: np.float64(0.2865706810160252), 4: np.float64(0.43670779908512924), 59: np.float64(2.294965352682056e-10), 40: np.float64(2.294965352682056e-10), 84: np.float64(2.294965352682056e-10), 0: np.float64(2.294965352682056e-10)}
err dic= {2: np.float64(0.022721518980859334), 3: np.float64(0.027570681016025167), 4: np.float64(0.18670779908512924), 59: np.float64(0.060999999770503466), 40: np.float64(0.06499999977050347), 84: np.float64(0.053999999770503467), 0: np.float64(0.05699999977050347)} 

err list= [np.float64(0.022721518980859334), np.float64(0.027570681016025167), np.float64(0.18670779908512924), np.float64(0.060999999770503466), np.float64(0.06499999977050347), np.float64(0.053999999770503467), np.float64(0.05699999977050347)]
results for assortment [2, 3, 4, 59, 40, 84] :

err MNL dic= {2: np.float64(0.11948223350253806), 3: np.float64(0.12331895093062606), 4: np.float64(0.11542935702199661), 59: np.float64(0.047449661590524536), 40: np.float64(0.05106387478849407), 84: np.float64(0.05233460236886634), 0: np.float64(0.20738240270727581)} 

err MNL list= [np.float64(0.11948223350253806), np.float64(0.12331895093062606), np.float64(0.11542935702199661), np.float64(0.047449661590524536), np.float64(0.05106387478849407), np.float64(0.05233460236886634), np.float64(0.20738240270727581)]
sampled assortment [7, 1, 9, 63, 27, 16] number: 1
#  Learning probs for MM model, A = [7, 1, 9, 63, 27, 16]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 17: 3, 100: 1} [8, 1, 2, 3, 5, 7, 100, 17]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 13: 0} [1, 3, 5, 6, 7, 9, 12, 13]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 3, 6: 1, 8: 1, 9: 0, 19: 3, 24: 5} [9, 4, 6, 8, 1, 2, 5, 19, 24]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 6: 1, 11: 1, 12: 1, 14: 1, 100: 0} [100, 1, 3, 5, 6, 11, 12, 14]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 10: 1, 11: 1, 12: 3} [2, 1, 3, 10, 11, 12]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 2: 6, 3: 0, 4: 4, 5: 0, 6: 2, 7: 0, 9: 7, 10: 0, 11: 4, 12: 4, 14: 0, 18: 9, 19: 7, 20: 5, 23: 9, 24: 10} [3, 5, 7, 10, 14, 6, 4, 11, 12, 20, 2, 1, 9, 19, 18, 23, 24]
#  Learning probs for MM model, A = [7, 1, 9, 63, 27, 16]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 13: 1, 14: 1, 100: 1} [8, 3, 4, 5, 7, 12, 13, 14, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 11: 0, 12: 0} [1, 3, 5, 6, 11, 12]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 3: 3, 4: 1, 5: 3, 6: 1, 8: 3, 9: 0, 13: 4, 15: 3, 20: 8} [9, 4, 6, 1, 3, 5, 8, 15, 13, 20]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 12: 1, 100: 0} [100, 1, 3, 12]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 10: 1, 11: 1, 14: 2} [2, 1, 10, 11, 14]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 3, 5: 0, 6: 3, 7: 1, 10: 0, 12: 4, 13: 8, 14: 0, 16: 8, 18: 7, 19: 6, 25: 9, 38: 8, 39: 12, 51: 13} [3, 5, 10, 14, 7, 4, 6, 12, 19, 1, 18, 13, 16, 38, 25, 39, 51]
empirical probabilities from test set: {7: 0.185, 1: 0.24, 9: 0.222, 63: 0.043, 27: 0.144, 16: 0.138, 0: 0.028}
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.025 

learned probs for this beta: {7: np.float64(0.14499648016342168), 1: np.float64(0.09295557321498855), 9: np.float64(0.1516370836434878), 63: np.float64(0.15260271574452558), 27: np.float64(0.15260271574452558), 16: np.float64(0.15260271574452558), 0: np.float64(0.15260271574452558)}
err dic= {7: np.float64(0.04000351983657832), 1: np.float64(0.14704442678501145), 9: np.float64(0.0703629163565122), 63: np.float64(0.10960271574452558), 27: np.float64(0.00860271574452559), 16: np.float64(0.014602715744525568), 0: np.float64(0.12460271574452558)} 

err list= [np.float64(0.04000351983657832), np.float64(0.14704442678501145), np.float64(0.0703629163565122), np.float64(0.10960271574452558), np.float64(0.00860271574452559), np.float64(0.014602715744525568), np.float64(0.12460271574452558)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.05 

learned probs for this beta: {7: np.float64(0.1522153879243919), 1: np.float64(0.12425771052146226), 9: np.float64(0.14787009747875543), 63: np.float64(0.14391420101884775), 27: np.float64(0.14391420101884775), 16: np.float64(0.14391420101884775), 0: np.float64(0.14391420101884775)}
err dic= {7: np.float64(0.032784612075608094), 1: np.float64(0.11574228947853774), 9: np.float64(0.07412990252124457), 63: np.float64(0.10091420101884775), 27: np.float64(8.579898115224083e-05), 16: np.float64(0.005914201018847737), 0: np.float64(0.11591420101884775)} 

err list= [np.float64(0.032784612075608094), np.float64(0.11574228947853774), np.float64(0.07412990252124457), np.float64(0.10091420101884775), np.float64(8.579898115224083e-05), np.float64(0.005914201018847737), np.float64(0.11591420101884775)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.1 

learned probs for this beta: {7: np.float64(0.16882231677621243), 1: np.float64(0.21822527676892362), 9: np.float64(0.13463226067868606), 63: np.float64(0.11958003644404457), 27: np.float64(0.11958003644404457), 16: np.float64(0.11958003644404457), 0: np.float64(0.11958003644404457)}
err dic= {7: np.float64(0.01617768322378757), 1: np.float64(0.021774723231076376), 9: np.float64(0.08736773932131395), 63: np.float64(0.07658003644404457), 27: np.float64(0.024419963555955423), 16: np.float64(0.018419963555955446), 0: np.float64(0.09158003644404457)} 

err list= [np.float64(0.01617768322378757), np.float64(0.021774723231076376), np.float64(0.08736773932131395), np.float64(0.07658003644404457), np.float64(0.024419963555955423), np.float64(0.018419963555955446), np.float64(0.09158003644404457)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.25 

learned probs for this beta: {7: np.float64(0.2068263153964506), 1: np.float64(0.5566949018709819), 9: np.float64(0.07216321498261014), 63: np.float64(0.041078891937489294), 27: np.float64(0.041078891937489294), 16: np.float64(0.041078891937489294), 0: np.float64(0.041078891937489294)}
err dic= {7: np.float64(0.021826315396450607), 1: np.float64(0.3166949018709819), 9: np.float64(0.14983678501738987), 63: np.float64(0.0019211080625107027), 27: np.float64(0.1029211080625107), 16: np.float64(0.09692110806251072), 0: np.float64(0.013078891937489293)} 

err list= [np.float64(0.021826315396450607), np.float64(0.3166949018709819), np.float64(0.14983678501738987), np.float64(0.0019211080625107027), np.float64(0.1029211080625107), np.float64(0.09692110806251072), np.float64(0.013078891937489293)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.5 

learned probs for this beta: {7: np.float64(0.2283967856862818), 1: np.float64(0.7260604829575136), 9: np.float64(0.0395275755620795), 63: np.float64(0.0015037889485313071), 27: np.float64(0.0015037889485313071), 16: np.float64(0.0015037889485313071), 0: np.float64(0.0015037889485313071)}
err dic= {7: np.float64(0.0433967856862818), 1: np.float64(0.4860604829575136), 9: np.float64(0.1824724244379205), 63: np.float64(0.04149621105146869), 27: np.float64(0.14249621105146867), 16: np.float64(0.1364962110514687), 0: np.float64(0.026496211051468693)} 

err list= [np.float64(0.0433967856862818), np.float64(0.4860604829575136), np.float64(0.1824724244379205), np.float64(0.04149621105146869), np.float64(0.14249621105146867), np.float64(0.1364962110514687), np.float64(0.026496211051468693)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  0.75 

learned probs for this beta: {7: np.float64(0.23103596285540867), 1: np.float64(0.7262836712680186), 9: np.float64(0.04261009660932761), 63: np.float64(1.756731681125658e-05), 27: np.float64(1.756731681125658e-05), 16: np.float64(1.756731681125658e-05), 0: np.float64(1.756731681125658e-05)}
err dic= {7: np.float64(0.046035962855408674), 1: np.float64(0.48628367126801864), 9: np.float64(0.1793899033906724), 63: np.float64(0.04298243268318874), 27: np.float64(0.14398243268318872), 16: np.float64(0.13798243268318874), 0: np.float64(0.027982432683188743)} 

err list= [np.float64(0.046035962855408674), np.float64(0.48628367126801864), np.float64(0.1793899033906724), np.float64(0.04298243268318874), np.float64(0.14398243268318872), np.float64(0.13798243268318874), np.float64(0.027982432683188743)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  1 

learned probs for this beta: {7: np.float64(0.23181749780867122), 1: np.float64(0.7225387433101912), 9: np.float64(0.04564295733887792), 63: np.float64(2.0038556491560576e-07), 27: np.float64(2.0038556491560576e-07), 16: np.float64(2.0038556491560576e-07), 0: np.float64(2.0038556491560576e-07)}
err dic= {7: np.float64(0.04681749780867123), 1: np.float64(0.4825387433101912), 9: np.float64(0.1763570426611221), 63: np.float64(0.042999799614435084), 27: np.float64(0.14399979961443507), 16: np.float64(0.1379997996144351), 0: np.float64(0.027999799614435085)} 

err list= [np.float64(0.04681749780867123), np.float64(0.4825387433101912), np.float64(0.1763570426611221), np.float64(0.042999799614435084), np.float64(0.14399979961443507), np.float64(0.1379997996144351), np.float64(0.027999799614435085)]
results for assortment [7, 1, 9, 63, 27, 16] :

beta is  1.25 

learned probs for this beta: {7: np.float64(0.23210552379493277), 1: np.float64(0.7203890765087382), 9: np.float64(0.04750539019546498), 63: np.float64(2.3752159579564124e-09), 27: np.float64(2.3752159579564124e-09), 16: np.float64(2.3752159579564124e-09), 0: np.float64(2.3752159579564124e-09)}
err dic= {7: np.float64(0.04710552379493277), 1: np.float64(0.4803890765087382), 9: np.float64(0.17449460980453502), 63: np.float64(0.042999997624784035), 27: np.float64(0.14399999762478402), 16: np.float64(0.13799999762478404), 0: np.float64(0.027999997624784043)} 

err list= [np.float64(0.04710552379493277), np.float64(0.4803890765087382), np.float64(0.17449460980453502), np.float64(0.042999997624784035), np.float64(0.14399999762478402), np.float64(0.13799999762478404), np.float64(0.027999997624784043)]
results for assortment [7, 1, 9, 63, 27, 16] :

err MNL dic= {7: np.float64(0.053115495273325125), 1: np.float64(0.10487875051376902), 9: np.float64(0.09412289354706124), 63: np.float64(0.06427496917385941), 27: np.float64(0.025319358816276213), 16: np.float64(0.015722975750102786), 0: np.float64(0.22888450472667485)} 

