Wanfeng Liang | Searcharxiv

arXiv2026

Spatial-sign-based multilinear principal component analysis for tensor data

Multilinear principal component analysis (MPCA) reduces the dimension of tensor-valued data while preserving their mode-specific structure, but its quadratic scatter criterion can be unstable under heavy-tailed distributions and contamination. We propose spatial-sign-based multilinear principal component analysis (SMPCA), a robust dimension-reduction method that centers the observations by their spatial median, removes radial magnitude through spatial-sign normalization, and estimates the mode-wise loading spaces by alternating eigendecompositions. Under a separable tensor elliptical model, we show that the target mode-wise loading spaces uniquely maximize the population criterion and that one complete sweep of exact population block updates recovers them from any initialization. We also characterize exactly when their tensor-product subspace coincides with a leading unrestricted subspace of vectorized spatial-sign PCA and, when finite second moments exist, ordinary vectorized PCA. At the sample level, we derive explicit statistical rates for the mode-wise subspaces and the joint multilinear projector, obtain corresponding reconstruction guarantees, establish consistency of the cumulative-contribution dimension selector, and prove that the objective values generated by exact cyclic updates are nondecreasing and convergent. Simulations and an empirical application show that SMPCA is more accurate and stable than competitors under heavy-tailed distributions and outlier contamination, while retaining competitive performance under light-tailed settings.

stat.ME↗

arXiv2023

Prediction De-Correlated Inference: A safe approach for post-prediction inference

In modern data analysis, it is common to use machine learning methods to predict outcomes on unlabeled datasets and then use these pseudo-outcomes in subsequent statistical inference. Inference in this setting is often called post-prediction inference. We propose a novel assumption-lean framework for statistical inference under post-prediction setting, called Prediction De-Correlated Inference (PDC). Our approach is safe, in the sense that PDC can automatically adapt to any black-box machine-learning model and consistently outperform the supervised counterparts. The PDC framework also offers easy extensibility for accommodating multiple predictive models. Both numerical results and real-world data analysis demonstrate the superiority of PDC over the state-of-the-art methods.

stat.ME↗