An Augmented Regression Model for Tensors with Missing Values

TL;DR

This paper presents a novel tensor regression framework that effectively handles missing data by integrating tensor completion, demonstrated through simulations and a case study showing improved performance over benchmarks.

Contribution

It introduces a new integrated tensor regression and completion method with an efficient alternating optimization algorithm for systems with incomplete observations.

Findings

Outperforms benchmark methods in simulations

Demonstrates effectiveness in a real case study

Handles missing tensor data efficiently

Abstract

Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations where the system output is measured in its complete form. In reality, however, it may not be feasible to obtain the complete output measurement of a system, which results in observations that contain missing values. This paper introduces a general framework that integrates tensor regression with tensor completion and proposes an efficient optimization framework that alternates between two steps for parameter estimation. Through multiple simulations and a case study, we evaluate the performance of the proposed method. The results indicate the superiority of the proposed method in comparison to a benchmark.