err MNL list= [np.float64(0.053115495273325125), np.float64(0.10487875051376902), np.float64(0.09412289354706124), np.float64(0.06427496917385941), np.float64(0.025319358816276213), np.float64(0.015722975750102786), np.float64(0.22888450472667485)]
sampled assortment [3, 1, 4, 64, 50, 92] number: 2
#  Learning probs for MM model, A = [3, 1, 4, 64, 50, 92]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1, 13: 1, 14: 1, 15: 1, 100: 1} [8, 1, 2, 3, 4, 7, 10, 12, 13, 14, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0} [1, 3, 4, 5, 6, 7, 11]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 3, 6: 1, 7: 4, 8: 3, 9: 0, 15: 3, 17: 8, 19: 4} [9, 4, 6, 1, 2, 5, 8, 15, 7, 19, 17]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 13: 1, 24: 1, 100: 0} [100, 1, 2, 3, 4, 5, 6, 13, 24]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 2, 6: 1, 10: 1, 11: 1, 17: 2} [2, 1, 6, 10, 11, 3, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {3: 0, 4: 3, 5: 0, 6: 2, 7: 1, 10: 0, 11: 4, 12: 4, 13: 8, 14: 1, 17: 8, 26: 8, 33: 9, 39: 8, 68: 9, 86: 10} [3, 5, 10, 7, 14, 6, 4, 11, 12, 13, 17, 26, 39, 33, 68, 86]
#  Learning probs for MM model, A = [3, 1, 4, 64, 50, 92]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {2: 1, 3: 1, 4: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 2, 3, 4, 7, 12, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 7: 0, 11: 0, 15: 0, 19: 0} [1, 3, 5, 6, 7, 11, 15, 19]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 3: 4, 4: 1, 5: 3, 6: 1, 7: 3, 8: 3, 9: 0, 15: 3, 19: 4, 21: 8} [9, 4, 6, 1, 5, 7, 8, 15, 3, 19, 21]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 13: 1, 100: 0} [100, 1, 3, 4, 5, 7, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 1} [2, 1, 3, 6, 10, 11, 14]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 3, 5: 0, 6: 2, 7: 1, 10: 0, 11: 5, 12: 5, 14: 2, 15: 9, 16: 7, 18: 7, 19: 5, 21: 7, 43: 14} [3, 5, 10, 7, 6, 14, 4, 11, 12, 19, 1, 16, 18, 21, 15, 43]
empirical probabilities from test set: {3: 0.251, 1: 0.254, 4: 0.257, 64: 0.063, 50: 0.077, 92: 0.053, 0: 0.045}
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.09868767980605092), 1: np.float64(0.1155961452583278), 4: np.float64(0.12781377115341813), 64: np.float64(0.16447560094555094), 50: np.float64(0.16447560094555094), 92: np.float64(0.16447560094555094), 0: np.float64(0.16447560094555094)}
err dic= {3: np.float64(0.15231232019394908), 1: np.float64(0.13840385474167222), 4: np.float64(0.12918622884658187), 64: np.float64(0.10147560094555094), 50: np.float64(0.08747560094555094), 92: np.float64(0.11147560094555095), 0: np.float64(0.11947560094555094)} 

err list= [np.float64(0.15231232019394908), np.float64(0.13840385474167222), np.float64(0.12918622884658187), np.float64(0.10147560094555094), np.float64(0.08747560094555094), np.float64(0.11147560094555095), np.float64(0.11947560094555094)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.14612973009120253), 1: np.float64(0.15350393825963493), 4: np.float64(0.13685550766512336), 64: np.float64(0.14087770599600982), 50: np.float64(0.14087770599600982), 92: np.float64(0.14087770599600982), 0: np.float64(0.14087770599600982)}
err dic= {3: np.float64(0.10487026990879747), 1: np.float64(0.10049606174036507), 4: np.float64(0.12014449233487665), 64: np.float64(0.07787770599600982), 50: np.float64(0.06387770599600982), 92: np.float64(0.08787770599600983), 0: np.float64(0.09587770599600982)} 

err list= [np.float64(0.10487026990879747), np.float64(0.10049606174036507), np.float64(0.12014449233487665), np.float64(0.07787770599600982), np.float64(0.06387770599600982), np.float64(0.08787770599600983), np.float64(0.09587770599600982)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.2565803023445596), 1: np.float64(0.2439783252397998), 4: np.float64(0.15408217159881385), 64: np.float64(0.08633980020420698), 50: np.float64(0.08633980020420698), 92: np.float64(0.08633980020420698), 0: np.float64(0.08633980020420698)}
err dic= {3: np.float64(0.0055803023445595845), 1: np.float64(0.010021674760200217), 4: np.float64(0.10291782840118616), 64: np.float64(0.02333980020420698), 50: np.float64(0.00933980020420698), 92: np.float64(0.03333980020420698), 0: np.float64(0.04133980020420698)} 

err list= [np.float64(0.0055803023445595845), np.float64(0.010021674760200217), np.float64(0.10291782840118616), np.float64(0.02333980020420698), np.float64(0.00933980020420698), np.float64(0.03333980020420698), np.float64(0.04133980020420698)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.41374323203465896), 1: np.float64(0.38516474779151033), 4: np.float64(0.1708157052125631), 64: np.float64(0.007569078740316821), 50: np.float64(0.007569078740316821), 92: np.float64(0.007569078740316821), 0: np.float64(0.007569078740316821)}
err dic= {3: np.float64(0.16274323203465896), 1: np.float64(0.13116474779151033), 4: np.float64(0.08618429478743692), 64: np.float64(0.05543092125968318), 50: np.float64(0.06943092125968318), 92: np.float64(0.04543092125968318), 0: np.float64(0.03743092125968318)} 

err list= [np.float64(0.16274323203465896), np.float64(0.13116474779151033), np.float64(0.08618429478743692), np.float64(0.05543092125968318), np.float64(0.06943092125968318), np.float64(0.04543092125968318), np.float64(0.03743092125968318)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.4088379844972689), 1: np.float64(0.43805618535204466), 4: np.float64(0.15281192180787512), 64: np.float64(7.347708570286363e-05), 50: np.float64(7.347708570286363e-05), 92: np.float64(7.347708570286363e-05), 0: np.float64(7.347708570286363e-05)}
err dic= {3: np.float64(0.15783798449726888), 1: np.float64(0.18405618535204465), 4: np.float64(0.10418807819212489), 64: np.float64(0.06292652291429714), 50: np.float64(0.07692652291429714), 92: np.float64(0.052926522914297135), 0: np.float64(0.044926522914297135)} 

err list= [np.float64(0.15783798449726888), np.float64(0.18405618535204465), np.float64(0.10418807819212489), np.float64(0.06292652291429714), np.float64(0.07692652291429714), np.float64(0.052926522914297135), np.float64(0.044926522914297135)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.3863915843033233), 1: np.float64(0.48038101669421734), 4: np.float64(0.1332254286546429), 64: np.float64(4.925869540705519e-07), 50: np.float64(4.925869540705519e-07), 92: np.float64(4.925869540705519e-07), 0: np.float64(4.925869540705519e-07)}
err dic= {3: np.float64(0.13539158430332332), 1: np.float64(0.22638101669421734), 4: np.float64(0.1237745713453571), 64: np.float64(0.06299950741304593), 50: np.float64(0.07699950741304593), 92: np.float64(0.052999507413045925), 0: np.float64(0.044999507413045925)} 

err list= [np.float64(0.13539158430332332), np.float64(0.22638101669421734), np.float64(0.1237745713453571), np.float64(0.06299950741304593), np.float64(0.07699950741304593), np.float64(0.052999507413045925), np.float64(0.044999507413045925)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  1 

learned probs for this beta: {3: np.float64(0.3639410944854112), 1: np.float64(0.5192332519084861), 4: np.float64(0.1168256398424294), 64: np.float64(3.440918360427746e-09), 50: np.float64(3.440918360427746e-09), 92: np.float64(3.440918360427746e-09), 0: np.float64(3.440918360427746e-09)}
err dic= {3: np.float64(0.11294109448541118), 1: np.float64(0.2652332519084861), 4: np.float64(0.14017436015757062), 64: np.float64(0.06299999655908164), 50: np.float64(0.07699999655908164), 92: np.float64(0.052999996559081636), 0: np.float64(0.044999996559081636)} 

err list= [np.float64(0.11294109448541118), np.float64(0.2652332519084861), np.float64(0.14017436015757062), np.float64(0.06299999655908164), np.float64(0.07699999655908164), np.float64(0.052999996559081636), np.float64(0.044999996559081636)]
results for assortment [3, 1, 4, 64, 50, 92] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.34273307211579895), 1: np.float64(0.5539039603653905), 4: np.float64(0.10336296741612223), 64: np.float64(2.5672076538501804e-11), 50: np.float64(2.5672076538501804e-11), 92: np.float64(2.5672076538501804e-11), 0: np.float64(2.5672076538501804e-11)}
err dic= {3: np.float64(0.09173307211579895), 1: np.float64(0.29990396036539047), 4: np.float64(0.1536370325838778), 64: np.float64(0.06299999997432792), 50: np.float64(0.07699999997432792), 92: np.float64(0.05299999997432792), 0: np.float64(0.04499999997432792)} 

err list= [np.float64(0.09173307211579895), np.float64(0.29990396036539047), np.float64(0.1536370325838778), np.float64(0.06299999997432792), np.float64(0.07699999997432792), np.float64(0.05299999997432792), np.float64(0.04499999997432792)]
results for assortment [3, 1, 4, 64, 50, 92] :

err MNL dic= {3: np.float64(0.11583354403708387), 1: np.float64(0.11546228402865572), 4: np.float64(0.12293973872734934), 64: np.float64(0.046460598398651506), 50: np.float64(0.03609523809523811), 92: np.float64(0.05330004214075012), 0: np.float64(0.21837968815844921)} 

err MNL list= [np.float64(0.11583354403708387), np.float64(0.11546228402865572), np.float64(0.12293973872734934), np.float64(0.046460598398651506), np.float64(0.03609523809523811), np.float64(0.05330004214075012), np.float64(0.21837968815844921)]
sampled assortment [4, 9, 2, 20, 43, 38] number: 3
#  Learning probs for MM model, A = [4, 9, 2, 20, 43, 38]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 12: 1, 13: 1, 100: 1} [8, 2, 3, 4, 5, 7, 11, 12, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 20: 0} [1, 3, 4, 5, 6, 7, 9, 11, 12, 20]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 4: 1, 5: 3, 6: 1, 7: 3, 8: 2, 9: 0, 12: 4, 15: 3, 17: 4, 18: 5, 19: 4} [9, 4, 6, 8, 1, 5, 7, 15, 12, 17, 19, 18]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 6: 1, 100: 0} [100, 1, 3, 6]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 4: 1, 10: 1, 11: 1, 17: 2} [2, 1, 4, 10, 11, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {3: 0, 4: 2, 5: 0, 6: 3, 7: 0, 8: 9, 9: 6, 10: 0, 11: 4, 12: 4, 14: 2, 16: 7, 18: 6, 19: 6, 27: 7} [3, 5, 7, 10, 4, 14, 6, 11, 12, 9, 18, 19, 16, 27, 8]
#  Learning probs for MM model, A = [4, 9, 2, 20, 43, 38]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 11: 1, 17: 2, 100: 1} [8, 1, 3, 4, 7, 10, 11, 100, 17]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0} [1, 3, 4, 5, 6, 7, 11]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {2: 3, 4: 1, 5: 3, 6: 1, 8: 3, 9: 0, 10: 4, 14: 3, 100: 4} [9, 4, 6, 2, 5, 8, 14, 10, 100]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 13: 1, 100: 0} [100, 1, 2, 3, 4, 5, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 14: 3} [2, 1, 6, 10, 11, 14]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 8, 2: 8, 3: 0, 4: 2, 5: 0, 6: 3, 7: 1, 9: 4, 10: 0, 11: 4, 12: 4, 13: 7, 14: 0, 20: 7, 24: 9, 25: 9, 35: 14, 41: 11, 92: 12} [3, 5, 10, 14, 7, 4, 6, 9, 11, 12, 13, 20, 1, 2, 24, 25, 41, 92, 35]
empirical probabilities from test set: {4: 0.231, 9: 0.206, 2: 0.239, 20: 0.141, 43: 0.071, 38: 0.075, 0: 0.037}
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.10600812891703279), 9: np.float64(0.15089529499090315), 2: np.float64(0.12780006490121001), 20: np.float64(0.15313250437510492), 43: np.float64(0.1540546689385833), 38: np.float64(0.1540546689385833), 0: np.float64(0.1540546689385833)}
err dic= {4: np.float64(0.12499187108296722), 9: np.float64(0.05510470500909684), 2: np.float64(0.11119993509878998), 20: np.float64(0.012132504375104936), 43: np.float64(0.0830546689385833), 38: np.float64(0.0790546689385833), 0: np.float64(0.1170546689385833)} 

