TenIPS: Inverse Propensity Sampling for Tensor Completion

TL;DR

This paper introduces TenIPS, a method for tensor completion under MNAR missing data, estimating propensities and reweighting observations to accurately recover the original tensor without prior propensity knowledge.

Contribution

The paper proposes a novel inverse propensity sampling approach for tensor completion that handles MNAR data without prior propensity information, with theoretical error bounds.

Findings

Effective tensor recovery under MNAR missingness.

Finite-sample error bounds established.

Numerical experiments confirm method's effectiveness.

Abstract

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most practical settings, observations are missing not at random (MNAR): the probability that a given entry is observed (also called the propensity) may depend on other entries in the tensor or even on the value of the missing entry. In this paper, we study the problem of completing a partially observed tensor with MNAR observations, without prior information about the propensities. To complete the tensor, we assume that both the original tensor and the tensor of propensities have low multilinear rank. The algorithm first estimates the propensities using a convex relaxation and then predicts missing values using a higher-order SVD approach, reweighting the observed tensor by the inverse propensities. We provide finite-sample error bounds on the resulting complete tensor. Numerical experiments demonstrate the effectiveness of our approach.