Under-Counted Tensor Completion with Neural Incorporation of Attributes

TL;DR

This paper introduces a novel low-rank Poisson tensor model with neural attribute integration for under-counted data, providing the first theoretical guarantees for accurate tensor completion in such scenarios.

Contribution

It proposes a new model and algorithm for under-counted tensor completion with theoretical analysis, bridging a gap in understanding the principles behind such data recovery.

Findings

Theoretical guarantees for recovering fully counted entries and under-counting probabilities.

Effective neural network integration for attribute extraction in tensor completion.

Successful validation through simulations and real-data experiments.

Abstract

Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry's under-counting probability can be provably recovered from partial observations -- under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.