err list= [np.float64(0.12499187108296722), np.float64(0.05510470500909684), np.float64(0.11119993509878998), np.float64(0.012132504375104936), np.float64(0.0830546689385833), np.float64(0.0790546689385833), np.float64(0.1170546689385833)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.14854696364588207), 9: np.float64(0.14500493611167156), 2: np.float64(0.13935950486420434), 20: np.float64(0.14208344017960542), 43: np.float64(0.14166838506621213), 38: np.float64(0.14166838506621213), 0: np.float64(0.14166838506621213)}
err dic= {4: np.float64(0.08245303635411794), 9: np.float64(0.06099506388832843), 2: np.float64(0.09964049513579565), 20: np.float64(0.0010834401796054327), 43: np.float64(0.07066838506621213), 38: np.float64(0.06666838506621213), 0: np.float64(0.10466838506621212)} 

err list= [np.float64(0.08245303635411794), np.float64(0.06099506388832843), np.float64(0.09964049513579565), np.float64(0.0010834401796054327), np.float64(0.07066838506621213), np.float64(0.06666838506621213), np.float64(0.10466838506621212)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.26065486464395654), 9: np.float64(0.12594956799732007), 2: np.float64(0.17033510869481341), 20: np.float64(0.11258182943875951), 43: np.float64(0.11015954307505021), 38: np.float64(0.11015954307505021), 0: np.float64(0.11015954307505021)}
err dic= {4: np.float64(0.02965486464395653), 9: np.float64(0.08005043200267992), 2: np.float64(0.06866489130518658), 20: np.float64(0.028418170561240477), 43: np.float64(0.03915954307505022), 38: np.float64(0.03515954307505022), 0: np.float64(0.07315954307505021)} 

err list= [np.float64(0.02965486464395653), np.float64(0.08005043200267992), np.float64(0.06866489130518658), np.float64(0.028418170561240477), np.float64(0.03915954307505022), np.float64(0.03515954307505022), np.float64(0.07315954307505021)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.567424956427495), 9: np.float64(0.05947801911710571), 2: np.float64(0.2476459065416944), 20: np.float64(0.03364940745842018), 43: np.float64(0.030600570151761666), 38: np.float64(0.030600570151761666), 0: np.float64(0.030600570151761666)}
err dic= {4: np.float64(0.33642495642749504), 9: np.float64(0.14652198088289428), 2: np.float64(0.00864590654169442), 20: np.float64(0.1073505925415798), 43: np.float64(0.04039942984823833), 38: np.float64(0.04439942984823833), 0: np.float64(0.006399429848238332)} 

err list= [np.float64(0.33642495642749504), np.float64(0.14652198088289428), np.float64(0.00864590654169442), np.float64(0.1073505925415798), np.float64(0.04039942984823833), np.float64(0.04439942984823833), np.float64(0.006399429848238332)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.6857825675225773), 9: np.float64(0.03425893189702831), 2: np.float64(0.27526173481579), 20: np.float64(0.001997617217137898), 43: np.float64(0.0008997161824888691), 38: np.float64(0.0008997161824888691), 0: np.float64(0.0008997161824888691)}
err dic= {4: np.float64(0.4547825675225773), 9: np.float64(0.17174106810297168), 2: np.float64(0.03626173481579004), 20: np.float64(0.1390023827828621), 43: np.float64(0.07010028381751113), 38: np.float64(0.07410028381751113), 0: np.float64(0.03610028381751113)} 

err list= [np.float64(0.4547825675225773), np.float64(0.17174106810297168), np.float64(0.03626173481579004), np.float64(0.1390023827828621), np.float64(0.07010028381751113), np.float64(0.07410028381751113), np.float64(0.03610028381751113)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.6744940766283125), 9: np.float64(0.036213566820210145), 2: np.float64(0.288948935067999), 20: np.float64(0.00031824829399102036), 43: np.float64(8.391063162382322e-06), 38: np.float64(8.391063162382322e-06), 0: np.float64(8.391063162382322e-06)}
err dic= {4: np.float64(0.44349407662831253), 9: np.float64(0.16978643317978984), 2: np.float64(0.04994893506799902), 20: np.float64(0.14068175170600897), 43: np.float64(0.0709916089368376), 38: np.float64(0.07499160893683761), 0: np.float64(0.03699160893683762)} 

err list= [np.float64(0.44349407662831253), np.float64(0.16978643317978984), np.float64(0.04994893506799902), np.float64(0.14068175170600897), np.float64(0.0709916089368376), np.float64(0.07499160893683761), np.float64(0.03699160893683762)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  1 

learned probs for this beta: {4: np.float64(0.6609915301176926), 9: np.float64(0.038447776003833395), 2: np.float64(0.30048118645447863), 20: np.float64(7.928939794744628e-05), 43: np.float64(7.267534926534577e-08), 38: np.float64(7.267534926534577e-08), 0: np.float64(7.267534926534577e-08)}
err dic= {4: np.float64(0.42999153011769264), 9: np.float64(0.1675522239961666), 2: np.float64(0.06148118645447864), 20: np.float64(0.14092071060205255), 43: np.float64(0.07099992732465073), 38: np.float64(0.07499992732465073), 0: np.float64(0.03699992732465073)} 

err list= [np.float64(0.42999153011769264), np.float64(0.1675522239961666), np.float64(0.06148118645447864), np.float64(0.14092071060205255), np.float64(0.07099992732465073), np.float64(0.07499992732465073), np.float64(0.03699992732465073)]
results for assortment [4, 9, 2, 20, 43, 38] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.6501311991433543), 9: np.float64(0.04030257782917193), 2: np.float64(0.3095469523037509), 20: np.float64(1.926882705119408e-05), 43: np.float64(6.322238743289821e-10), 38: np.float64(6.322238743289821e-10), 0: np.float64(6.322238743289821e-10)}
err dic= {4: np.float64(0.4191311991433543), 9: np.float64(0.16569742217082806), 2: np.float64(0.07054695230375091), 20: np.float64(0.1409807311729488), 43: np.float64(0.07099999936777612), 38: np.float64(0.07499999936777613), 0: np.float64(0.03699999936777612)} 

err list= [np.float64(0.4191311991433543), np.float64(0.16569742217082806), np.float64(0.07054695230375091), np.float64(0.1409807311729488), np.float64(0.07099999936777612), np.float64(0.07499999936777613), np.float64(0.03699999936777612)]
results for assortment [4, 9, 2, 20, 43, 38] :

err MNL dic= {4: np.float64(0.09932574503311259), 9: np.float64(0.07722309602649005), 2: np.float64(0.1073774834437086), 20: np.float64(0.016931291390728465), 43: np.float64(0.04235885761589403), 38: np.float64(0.036806705298013234), 0: np.float64(0.22169205298013242)} 

err MNL list= [np.float64(0.09932574503311259), np.float64(0.07722309602649005), np.float64(0.1073774834437086), np.float64(0.016931291390728465), np.float64(0.04235885761589403), np.float64(0.036806705298013234), np.float64(0.22169205298013242)]
sampled assortment [1, 8, 2, 59, 67, 81] number: 4
#  Learning probs for MM model, A = [1, 8, 2, 59, 67, 81]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {2: 1, 4: 1, 7: 1, 8: 0, 10: 1, 13: 1, 100: 1} [8, 2, 4, 7, 10, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 20: 0} [1, 3, 4, 5, 6, 7, 20]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 4, 4: 1, 5: 3, 6: 1, 8: 3, 9: 0, 11: 6, 12: 4, 13: 3, 15: 3, 16: 6} [9, 4, 6, 1, 2, 5, 8, 13, 15, 3, 12, 11, 16]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 12: 1, 14: 1, 100: 0} [100, 1, 3, 4, 12, 14]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 13: 4} [2, 1, 3, 6, 10, 11, 13]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {2: 8, 3: 0, 4: 4, 5: 0, 6: 3, 7: 1, 8: 8, 9: 4, 10: 0, 12: 4, 14: 2, 19: 6} [3, 5, 10, 7, 14, 6, 4, 9, 12, 19, 2, 8]
#  Learning probs for MM model, A = [1, 8, 2, 59, 67, 81]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 100: 1} [8, 3, 4, 7, 10, 11, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 20: 0} [1, 3, 4, 5, 6, 7, 9, 11, 12, 20]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 3: 3, 4: 1, 5: 3, 6: 1, 8: 3, 9: 0, 14: 6, 15: 4} [9, 4, 6, 1, 3, 5, 8, 15, 14]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 10: 1, 11: 1, 12: 1, 100: 0} [100, 1, 3, 5, 10, 11, 12]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1} [2, 1, 3, 6, 9, 10, 11]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {3: 0, 4: 3, 5: 0, 6: 2, 7: 0, 10: 0, 11: 5, 12: 4, 14: 0, 16: 7, 19: 6, 29: 9, 37: 8, 39: 9, 73: 10} [3, 5, 7, 10, 14, 6, 4, 12, 11, 19, 16, 37, 29, 39, 73]
empirical probabilities from test set: {1: 0.244, 8: 0.263, 2: 0.26, 59: 0.084, 67: 0.056, 81: 0.05, 0: 0.043}
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.025 

learned probs for this beta: {1: np.float64(0.12332436782958331), 8: np.float64(0.13872628036464593), 2: np.float64(0.14085512569951977), 59: np.float64(0.1492735565265623), 67: np.float64(0.1492735565265623), 81: np.float64(0.1492735565265623), 0: np.float64(0.1492735565265623)}
err dic= {1: np.float64(0.12067563217041669), 8: np.float64(0.12427371963535408), 2: np.float64(0.11914487430048024), 59: np.float64(0.06527355652656229), 67: np.float64(0.0932735565265623), 81: np.float64(0.09927355652656229), 0: np.float64(0.1062735565265623)} 

err list= [np.float64(0.12067563217041669), np.float64(0.12427371963535408), np.float64(0.11914487430048024), np.float64(0.06527355652656229), np.float64(0.0932735565265623), np.float64(0.09927355652656229), np.float64(0.1062735565265623)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.05 

learned probs for this beta: {1: np.float64(0.17352020582097402), 8: np.float64(0.14497707574507215), 2: np.float64(0.13690477400771292), 59: np.float64(0.13614948610656058), 67: np.float64(0.13614948610656058), 81: np.float64(0.13614948610656058), 0: np.float64(0.13614948610656058)}
err dic= {1: np.float64(0.07047979417902597), 8: np.float64(0.11802292425492786), 2: np.float64(0.12309522599228709), 59: np.float64(0.052149486106560575), 67: np.float64(0.08014948610656059), 81: np.float64(0.08614948610656058), 0: np.float64(0.09314948610656058)} 

