| With the increasing digitization of modern society,data production and usage scenarios are constantly increasing.How to make full use of the potential information contained in the data to help various subjects make scientific decisions is an important topic.Meanwhile,the exponential growth of data volume has brought about high requirements for computing power.How to design high-performance,low-resourceconsuming algorithms for data processing is also crucial.In the real world,an important application scenario is assortment optimization,that is,retailers select the optimal subset from a given product set to achieve the maximum expected revenue under certain operating constraints.As an important part of revenue management,assortment optimization also needs to make full use of user features data for quantitative and efficient solutions.The data-driven conditional multinomial logit choice model with customer features performs well in the assortment 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 estimation 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. |
