Partial Modal Tensor Regression

TL;DR

This paper introduces Partial Modal Tensor Regression (PMTR), a robust method for modeling the relationship between tensor-valued predictors and a response by leveraging the conditional mode instead of mean or quantile. PMTR preserves tensor structure through partial modal tensor covariance, enabling dimension reduction without vectorization while maintaining interpretability under asymmetric or heavy-tailed distributions.

Why It Matters

PMTR offers a more robust alternative to traditional tensor regression in real-world scenarios where data are skewed, noisy, or contain outliers—common in fields like neuroscience, computer vision, and genomics. By preserving tensor structure and focusing on the mode, it improves model interpretability and statistical efficiency in high-dimensional settings.

Key Findings

• PMTR uses conditional mode to guide tensor dimension reduction, enhancing robustness to distributional anomalies.
• The method avoids vectorization, preserving the intrinsic multiway structure of tensor data.
• Theoretical consistency and asymptotic properties are established, with a data-driven procedure for selecting effective dimensions across tensor modes.