err list= [np.float64(0.07047979417902597), np.float64(0.11802292425492786), np.float64(0.12309522599228709), np.float64(0.052149486106560575), np.float64(0.08014948610656059), np.float64(0.08614948610656058), np.float64(0.09314948610656058)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.1 

learned probs for this beta: {1: np.float64(0.3076881049596484), 8: np.float64(0.1630748238817118), 2: np.float64(0.125557898787606), 59: np.float64(0.1009197930927585), 67: np.float64(0.1009197930927585), 81: np.float64(0.1009197930927585), 0: np.float64(0.1009197930927585)}
err dic= {1: np.float64(0.06368810495964838), 8: np.float64(0.09992517611828822), 2: np.float64(0.134442101212394), 59: np.float64(0.016919793092758498), 67: np.float64(0.0449197930927585), 81: np.float64(0.0509197930927585), 0: np.float64(0.057919793092758506)} 

err list= [np.float64(0.06368810495964838), np.float64(0.09992517611828822), np.float64(0.134442101212394), np.float64(0.016919793092758498), np.float64(0.0449197930927585), np.float64(0.0509197930927585), np.float64(0.057919793092758506)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.25 

learned probs for this beta: {1: np.float64(0.6060923436134503), 8: np.float64(0.21438748189177004), 2: np.float64(0.089889598701528), 59: np.float64(0.022407643948312645), 67: np.float64(0.022407643948312645), 81: np.float64(0.022407643948312645), 0: np.float64(0.022407643948312645)}
err dic= {1: np.float64(0.36209234361345033), 8: np.float64(0.048612518108229974), 2: np.float64(0.170110401298472), 59: np.float64(0.061592356051687364), 67: np.float64(0.03359235605168735), 81: np.float64(0.027592356051687358), 0: np.float64(0.02059235605168735)} 

err list= [np.float64(0.36209234361345033), np.float64(0.048612518108229974), np.float64(0.170110401298472), np.float64(0.061592356051687364), np.float64(0.03359235605168735), np.float64(0.027592356051687358), np.float64(0.02059235605168735)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.5 

learned probs for this beta: {1: np.float64(0.6790888943315818), 8: np.float64(0.22423696026903592), 2: np.float64(0.08230253795095929), 59: np.float64(0.003592901862105777), 67: np.float64(0.003592901862105777), 81: np.float64(0.003592901862105777), 0: np.float64(0.003592901862105777)}
err dic= {1: np.float64(0.4350888943315818), 8: np.float64(0.038763039730964094), 2: np.float64(0.17769746204904072), 59: np.float64(0.08040709813789423), 67: np.float64(0.05240709813789422), 81: np.float64(0.046407098137894225), 0: np.float64(0.03940709813789422)} 

err list= [np.float64(0.4350888943315818), np.float64(0.038763039730964094), np.float64(0.17769746204904072), np.float64(0.08040709813789423), np.float64(0.05240709813789422), np.float64(0.046407098137894225), np.float64(0.03940709813789422)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  0.75 

learned probs for this beta: {1: np.float64(0.6779166870498053), 8: np.float64(0.21990667811121856), 2: np.float64(0.08916807779237809), 59: np.float64(0.0032521392616494883), 67: np.float64(0.0032521392616494883), 81: np.float64(0.0032521392616494883), 0: np.float64(0.0032521392616494883)}
err dic= {1: np.float64(0.43391668704980535), 8: np.float64(0.043093321888781455), 2: np.float64(0.17083192220762192), 59: np.float64(0.08074786073835051), 67: np.float64(0.05274786073835051), 81: np.float64(0.046747860738350515), 0: np.float64(0.03974786073835051)} 

err list= [np.float64(0.43391668704980535), np.float64(0.043093321888781455), np.float64(0.17083192220762192), np.float64(0.08074786073835051), np.float64(0.05274786073835051), np.float64(0.046747860738350515), np.float64(0.03974786073835051)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  1 

learned probs for this beta: {1: np.float64(0.6744137811665986), 8: np.float64(0.21685724282951946), 2: np.float64(0.09572892268321814), 59: np.float64(0.0032500133301659627), 67: np.float64(0.0032500133301659627), 81: np.float64(0.0032500133301659627), 0: np.float64(0.0032500133301659627)}
err dic= {1: np.float64(0.43041378116659856), 8: np.float64(0.04614275717048055), 2: np.float64(0.16427107731678187), 59: np.float64(0.08074998666983405), 67: np.float64(0.05274998666983404), 81: np.float64(0.04674998666983404), 0: np.float64(0.039749986669834037)} 

err list= [np.float64(0.43041378116659856), np.float64(0.04614275717048055), np.float64(0.16427107731678187), np.float64(0.08074998666983405), np.float64(0.05274998666983404), np.float64(0.04674998666983404), np.float64(0.039749986669834037)]
results for assortment [1, 8, 2, 59, 67, 81] :

beta is  1.25 

learned probs for this beta: {1: np.float64(0.6704269549234964), 8: np.float64(0.2149946122044048), 2: np.float64(0.10157843252180511), 59: np.float64(0.0032500000875734063), 67: np.float64(0.0032500000875734063), 81: np.float64(0.0032500000875734063), 0: np.float64(0.0032500000875734063)}
err dic= {1: np.float64(0.42642695492349636), 8: np.float64(0.04800538779559521), 2: np.float64(0.1584215674781949), 59: np.float64(0.0807499999124266), 67: np.float64(0.0527499999124266), 81: np.float64(0.04674999991242659), 0: np.float64(0.03974999991242659)} 

err list= [np.float64(0.42642695492349636), np.float64(0.04800538779559521), np.float64(0.1584215674781949), np.float64(0.0807499999124266), np.float64(0.0527499999124266), np.float64(0.04674999991242659), np.float64(0.03974999991242659)]
results for assortment [1, 8, 2, 59, 67, 81] :

err MNL dic= {1: np.float64(0.10386786018755328), 8: np.float64(0.13038064791133847), 2: np.float64(0.12445012787723786), 59: np.float64(0.025281756180733153), 67: np.float64(0.05210954816709291), 81: np.float64(0.05789641943734014), 0: np.float64(0.22341091219096332)} 

err MNL list= [np.float64(0.10386786018755328), np.float64(0.13038064791133847), np.float64(0.12445012787723786), np.float64(0.025281756180733153), np.float64(0.05210954816709291), np.float64(0.05789641943734014), np.float64(0.22341091219096332)]
sampled assortment [4, 1, 9, 55, 90, 94] number: 5
#  Learning probs for MM model, A = [4, 1, 9, 55, 90, 94]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 15: 1, 100: 1} [8, 2, 3, 4, 5, 7, 10, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0} [1, 4, 5, 6, 7, 9]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 3: 4, 4: 1, 5: 2, 6: 1, 8: 3, 9: 0, 10: 4, 14: 4} [9, 4, 6, 5, 1, 8, 3, 10, 14]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 6: 1, 10: 1, 12: 1, 13: 1, 100: 0} [100, 1, 3, 5, 6, 10, 12, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 16: 3} [2, 1, 3, 6, 10, 11, 16]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 4, 5: 1, 6: 3, 7: 2, 8: 6, 10: 0, 11: 4, 12: 4, 13: 7, 14: 1, 20: 6, 100: 11} [3, 10, 5, 14, 7, 6, 4, 11, 12, 8, 20, 1, 13, 100]
#  Learning probs for MM model, A = [4, 1, 9, 55, 90, 94]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 12: 1, 100: 1} [8, 1, 2, 3, 4, 5, 7, 12, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 11: 0} [1, 3, 4, 5, 6, 7, 10, 11]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 3, 4: 1, 5: 3, 6: 1, 8: 3, 9: 0, 10: 4, 19: 3, 27: 7, 29: 6} [9, 4, 6, 1, 2, 3, 5, 8, 19, 10, 29, 27]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 13: 1, 100: 0} [100, 1, 3, 4, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1} [2, 1, 6, 10, 11]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 2: 6, 3: 0, 4: 1, 5: 1, 6: 3, 7: 1, 9: 8, 10: 0, 11: 4, 12: 4, 13: 7, 14: 1, 16: 9, 19: 4, 21: 5, 25: 9, 77: 14} [3, 10, 4, 5, 7, 14, 6, 11, 12, 19, 21, 2, 1, 13, 9, 16, 25, 77]
empirical probabilities from test set: {4: 0.252, 1: 0.272, 9: 0.234, 55: 0.071, 90: 0.053, 94: 0.065, 0: 0.053}
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.025 

learned probs for this beta: {4: np.float64(0.1059648644518033), 1: np.float64(0.09897360146090976), 9: np.float64(0.15895252602035453), 55: np.float64(0.15902725201673332), 90: np.float64(0.15902725201673332), 94: np.float64(0.15902725201673332), 0: np.float64(0.15902725201673332)}
err dic= {4: np.float64(0.1460351355481967), 1: np.float64(0.17302639853909024), 9: np.float64(0.07504747397964548), 55: np.float64(0.08802725201673332), 90: np.float64(0.10602725201673333), 94: np.float64(0.09402725201673331), 0: np.float64(0.10602725201673333)} 

err list= [np.float64(0.1460351355481967), np.float64(0.17302639853909024), np.float64(0.07504747397964548), np.float64(0.08802725201673332), np.float64(0.10602725201673333), np.float64(0.09402725201673331), np.float64(0.10602725201673333)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.05 

learned probs for this beta: {4: np.float64(0.14525253132783583), 1: np.float64(0.1492444041928815), 9: np.float64(0.14548067431809733), 55: np.float64(0.14000559754029626), 90: np.float64(0.14000559754029626), 94: np.float64(0.14000559754029626), 0: np.float64(0.14000559754029626)}
err dic= {4: np.float64(0.10674746867216417), 1: np.float64(0.1227555958071185), 9: np.float64(0.08851932568190268), 55: np.float64(0.06900559754029627), 90: np.float64(0.08700559754029627), 94: np.float64(0.07500559754029626), 0: np.float64(0.08700559754029627)} 

err list= [np.float64(0.10674746867216417), np.float64(0.1227555958071185), np.float64(0.08851932568190268), np.float64(0.06900559754029627), np.float64(0.08700559754029627), np.float64(0.07500559754029626), np.float64(0.08700559754029627)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.1 

learned probs for this beta: {4: np.float64(0.23243723685633297), 1: np.float64(0.27741207115684313), 9: np.float64(0.10944959858689607), 55: np.float64(0.09517527334998188), 90: np.float64(0.09517527334998188), 94: np.float64(0.09517527334998188), 0: np.float64(0.09517527334998188)}
err dic= {4: np.float64(0.019562763143667034), 1: np.float64(0.005412071156843112), 9: np.float64(0.12455040141310394), 55: np.float64(0.024175273349981888), 90: np.float64(0.04217527334998188), 94: np.float64(0.03017527334998188), 0: np.float64(0.04217527334998188)} 

err list= [np.float64(0.019562763143667034), np.float64(0.005412071156843112), np.float64(0.12455040141310394), np.float64(0.024175273349981888), np.float64(0.04217527334998188), np.float64(0.03017527334998188), np.float64(0.04217527334998188)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.25 

learned probs for this beta: {4: np.float64(0.33544316824345144), 1: np.float64(0.5650508625860852), 9: np.float64(0.03723770223592051), 55: np.float64(0.015567066733635728), 90: np.float64(0.015567066733635728), 94: np.float64(0.015567066733635728), 0: np.float64(0.015567066733635728)}
err dic= {4: np.float64(0.08344316824345144), 1: np.float64(0.29305086258608515), 9: np.float64(0.1967622977640795), 55: np.float64(0.05543293326636427), 90: np.float64(0.03743293326636427), 94: np.float64(0.049432933266364276), 0: np.float64(0.03743293326636427)} 

