TenIPS: Inverse Propensity Sampling for Tensor Completion
This work is significant for researchers and practitioners dealing with incomplete multiway data, as it provides a method to handle MNAR observations, which are more realistic than the commonly assumed MCAR.
This paper addresses the problem of completing tensors where observations are missing not at random (MNAR), a common scenario in real-world data. The authors propose an algorithm that first estimates observation propensities using a convex relaxation and then predicts missing values by reweighting observed entries with inverse propensities, achieving this with a higher-order SVD approach.
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.