The data-driven conditional multinomial logit choice model with customer features performs well in the assort-ment personalization problem when the low-rank structure of the parameter matrix is considered. However, despite recent theoretical and algorithmic advances, parameter estimation in the choice model still poses a challenging task, especially when there are more predictors than observations. For this reason, we suggest a penalized likelihood approach based on a feature matrix to recover the sparse structure from populations and products toward the assortment. Our proposed method considers simultaneously low-rank and sparsity structures, which can further reduce model complexity and improve its es-timation and prediction accuracy. A new algorithm, sparse factorial gradient descent (SFGD), was proposed to estimate the parameter matrix, which has high interpretability and efficient computing performance. As a first-order method, the SFGD works well in high-dimensional scenarios because of the absence of the Hessian matrix. Simulation studies show that the SFGD algorithm outperforms state-of-the-art methods in terms of estimation, sparsity recovery, and average regret. We also demonstrate the effectiveness of our proposed method using advertising behavior data analysis.

Jingyu Shao;Ruipeng Dong;Zemin Zheng

International Institute of Finance,School of Management,University of Science and Technology of China,Hefei 230026,China

中国科学技术大学学报

[1]Jingyu Shao;Ruipeng Dong;Zemin Zheng-.Sparse assortment personalization in high dimensions)[J].中国科学技术大学学报,2022(03):32-43

assort,SFGD

Sparse,assortment,personalization,high,dimensions,data,driven,conditional,multinomial,logit,choice,model,customer,features,well,problem,when,low,rank,parameter,matrix,considered,However,despite,recent,theoretical,algorithmic,advances,estimation,still,poses,challenging,task,especially,there,are,more,predictors,than,observations,For,this,reason,suggest,penalized,likelihood,approach,sparse,from,populations,products,toward,Our,proposed,considers,simultaneously,sparsity,structures,which,can,further,reduce,complexity,improve,its,prediction,accuracy,new,factorial,gradient,descent,was,estimate,has,interpretability,efficient,computing,performance,first,order,works,dimensional,scenarios,because,absence,Hessian,Simulation,studies,show,that,outperforms,state,art,methods,terms,recovery,average,regret,We,also,demonstrate,effectiveness,our,using,advertising,behavior,analysis

0.634799