err list= [np.float64(0.08344316824345144), np.float64(0.29305086258608515), np.float64(0.1967622977640795), np.float64(0.05543293326636427), np.float64(0.03743293326636427), np.float64(0.049432933266364276), np.float64(0.03743293326636427)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.5 

learned probs for this beta: {4: np.float64(0.2672959589044826), 1: np.float64(0.7041848622905835), 9: np.float64(0.027188831602820353), 55: np.float64(0.0003325868005284569), 90: np.float64(0.0003325868005284569), 94: np.float64(0.0003325868005284569), 0: np.float64(0.0003325868005284569)}
err dic= {4: np.float64(0.015295958904482598), 1: np.float64(0.4321848622905835), 9: np.float64(0.20681116839717967), 55: np.float64(0.07066741319947153), 90: np.float64(0.05266741319947154), 94: np.float64(0.06466741319947154), 0: np.float64(0.05266741319947154)} 

err list= [np.float64(0.015295958904482598), np.float64(0.4321848622905835), np.float64(0.20681116839717967), np.float64(0.07066741319947153), np.float64(0.05266741319947154), np.float64(0.06466741319947154), np.float64(0.05266741319947154)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  0.75 

learned probs for this beta: {4: np.float64(0.1983701508900412), 1: np.float64(0.7703512973733595), 9: np.float64(0.03126423088896322), 55: np.float64(3.580211908992039e-06), 90: np.float64(3.580211908992039e-06), 94: np.float64(3.580211908992039e-06), 0: np.float64(3.580211908992039e-06)}
err dic= {4: np.float64(0.0536298491099588), 1: np.float64(0.4983512973733595), 9: np.float64(0.2027357691110368), 55: np.float64(0.070996419788091), 90: np.float64(0.052996419788091005), 94: np.float64(0.06499641978809101), 0: np.float64(0.052996419788091005)} 

err list= [np.float64(0.0536298491099588), np.float64(0.4983512973733595), np.float64(0.2027357691110368), np.float64(0.070996419788091), np.float64(0.052996419788091005), np.float64(0.06499641978809101), np.float64(0.052996419788091005)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  1 

learned probs for this beta: {4: np.float64(0.14507598394123192), 1: np.float64(0.8200049858541858), 9: np.float64(0.034918877983469966), 55: np.float64(3.805527806349336e-08), 90: np.float64(3.805527806349336e-08), 94: np.float64(3.805527806349336e-08), 0: np.float64(3.805527806349336e-08)}
err dic= {4: np.float64(0.10692401605876808), 1: np.float64(0.5480049858541858), 9: np.float64(0.19908112201653005), 55: np.float64(0.07099996194472193), 90: np.float64(0.05299996194472194), 94: np.float64(0.06499996194472193), 0: np.float64(0.05299996194472194)} 

err list= [np.float64(0.10692401605876808), np.float64(0.5480049858541858), np.float64(0.19908112201653005), np.float64(0.07099996194472193), np.float64(0.05299996194472194), np.float64(0.06499996194472193), np.float64(0.05299996194472194)]
results for assortment [4, 1, 9, 55, 90, 94] :

beta is  1.25 

learned probs for this beta: {4: np.float64(0.10610819418859835), 1: np.float64(0.8560111848039945), 9: np.float64(0.037880619364925164), 55: np.float64(4.1062046527805483e-10), 90: np.float64(4.1062046527805483e-10), 94: np.float64(4.1062046527805483e-10), 0: np.float64(4.1062046527805483e-10)}
err dic= {4: np.float64(0.14589180581140165), 1: np.float64(0.5840111848039945), 9: np.float64(0.19611938063507484), 55: np.float64(0.07099999958937953), 90: np.float64(0.05299999958937953), 94: np.float64(0.06499999958937953), 0: np.float64(0.05299999958937953)} 

err list= [np.float64(0.14589180581140165), np.float64(0.5840111848039945), np.float64(0.19611938063507484), np.float64(0.07099999958937953), np.float64(0.05299999958937953), np.float64(0.06499999958937953), np.float64(0.05299999958937953)]
results for assortment [4, 1, 9, 55, 90, 94] :

err MNL dic= {4: np.float64(0.11697957451323679), 1: np.float64(0.13247005146161603), 9: np.float64(0.10195055440606929), 55: np.float64(0.0389262560348029), 90: np.float64(0.05713846888429094), 94: np.float64(0.04306939360178258), 0: np.float64(0.2122660618600456)} 

err MNL list= [np.float64(0.11697957451323679), np.float64(0.13247005146161603), np.float64(0.10195055440606929), np.float64(0.0389262560348029), np.float64(0.05713846888429094), np.float64(0.04306939360178258), np.float64(0.2122660618600456)]
sampled assortment [3, 4, 1, 57, 67, 10] number: 6
#  Learning probs for MM model, A = [3, 4, 1, 57, 67, 10]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 7: 1, 8: 0, 10: 1, 11: 1, 13: 1, 15: 1, 100: 1} [8, 3, 7, 10, 11, 13, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 7: 0, 11: 0, 16: 0, 18: 0} [1, 3, 5, 6, 7, 11, 16, 18]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 3, 6: 1, 7: 4, 8: 3, 9: 0, 12: 5, 14: 4, 15: 3} [9, 4, 6, 1, 2, 5, 8, 15, 7, 14, 12]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 5: 1, 12: 1, 13: 1, 100: 0} [100, 1, 2, 3, 5, 12, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 10: 1, 11: 1, 14: 2, 17: 2} [2, 1, 3, 6, 10, 11, 14, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 4, 5: 0, 6: 2, 7: 0, 10: 0, 11: 5, 12: 4, 14: 0, 16: 8, 17: 9, 20: 6, 34: 9} [3, 5, 7, 10, 14, 6, 4, 12, 11, 20, 1, 16, 17, 34]
#  Learning probs for MM model, A = [3, 4, 1, 57, 67, 10]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 11: 1, 12: 1, 15: 1, 100: 1} [8, 3, 4, 5, 7, 11, 12, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 11: 0, 12: 0, 20: 0} [1, 3, 4, 5, 6, 7, 11, 12, 20]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 3, 4: 1, 5: 3, 6: 1, 7: 3, 8: 3, 9: 0, 19: 3, 24: 8, 25: 4, 26: 6, 27: 8} [9, 4, 6, 1, 2, 3, 5, 7, 8, 19, 25, 26, 24, 27]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 6: 1, 100: 0} [100, 1, 3, 5, 6]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 6: 1, 9: 1, 10: 1, 11: 1, 14: 1, 17: 3} [2, 1, 6, 9, 10, 11, 14, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 3: 0, 4: 3, 5: 0, 6: 2, 7: 0, 9: 5, 10: 0, 11: 5, 12: 5, 14: 1, 16: 7, 17: 11, 23: 7, 25: 8, 27: 8} [3, 5, 7, 10, 14, 6, 4, 9, 11, 12, 1, 16, 23, 25, 27, 17]
empirical probabilities from test set: {3: 0.211, 4: 0.22, 1: 0.218, 57: 0.053, 67: 0.059, 10: 0.205, 0: 0.034}
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.11158585057639754), 4: np.float64(0.131658653482152), 1: np.float64(0.113728252075348), 57: np.float64(0.16287080558032221), 67: np.float64(0.16287080558032221), 10: np.float64(0.15441482712513677), 0: np.float64(0.16287080558032221)}
err dic= {3: np.float64(0.09941414942360245), 4: np.float64(0.088341346517848), 1: np.float64(0.104271747924652), 57: np.float64(0.10987080558032222), 67: np.float64(0.10387080558032222), 10: np.float64(0.05058517287486322), 0: np.float64(0.1288708055803222)} 

err list= [np.float64(0.09941414942360245), np.float64(0.088341346517848), np.float64(0.104271747924652), np.float64(0.10987080558032222), np.float64(0.10387080558032222), np.float64(0.05058517287486322), np.float64(0.1288708055803222)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.15199179834939328), 4: np.float64(0.16014538360603114), 1: np.float64(0.1482558049151302), 57: np.float64(0.1344740362434237), 67: np.float64(0.1344740362434237), 10: np.float64(0.13618490439917333), 0: np.float64(0.1344740362434237)}
err dic= {3: np.float64(0.05900820165060672), 4: np.float64(0.05985461639396886), 1: np.float64(0.06974419508486979), 57: np.float64(0.0814740362434237), 67: np.float64(0.07547403624342369), 10: np.float64(0.06881509560082666), 0: np.float64(0.10047403624342369)} 

err list= [np.float64(0.05900820165060672), np.float64(0.05985461639396886), np.float64(0.06974419508486979), np.float64(0.0814740362434237), np.float64(0.07547403624342369), np.float64(0.06881509560082666), np.float64(0.10047403624342369)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.23622357062395627), 4: np.float64(0.20919949168291607), 1: np.float64(0.22447693310371566), 57: np.float64(0.07683341112102679), 67: np.float64(0.07683341112102679), 10: np.float64(0.09959977122633179), 0: np.float64(0.07683341112102679)}
err dic= {3: np.float64(0.025223570623956276), 4: np.float64(0.010800508317083929), 1: np.float64(0.006476933103715665), 57: np.float64(0.02383341112102679), 67: np.float64(0.017833411121026793), 10: np.float64(0.1054002287736682), 0: np.float64(0.04283341112102679)} 

err list= [np.float64(0.025223570623956276), np.float64(0.010800508317083929), np.float64(0.006476933103715665), np.float64(0.02383341112102679), np.float64(0.017833411121026793), np.float64(0.1054002287736682), np.float64(0.04283341112102679)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.34321938209187386), 4: np.float64(0.21930636118822838), 1: np.float64(0.3598790324613851), 57: np.float64(0.007471633683006259), 67: np.float64(0.007471633683006259), 10: np.float64(0.055180323209494196), 0: np.float64(0.007471633683006259)}
err dic= {3: np.float64(0.13221938209187387), 4: np.float64(0.0006936388117716186), 1: np.float64(0.14187903246138509), 57: np.float64(0.04552836631699374), 67: np.float64(0.051528366316993736), 10: np.float64(0.14981967679050578), 0: np.float64(0.02652836631699374)} 

err list= [np.float64(0.13221938209187387), np.float64(0.0006936388117716186), np.float64(0.14187903246138509), np.float64(0.04552836631699374), np.float64(0.051528366316993736), np.float64(0.14981967679050578), np.float64(0.02652836631699374)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.34803803519492615), 4: np.float64(0.1837754507997656), 1: np.float64(0.4332080725375349), 57: np.float64(6.780937228575195e-05), 67: np.float64(6.780937228575195e-05), 10: np.float64(0.03477501335091639), 0: np.float64(6.780937228575195e-05)}
err dic= {3: np.float64(0.13703803519492616), 4: np.float64(0.03622454920023441), 1: np.float64(0.2152080725375349), 57: np.float64(0.052932190627714246), 67: np.float64(0.058932190627714244), 10: np.float64(0.1702249866490836), 0: np.float64(0.03393219062771425)} 

err list= [np.float64(0.13703803519492616), np.float64(0.03622454920023441), np.float64(0.2152080725375349), np.float64(0.052932190627714246), np.float64(0.058932190627714244), np.float64(0.1702249866490836), np.float64(0.03393219062771425)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.3373922385405248), 4: np.float64(0.15550217090363114), 1: np.float64(0.4857209950487971), 57: np.float64(5.23138854113666e-07), 67: np.float64(5.23138854113666e-07), 10: np.float64(0.021383026090484567), 0: np.float64(5.23138854113666e-07)}
err dic= {3: np.float64(0.1263922385405248), 4: np.float64(0.06449782909636886), 1: np.float64(0.2677209950487971), 57: np.float64(0.05299947686114589), 67: np.float64(0.058999476861145886), 10: np.float64(0.18361697390951542), 0: np.float64(0.03399947686114589)} 

