Covariate-Assisted Sparse Tensor Completion and Inference

• Activity Number: 416 - SLDS CSpeed 7
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Hilda Somnooma Ibriga* and Will Wei Sun
• Companies: Purdue University and Purdue University
• Keywords: high-dimensional statistics; low-rank tensor completion; non-convex optimization; machine Learning; clustering; inference

Abstract

We aim to provably complete a sparse and highly-missing tensor in the presence of covariate information along tensor modes and to study the uncertainty quantification of the recovered tensor factors and entries. Our motivation comes from online advertising where users click-through-rates (CTR) on ads over various devices form a CTR tensor that has about 96% missing entries and has many zeros on non-missing entries, making the standalone tensor completion method unsatisfactory. We propose Covariate-assisted Sparse Tensor Completion (COSTCO) to incorporate covariate information for the recovery of the sparse tensor. Theoretically, we derive the error bound for the recovered tensor components and explicitly quantify the improvements on both the reveal probability condition and the tensor recovery accuracy due to covariates. We also derive the distribution theory of the recovered tensor factors and entries which allows us to build tighter confidence intervals compared to that of the standalone tensor recovery. We apply COSTCO to an advertisement dataset consisting of a CTR tensor and ad covariate matrix, leading to 23% accuracy improvement over the baseline.