Sparse assortment personalization in high dimensions

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.