err list= [np.float64(0.1263922385405248), np.float64(0.06449782909636886), np.float64(0.2677209950487971), np.float64(0.05299947686114589), np.float64(0.058999476861145886), np.float64(0.18361697390951542), np.float64(0.03399947686114589)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  1 

learned probs for this beta: {3: np.float64(0.3247578293368032), 4: np.float64(0.1324581540157956), 1: np.float64(0.5304799229228083), 57: np.float64(4.557712212621601e-09), 67: np.float64(4.557712212621601e-09), 10: np.float64(0.01230408005145635), 0: np.float64(4.557712212621601e-09)}
err dic= {3: np.float64(0.1137578293368032), 4: np.float64(0.08754184598420439), 1: np.float64(0.31247992292280835), 57: np.float64(0.052999995442287784), 67: np.float64(0.05899999544228778), 10: np.float64(0.19269591994854363), 0: np.float64(0.03399999544228779)} 

err list= [np.float64(0.1137578293368032), np.float64(0.08754184598420439), np.float64(0.31247992292280835), np.float64(0.052999995442287784), np.float64(0.05899999544228778), np.float64(0.19269591994854363), np.float64(0.03399999544228779)]
results for assortment [3, 4, 1, 57, 67, 10] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.3115644177202708), 4: np.float64(0.11398902734395483), 1: np.float64(0.567716020539158), 57: np.float64(4.302606839058286e-11), 67: np.float64(4.302606839058286e-11), 10: np.float64(0.006730534267537919), 0: np.float64(4.302606839058286e-11)}
err dic= {3: np.float64(0.10056441772027083), 4: np.float64(0.10601097265604517), 1: np.float64(0.34971602053915807), 57: np.float64(0.05299999995697393), 67: np.float64(0.05899999995697393), 10: np.float64(0.19826946573246207), 0: np.float64(0.033999999956973934)} 

err list= [np.float64(0.10056441772027083), np.float64(0.10601097265604517), np.float64(0.34971602053915807), np.float64(0.05299999995697393), np.float64(0.05899999995697393), np.float64(0.19826946573246207), np.float64(0.033999999956973934)]
results for assortment [3, 4, 1, 57, 67, 10] :

err MNL dic= {3: np.float64(0.0785407805079496), 4: np.float64(0.0886248193268635), 1: np.float64(0.08223704315506916), 57: np.float64(0.056384678918026045), 67: np.float64(0.045738798265537894), 10: np.float64(0.07682531488746644), 0: np.float64(0.22410448069378489)} 

err MNL list= [np.float64(0.0785407805079496), np.float64(0.0886248193268635), np.float64(0.08223704315506916), np.float64(0.056384678918026045), np.float64(0.045738798265537894), np.float64(0.07682531488746644), np.float64(0.22410448069378489)]
sampled assortment [2, 7, 1, 13, 20, 88] number: 7
#  Learning probs for MM model, A = [2, 7, 1, 13, 20, 88]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 7: 1, 8: 0, 10: 1, 12: 1, 15: 1, 100: 1} [8, 1, 3, 4, 7, 10, 12, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 10: 0, 12: 0} [1, 3, 4, 5, 6, 7, 9, 10, 12]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 3, 4: 1, 5: 2, 6: 1, 7: 4, 8: 2, 9: 0, 10: 4, 12: 5, 15: 3, 19: 4, 26: 7, 30: 10, 33: 6} [9, 4, 6, 5, 8, 1, 2, 3, 15, 7, 10, 19, 12, 33, 26, 30]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 6: 1, 12: 1, 15: 1, 100: 0} [100, 1, 3, 5, 6, 12, 15]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 10: 1, 11: 1, 14: 2, 17: 2} [2, 1, 10, 11, 14, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 6, 3: 0, 4: 3, 5: 0, 6: 2, 7: 1, 9: 6, 10: 0, 11: 5, 12: 5, 14: 0, 16: 8, 21: 7, 23: 11, 25: 8, 34: 9, 82: 15} [3, 5, 10, 14, 7, 6, 4, 11, 12, 1, 9, 21, 16, 25, 34, 23, 82]
#  Learning probs for MM model, A = [2, 7, 1, 13, 20, 88]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {2: 1, 3: 1, 5: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 2, 3, 5, 7, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 5: 0, 6: 0, 7: 0, 18: 0} [1, 3, 5, 6, 7, 18]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 3: 3, 4: 1, 5: 3, 6: 1, 7: 3, 8: 3, 9: 0, 12: 4, 17: 5} [9, 4, 6, 1, 3, 5, 7, 8, 12, 17]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 4: 1, 5: 1, 12: 1, 13: 1, 100: 0} [100, 1, 3, 4, 5, 12, 13]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 6: 1, 10: 1, 11: 1, 20: 3} [2, 1, 6, 10, 11, 20]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {3: 0, 4: 1, 5: 0, 6: 2, 7: 0, 9: 6, 10: 0, 11: 4, 12: 4, 14: 0, 20: 6, 21: 6, 25: 8, 41: 10} [3, 5, 7, 10, 14, 4, 6, 11, 12, 9, 20, 21, 25, 41]
empirical probabilities from test set: {2: 0.235, 7: 0.185, 1: 0.207, 13: 0.153, 20: 0.147, 88: 0.037, 0: 0.036}
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.13937992225261886), 7: np.float64(0.11409460849171003), 1: np.float64(0.10977895742120143), 13: np.float64(0.13483334802295271), 20: np.float64(0.1569400057553198), 88: np.float64(0.17248657902809894), 0: np.float64(0.17248657902809894)}
err dic= {2: np.float64(0.09562007774738113), 7: np.float64(0.07090539150828996), 1: np.float64(0.09722104257879856), 13: np.float64(0.018166651977047282), 20: np.float64(0.009940005755319808), 88: np.float64(0.13548657902809894), 0: np.float64(0.13648657902809894)} 

err list= [np.float64(0.09562007774738113), np.float64(0.07090539150828996), np.float64(0.09722104257879856), np.float64(0.018166651977047282), np.float64(0.009940005755319808), np.float64(0.13548657902809894), np.float64(0.13648657902809894)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.14351469337463185), 7: np.float64(0.13073761112716015), 1: np.float64(0.13951547843253387), 13: np.float64(0.13642292024214792), 20: np.float64(0.1448545951227022), 88: np.float64(0.15247735085041236), 0: np.float64(0.15247735085041236)}
err dic= {2: np.float64(0.09148530662536813), 7: np.float64(0.05426238887283985), 1: np.float64(0.06748452156746612), 13: np.float64(0.01657707975785208), 20: np.float64(0.0021454048772977796), 88: np.float64(0.11547735085041236), 0: np.float64(0.11647735085041236)} 

err list= [np.float64(0.09148530662536813), np.float64(0.05426238887283985), np.float64(0.06748452156746612), np.float64(0.01657707975785208), np.float64(0.0021454048772977796), np.float64(0.11547735085041236), np.float64(0.11647735085041236)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.15391217851505107), 7: np.float64(0.16744023834232108), 1: np.float64(0.22459609113027412), 13: np.float64(0.13480363767294107), 20: np.float64(0.11256809475508299), 88: np.float64(0.1033398797921649), 0: np.float64(0.1033398797921649)}
err dic= {2: np.float64(0.08108782148494892), 7: np.float64(0.01755976165767892), 1: np.float64(0.017596091130274133), 13: np.float64(0.01819636232705893), 20: np.float64(0.034431905244917), 88: np.float64(0.06633987979216491), 0: np.float64(0.06733987979216491)} 

err list= [np.float64(0.08108782148494892), np.float64(0.01755976165767892), np.float64(0.017596091130274133), np.float64(0.01819636232705893), np.float64(0.034431905244917), np.float64(0.06633987979216491), np.float64(0.06733987979216491)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.17285410170160564), 7: np.float64(0.20698532098233124), 1: np.float64(0.45703235211217436), 13: np.float64(0.10229304776196095), 20: np.float64(0.03532293132729729), 88: np.float64(0.012756123057315159), 0: np.float64(0.012756123057315159)}
err dic= {2: np.float64(0.06214589829839434), 7: np.float64(0.021985320982331247), 1: np.float64(0.25003235211217434), 13: np.float64(0.050706952238039046), 20: np.float64(0.1116770686727027), 88: np.float64(0.024243876942684837), 0: np.float64(0.023243876942684837)} 

err list= [np.float64(0.06214589829839434), np.float64(0.021985320982331247), np.float64(0.25003235211217434), np.float64(0.050706952238039046), np.float64(0.1116770686727027), np.float64(0.024243876942684837), np.float64(0.023243876942684837)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.21577460786271838), 7: np.float64(0.14480507938795714), 1: np.float64(0.5775566673718993), 13: np.float64(0.052605317164962716), 20: np.float64(0.008997235602872609), 88: np.float64(0.0001305463047950014), 0: np.float64(0.0001305463047950014)}
err dic= {2: np.float64(0.01922539213728161), 7: np.float64(0.040194920612042856), 1: np.float64(0.3705566673718993), 13: np.float64(0.10039468283503727), 20: np.float64(0.1380027643971274), 88: np.float64(0.036869453695204994), 0: np.float64(0.03586945369520499)} 

err list= [np.float64(0.01922539213728161), np.float64(0.040194920612042856), np.float64(0.3705566673718993), np.float64(0.10039468283503727), np.float64(0.1380027643971274), np.float64(0.036869453695204994), np.float64(0.03586945369520499)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.25324023831103604), 7: np.float64(0.09170701933577573), 1: np.float64(0.6284599818822998), 13: np.float64(0.023764158016007154), 20: np.float64(0.0028266190334751322), 88: np.float64(9.917107030781984e-07), 0: np.float64(9.917107030781984e-07)}
err dic= {2: np.float64(0.01824023831103605), 7: np.float64(0.09329298066422427), 1: np.float64(0.42145998188229983), 13: np.float64(0.12923584198399285), 20: np.float64(0.14417338096652485), 88: np.float64(0.03699900828929692), 0: np.float64(0.03599900828929692)} 

err list= [np.float64(0.01824023831103605), np.float64(0.09329298066422427), np.float64(0.42145998188229983), np.float64(0.12923584198399285), np.float64(0.14417338096652485), np.float64(0.03699900828929692), np.float64(0.03599900828929692)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  1 

learned probs for this beta: {2: np.float64(0.2789911076123349), 7: np.float64(0.05898138767568144), 1: np.float64(0.6512880199511569), 13: np.float64(0.009896775455413113), 20: np.float64(0.0008426948820010037), 88: np.float64(7.2117063268631124e-09), 0: np.float64(7.2117063268631124e-09)}
err dic= {2: np.float64(0.043991107612334934), 7: np.float64(0.12601861232431855), 1: np.float64(0.44428801995115696), 13: np.float64(0.14310322454458688), 20: np.float64(0.146157305117999), 88: np.float64(0.03699999278829367), 0: np.float64(0.03599999278829367)} 

err list= [np.float64(0.043991107612334934), np.float64(0.12601861232431855), np.float64(0.44428801995115696), np.float64(0.14310322454458688), np.float64(0.146157305117999), np.float64(0.03699999278829367), np.float64(0.03599999278829367)]
results for assortment [2, 7, 1, 13, 20, 88] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.2958641854283474), 7: np.float64(0.04091605081506276), 1: np.float64(0.6590582877337212), 13: np.float64(0.003917027958575415), 20: np.float64(0.00024444796112470203), 88: np.float64(5.158423542998751e-11), 0: np.float64(5.158423542998751e-11)}
err dic= {2: np.float64(0.06086418542834743), 7: np.float64(0.14408394918493722), 1: np.float64(0.45205828773372125), 13: np.float64(0.1490829720414246), 20: np.float64(0.1467555520388753), 88: np.float64(0.03699999994841576), 0: np.float64(0.03599999994841576)} 

