Covariate-assisted Sparse Tensor Completion

TL;DR

This paper introduces COSTCO, a method that leverages covariate information to improve the completion of sparse, highly-missing tensors, demonstrated on advertising data with significant accuracy gains and meaningful ad clustering.

Contribution

The paper proposes a novel covariate-assisted tensor completion method with theoretical error bounds and practical effectiveness in advertising applications.

Findings

Achieved 23% accuracy improvement over baseline in CTR tensor completion.

Derived explicit error bounds showing covariates enhance recovery accuracy.

Revealed meaningful ad clusters useful for targeted advertising.

Abstract

We aim to provably complete a sparse and highly-missing tensor in the presence of covariate information along tensor modes. 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, which makes the standalone tensor completion method unsatisfactory. Beside the CTR tensor, additional ad features or user characteristics are often available. In this paper, we propose Covariate-assisted Sparse Tensor Completion (COSTCO) to incorporate covariate information for the recovery of the sparse tensor. The key idea is to jointly extract latent components from both the tensor and the covariate matrix to learn a synthetic representation. 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. Finally, we apply COSTCO to an advertisement dataset consisting of a CTR tensor and ad covariate matrix, leading to 23% accuracy improvement over the baseline. An important by-product is that ad latent components from COSTCO reveal interesting ad clusters, which are useful for better ad targeting.