Under-Counted Tensor Completion with Neural Incorporation of Attributes
This work addresses systematic under-counting in multi-aspect data for applications like epidemiology and ecology, offering the first theoretical support for such methods.
The paper tackles the problem of under-counted tensor completion by proposing a low-rank Poisson tensor model with a neural network to extract side information, and provides theoretical guarantees for recovering fully counted entries and under-counting probabilities from partial observations, supported by simulations and real-data experiments.
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.