err list= [np.float64(0.06086418542834743), np.float64(0.14408394918493722), np.float64(0.45205828773372125), np.float64(0.1490829720414246), np.float64(0.1467555520388753), np.float64(0.03699999994841576), np.float64(0.03599999994841576)]
results for assortment [2, 7, 1, 13, 20, 88] :

err MNL dic= {2: np.float64(0.10536942675159236), 7: np.float64(0.054197452229299364), 1: np.float64(0.07298726114649681), 13: np.float64(0.029585987261146515), 20: np.float64(0.024808917197452235), 88: np.float64(0.06817197452229298), 0: np.float64(0.21877707006369426)} 

err MNL list= [np.float64(0.10536942675159236), np.float64(0.054197452229299364), np.float64(0.07298726114649681), np.float64(0.029585987261146515), np.float64(0.024808917197452235), np.float64(0.06817197452229298), np.float64(0.21877707006369426)]
sampled assortment [3, 4, 2, 46, 33, 57] number: 8
#  Learning probs for MM model, A = [3, 4, 2, 46, 33, 57]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 4: 1, 5: 1, 7: 1, 8: 0, 10: 1, 12: 1, 15: 1, 100: 1} [8, 1, 3, 4, 5, 7, 10, 12, 15, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0} [1, 3, 4, 5, 6, 7, 9, 12]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 2, 6: 1, 7: 3, 8: 2, 9: 0, 15: 3} [9, 4, 6, 5, 8, 1, 2, 7, 15]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 6: 1, 11: 1, 12: 1, 13: 1, 19: 1, 100: 0} [100, 1, 3, 6, 11, 12, 13, 19]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 4: 3, 6: 1, 10: 1, 11: 1, 14: 1} [2, 1, 3, 6, 10, 11, 14, 4]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {3: 0, 4: 2, 5: 0, 6: 1, 7: 0, 8: 9, 9: 6, 10: 0, 11: 4, 12: 4, 14: 2, 18: 7, 19: 7, 20: 6, 22: 10, 41: 9} [3, 5, 7, 10, 6, 4, 14, 11, 12, 9, 20, 18, 19, 8, 41, 22]
#  Learning probs for MM model, A = [3, 4, 2, 46, 33, 57]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 7: 1, 8: 0, 13: 1, 100: 1} [8, 3, 4, 7, 13, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 12: 0, 13: 0, 16: 0} [1, 3, 4, 5, 6, 7, 9, 12, 13, 16]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 3: 4, 4: 1, 5: 3, 6: 1, 8: 1, 9: 0, 10: 5, 12: 5, 14: 5, 15: 3, 19: 4} [9, 4, 6, 8, 1, 2, 5, 15, 3, 19, 10, 12, 14]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 2: 1, 3: 1, 6: 1, 12: 1, 14: 1, 17: 2, 100: 0} [100, 1, 2, 3, 6, 12, 14, 17]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 9: 1, 10: 1, 11: 1, 17: 2} [2, 1, 3, 6, 9, 10, 11, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 2: 7, 3: 0, 4: 2, 5: 0, 6: 2, 7: 1, 9: 5, 10: 0, 12: 4, 13: 7, 14: 0, 16: 8, 18: 8, 19: 5, 21: 7, 99: 14} [3, 5, 10, 14, 7, 4, 6, 12, 9, 19, 1, 2, 13, 21, 16, 18, 99]
empirical probabilities from test set: {3: 0.237, 4: 0.244, 2: 0.249, 46: 0.073, 33: 0.109, 57: 0.054, 0: 0.034}
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.025 

learned probs for this beta: {3: np.float64(0.1093082302216563), 4: np.float64(0.12733461016072584), 2: np.float64(0.1369408793483265), 46: np.float64(0.15660407006732277), 33: np.float64(0.15660407006732277), 57: np.float64(0.15660407006732277), 0: np.float64(0.15660407006732277)}
err dic= {3: np.float64(0.12769176977834368), 4: np.float64(0.11666538983927416), 2: np.float64(0.1120591206516735), 46: np.float64(0.08360407006732277), 33: np.float64(0.04760407006732277), 57: np.float64(0.10260407006732278), 0: np.float64(0.12260407006732277)} 

err list= [np.float64(0.12769176977834368), np.float64(0.11666538983927416), np.float64(0.1120591206516735), np.float64(0.08360407006732277), np.float64(0.04760407006732277), np.float64(0.10260407006732278), np.float64(0.12260407006732277)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.05 

learned probs for this beta: {3: np.float64(0.1634711554733316), 4: np.float64(0.15679573373660463), 2: np.float64(0.144625577573545), 46: np.float64(0.13377688330413007), 33: np.float64(0.13377688330413007), 57: np.float64(0.13377688330413007), 0: np.float64(0.13377688330413007)}
err dic= {3: np.float64(0.07352884452666839), 4: np.float64(0.08720426626339536), 2: np.float64(0.104374422426455), 46: np.float64(0.06077688330413007), 33: np.float64(0.024776883304130068), 57: np.float64(0.07977688330413008), 0: np.float64(0.09977688330413007)} 

err list= [np.float64(0.07352884452666839), np.float64(0.08720426626339536), np.float64(0.104374422426455), np.float64(0.06077688330413007), np.float64(0.024776883304130068), np.float64(0.07977688330413008), np.float64(0.09977688330413007)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.1 

learned probs for this beta: {3: np.float64(0.2876676308660693), 4: np.float64(0.2189221556135483), 2: np.float64(0.16330245888952927), 46: np.float64(0.08252693865771352), 33: np.float64(0.08252693865771352), 57: np.float64(0.08252693865771352), 0: np.float64(0.08252693865771352)}
err dic= {3: np.float64(0.05066763086606929), 4: np.float64(0.025077844386451692), 2: np.float64(0.08569754111047073), 46: np.float64(0.009526938657713521), 33: np.float64(0.026473061342286483), 57: np.float64(0.028526938657713517), 0: np.float64(0.048526938657713514)} 

err list= [np.float64(0.05066763086606929), np.float64(0.025077844386451692), np.float64(0.08569754111047073), np.float64(0.009526938657713521), np.float64(0.026473061342286483), np.float64(0.028526938657713517), np.float64(0.048526938657713514)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.25 

learned probs for this beta: {3: np.float64(0.47777939108031164), 4: np.float64(0.289166338144221), 2: np.float64(0.2020398773862168), 46: np.float64(0.0077535983473125914), 33: np.float64(0.0077535983473125914), 57: np.float64(0.0077535983473125914), 0: np.float64(0.0077535983473125914)}
err dic= {3: np.float64(0.24077939108031166), 4: np.float64(0.045166338144221), 2: np.float64(0.04696012261378321), 46: np.float64(0.0652464016526874), 33: np.float64(0.1012464016526874), 57: np.float64(0.04624640165268741), 0: np.float64(0.02624640165268741)} 

err list= [np.float64(0.24077939108031166), np.float64(0.045166338144221), np.float64(0.04696012261378321), np.float64(0.0652464016526874), np.float64(0.1012464016526874), np.float64(0.04624640165268741), np.float64(0.02624640165268741)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.5 

learned probs for this beta: {3: np.float64(0.5084616617636535), 4: np.float64(0.26768390260906655), 2: np.float64(0.22358017987855344), 46: np.float64(6.856393718171601e-05), 33: np.float64(6.856393718171601e-05), 57: np.float64(6.856393718171601e-05), 0: np.float64(6.856393718171601e-05)}
err dic= {3: np.float64(0.2714616617636535), 4: np.float64(0.023683902609066554), 2: np.float64(0.025419820121446557), 46: np.float64(0.07293143606281828), 33: np.float64(0.10893143606281828), 57: np.float64(0.053931436062818285), 0: np.float64(0.03393143606281829)} 

err list= [np.float64(0.2714616617636535), np.float64(0.023683902609066554), np.float64(0.025419820121446557), np.float64(0.07293143606281828), np.float64(0.10893143606281828), np.float64(0.053931436062818285), np.float64(0.03393143606281829)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  0.75 

learned probs for this beta: {3: np.float64(0.5210081090249435), 4: np.float64(0.23770533108354416), 2: np.float64(0.24128480136070168), 46: np.float64(4.396327026621571e-07), 33: np.float64(4.396327026621571e-07), 57: np.float64(4.396327026621571e-07), 0: np.float64(4.396327026621571e-07)}
err dic= {3: np.float64(0.28400810902494356), 4: np.float64(0.006294668916455831), 2: np.float64(0.007715198639298315), 46: np.float64(0.07299956036729734), 33: np.float64(0.10899956036729734), 57: np.float64(0.05399956036729734), 0: np.float64(0.03399956036729734)} 

err list= [np.float64(0.28400810902494356), np.float64(0.006294668916455831), np.float64(0.007715198639298315), np.float64(0.07299956036729734), np.float64(0.10899956036729734), np.float64(0.05399956036729734), np.float64(0.03399956036729734)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  1 

learned probs for this beta: {3: np.float64(0.5335639222721307), 4: np.float64(0.20868573108902327), 2: np.float64(0.25775033473122866), 46: np.float64(2.9769043775037604e-09), 33: np.float64(2.9769043775037604e-09), 57: np.float64(2.9769043775037604e-09), 0: np.float64(2.9769043775037604e-09)}
err dic= {3: np.float64(0.2965639222721307), 4: np.float64(0.03531426891097672), 2: np.float64(0.00875033473122866), 46: np.float64(0.07299999702309562), 33: np.float64(0.10899999702309562), 57: np.float64(0.053999997023095624), 0: np.float64(0.03399999702309563)} 

err list= [np.float64(0.2965639222721307), np.float64(0.03531426891097672), np.float64(0.00875033473122866), np.float64(0.07299999702309562), np.float64(0.10899999702309562), np.float64(0.053999997023095624), np.float64(0.03399999702309563)]
results for assortment [3, 4, 2, 46, 33, 57] :

beta is  1.25 

learned probs for this beta: {3: np.float64(0.5457298011335542), 4: np.float64(0.18201327835936487), 2: np.float64(0.27225692042074406), 46: np.float64(2.158416651549407e-11), 33: np.float64(2.158416651549407e-11), 57: np.float64(2.158416651549407e-11), 0: np.float64(2.158416651549407e-11)}
err dic= {3: np.float64(0.3087298011335542), 4: np.float64(0.06198672164063512), 2: np.float64(0.023256920420744065), 46: np.float64(0.07299999997841583), 33: np.float64(0.10899999997841583), 57: np.float64(0.053999999978415834), 0: np.float64(0.03399999997841584)} 

err list= [np.float64(0.3087298011335542), np.float64(0.06198672164063512), np.float64(0.023256920420744065), np.float64(0.07299999997841583), np.float64(0.10899999997841583), np.float64(0.053999999978415834), np.float64(0.03399999997841584)]
results for assortment [3, 4, 2, 46, 33, 57] :

err MNL dic= {3: np.float64(0.10328452318916101), 4: np.float64(0.11137884314747262), 2: np.float64(0.11643095362167796), 46: np.float64(0.0402881709223554), 33: np.float64(0.007831683168316839), 57: np.float64(0.056422094841063065), 0: np.float64(0.22655237102657635)} 

err MNL list= [np.float64(0.10328452318916101), np.float64(0.11137884314747262), np.float64(0.11643095362167796), np.float64(0.0402881709223554), np.float64(0.007831683168316839), np.float64(0.056422094841063065), np.float64(0.22655237102657635)]
sampled assortment [2, 9, 1, 87, 36, 29] number: 9
#  Learning probs for MM model, A = [2, 9, 1, 87, 36, 29]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {3: 1, 4: 1, 7: 1, 8: 0, 100: 1} [8, 3, 4, 7, 100]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 10: 0, 20: 0} [1, 3, 4, 5, 6, 7, 10, 20]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 3, 4: 1, 5: 3, 6: 1, 7: 4, 8: 1, 9: 0, 13: 3, 15: 3, 17: 4} [9, 4, 6, 8, 1, 2, 5, 13, 15, 7, 17]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 5: 1, 12: 1, 14: 1, 100: 0} [100, 1, 3, 5, 12, 14]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 4: 2, 10: 1, 11: 1, 17: 2} [2, 1, 3, 10, 11, 4, 17]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 6, 2: 8, 3: 0, 4: 4, 5: 0, 6: 3, 7: 1, 8: 6, 9: 4, 10: 0, 11: 4, 12: 4, 13: 8, 14: 1, 16: 7, 19: 5, 25: 8, 41: 12, 49: 13} [3, 5, 10, 7, 14, 6, 4, 9, 11, 12, 19, 1, 8, 16, 2, 13, 25, 41, 49]
#  Learning probs for MM model, A = [2, 9, 1, 87, 36, 29]
#cluster  3 with weight 0.2095
Learned cluster center of cluster 3:  {1: 1, 3: 1, 5: 1, 7: 1, 8: 0, 12: 2, 100: 1} [8, 1, 3, 5, 7, 100, 12]
#cluster  6 with weight 0.38775
Learned cluster center of cluster 6:  {1: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 9: 0, 11: 0, 12: 0, 15: 0} [1, 3, 4, 5, 6, 7, 9, 11, 12, 15]
#cluster  1 with weight 0.04975
Learned cluster center of cluster 1:  {1: 3, 2: 4, 4: 1, 5: 3, 6: 1, 7: 3, 8: 2, 9: 0, 12: 4, 13: 3, 15: 3, 26: 6, 27: 6} [9, 4, 6, 8, 1, 5, 7, 13, 15, 2, 12, 26, 27]
#cluster  4 with weight 0.20375
Learned cluster center of cluster 4:  {1: 1, 3: 1, 14: 1, 100: 0} [100, 1, 3, 14]
#cluster  5 with weight 0.1265
Learned cluster center of cluster 5:  {1: 1, 2: 0, 3: 1, 6: 1, 7: 4, 10: 1, 11: 1, 17: 2, 19: 3} [2, 1, 3, 6, 10, 11, 17, 19, 7]
#cluster  2 with weight 0.02275
Learned cluster center of cluster 2:  {1: 7, 2: 7, 3: 0, 4: 2, 5: 0, 6: 2, 7: 0, 10: 0, 11: 5, 12: 4, 13: 8, 14: 1, 15: 8, 21: 6, 27: 8} [3, 5, 7, 10, 14, 4, 6, 12, 11, 21, 1, 2, 13, 15, 27]
empirical probabilities from test set: {2: 0.275, 9: 0.213, 1: 0.242, 87: 0.036, 36: 0.096, 29: 0.097, 0: 0.041}
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.025 

learned probs for this beta: {2: np.float64(0.14591548715320557), 9: np.float64(0.13777725065817506), 1: np.float64(0.10635726339826017), 87: np.float64(0.15248749969758965), 36: np.float64(0.15248749969758965), 29: np.float64(0.15248749969758965), 0: np.float64(0.15248749969758965)}
err dic= {2: np.float64(0.12908451284679445), 9: np.float64(0.07522274934182493), 1: np.float64(0.1356427366017398), 87: np.float64(0.11648749969758965), 36: np.float64(0.05648749969758965), 29: np.float64(0.05548749969758965), 0: np.float64(0.11148749969758964)} 

err list= [np.float64(0.12908451284679445), np.float64(0.07522274934182493), np.float64(0.1356427366017398), np.float64(0.11648749969758965), np.float64(0.05648749969758965), np.float64(0.05548749969758965), np.float64(0.11148749969758964)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.05 

learned probs for this beta: {2: np.float64(0.14445643940249667), 9: np.float64(0.15187049685785103), 1: np.float64(0.16379193228448335), 87: np.float64(0.13497028286379287), 36: np.float64(0.13497028286379287), 29: np.float64(0.13497028286379287), 0: np.float64(0.13497028286379287)}
err dic= {2: np.float64(0.13054356059750336), 9: np.float64(0.06112950314214896), 1: np.float64(0.07820806771551664), 87: np.float64(0.09897028286379286), 36: np.float64(0.038970282863792866), 29: np.float64(0.037970282863792865), 0: np.float64(0.09397028286379286)} 

err list= [np.float64(0.13054356059750336), np.float64(0.06112950314214896), np.float64(0.07820806771551664), np.float64(0.09897028286379286), np.float64(0.038970282863792866), np.float64(0.037970282863792865), np.float64(0.09397028286379286)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.1 

learned probs for this beta: {2: np.float64(0.13783373909249144), 9: np.float64(0.17267118714466018), 1: np.float64(0.30860076721174823), 87: np.float64(0.09522357663777521), 36: np.float64(0.09522357663777521), 29: np.float64(0.09522357663777521), 0: np.float64(0.09522357663777521)}
err dic= {2: np.float64(0.13716626090750858), 9: np.float64(0.04032881285533982), 1: np.float64(0.06660076721174824), 87: np.float64(0.059223576637775215), 36: np.float64(0.0007764233622247901), 29: np.float64(0.001776423362224791), 0: np.float64(0.05422357663777521)} 

err list= [np.float64(0.13716626090750858), np.float64(0.04032881285533982), np.float64(0.06660076721174824), np.float64(0.059223576637775215), np.float64(0.0007764233622247901), np.float64(0.001776423362224791), np.float64(0.05422357663777521)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.25 

learned probs for this beta: {2: np.float64(0.10464475120175627), 9: np.float64(0.1445469452610287), 1: np.float64(0.65658229794015), 87: np.float64(0.023556501399266176), 36: np.float64(0.023556501399266176), 29: np.float64(0.023556501399266176), 0: np.float64(0.023556501399266176)}
err dic= {2: np.float64(0.17035524879824376), 9: np.float64(0.06845305473897129), 1: np.float64(0.41458229794015), 87: np.float64(0.012443498600733821), 36: np.float64(0.07244349860073382), 29: np.float64(0.07344349860073382), 0: np.float64(0.017443498600733826)} 

err list= [np.float64(0.17035524879824376), np.float64(0.06845305473897129), np.float64(0.41458229794015), np.float64(0.012443498600733821), np.float64(0.07244349860073382), np.float64(0.07344349860073382), np.float64(0.017443498600733826)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.5 

learned probs for this beta: {2: np.float64(0.08896266592851841), 9: np.float64(0.07836829838511294), 1: np.float64(0.8293828390947575), 87: np.float64(0.0008215491479028757), 36: np.float64(0.0008215491479028757), 29: np.float64(0.0008215491479028757), 0: np.float64(0.0008215491479028757)}
err dic= {2: np.float64(0.1860373340714816), 9: np.float64(0.13463170161488705), 1: np.float64(0.5873828390947575), 87: np.float64(0.03517845085209712), 36: np.float64(0.09517845085209713), 29: np.float64(0.09617845085209713), 0: np.float64(0.040178450852097126)} 

err list= [np.float64(0.1860373340714816), np.float64(0.13463170161488705), np.float64(0.5873828390947575), np.float64(0.03517845085209712), np.float64(0.09517845085209713), np.float64(0.09617845085209713), np.float64(0.040178450852097126)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  0.75 

learned probs for this beta: {2: np.float64(0.09334876989205089), 9: np.float64(0.0570408926019822), 1: np.float64(0.8495686688877367), 87: np.float64(1.0417154557522136e-05), 36: np.float64(1.0417154557522136e-05), 29: np.float64(1.0417154557522136e-05), 0: np.float64(1.0417154557522136e-05)}
err dic= {2: np.float64(0.18165123010794915), 9: np.float64(0.1559591073980178), 1: np.float64(0.6075686688877368), 87: np.float64(0.03598958284544247), 36: np.float64(0.09598958284544248), 29: np.float64(0.09698958284544248), 0: np.float64(0.04098958284544248)} 

err list= [np.float64(0.18165123010794915), np.float64(0.1559591073980178), np.float64(0.6075686688877368), np.float64(0.03598958284544247), np.float64(0.09598958284544248), np.float64(0.09698958284544248), np.float64(0.04098958284544248)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  1 

learned probs for this beta: {2: np.float64(0.09861308601949086), 9: np.float64(0.05101504680475371), 1: np.float64(0.8503713346822175), 87: np.float64(1.331233844988544e-07), 36: np.float64(1.331233844988544e-07), 29: np.float64(1.331233844988544e-07), 0: np.float64(1.331233844988544e-07)}
err dic= {2: np.float64(0.17638691398050915), 9: np.float64(0.16198495319524628), 1: np.float64(0.6083713346822175), 87: np.float64(0.0359998668766155), 36: np.float64(0.0959998668766155), 29: np.float64(0.0969998668766155), 0: np.float64(0.040999866876615505)} 

err list= [np.float64(0.17638691398050915), np.float64(0.16198495319524628), np.float64(0.6083713346822175), np.float64(0.0359998668766155), np.float64(0.0959998668766155), np.float64(0.0969998668766155), np.float64(0.040999866876615505)]
results for assortment [2, 9, 1, 87, 36, 29] :

beta is  1.25 

learned probs for this beta: {2: np.float64(0.10339671581870863), 9: np.float64(0.04973680199052645), 1: np.float64(0.8468664750454438), 87: np.float64(1.786330212313422e-09), 36: np.float64(1.786330212313422e-09), 29: np.float64(1.786330212313422e-09), 0: np.float64(1.786330212313422e-09)}
err dic= {2: np.float64(0.1716032841812914), 9: np.float64(0.16326319800947353), 1: np.float64(0.6048664750454438), 87: np.float64(0.03599999821366978), 36: np.float64(0.0959999982136698), 29: np.float64(0.0969999982136698), 0: np.float64(0.040999998213669786)} 

err list= [np.float64(0.1716032841812914), np.float64(0.16326319800947353), np.float64(0.6048664750454438), np.float64(0.03599999821366978), np.float64(0.0959999982136698), np.float64(0.0969999982136698), np.float64(0.040999998213669786)]
results for assortment [2, 9, 1, 87, 36, 29] :

err MNL dic= {2: np.float64(0.1424102256736332), 9: np.float64(0.08327674988273309), 1: np.float64(0.10492802418304059), 87: np.float64(0.07115588679835305), 36: np.float64(0.018139782144160108), 29: np.float64(0.021726220878719962), 0: np.float64(0.21959310991817374)} 

err MNL list= [np.float64(0.1424102256736332), np.float64(0.08327674988273309), np.float64(0.10492802418304059), np.float64(0.07115588679835305), np.float64(0.018139782144160108), np.float64(0.021726220878719962), np.float64(0.21959310991817374)]
****final outcomes:*****
beta range: [0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 1, 1.25]
 mean error for all betas:

mean_err= [0.09712857 0.08711873 0.07522658 0.08603295 0.1023911  0.11425776
 0.1227667  0.12902324]
mean_std= [0.         0.01000984 0.01869879 0.02475009 0.03950201 0.04477085
 0.04639499 0.04644828]
MNL: [0.10235158 0.08375985 0.10121016 0.08595932 0.10248532 0.10040005
 0.09320799 0.08198544 0.09459838 0.09446143]
 mean error for MNL:

mean_err_MNL= 0.09404195247316942
mean_std_MNL= 0.007414447235843811
