# Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm

arXiv: https://arxiv.org/abs/2310.08798 · HTML: https://mlsanity.com/paper/2310.08798/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 71 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Parsimonious Tensor Response Regression](https://mlsanity.com/paper/1501.07815/) (2015)
- [Dynamic Tensor Recommender Systems](https://mlsanity.com/paper/2003.05568/) (2020)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [Covariate-Adjusted Tensor Classification in High-Dimensions](https://mlsanity.com/paper/1805.04421/) (2018)
- [Gaussian Graphical Model Estimation with False Discovery Rate Control](https://mlsanity.com/paper/1306.0976/) (2013)
- [Partially Observed Dynamic Tensor Response Regression](https://mlsanity.com/paper/2002.09735/) (2020)
- [Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing](https://mlsanity.com/paper/2109.15287/) (2021)
- [Tests for separability in nonparametric covariance operators of random surfaces](https://mlsanity.com/paper/1505.02023/) (2015)
- [Graph Estimation for Matrix-variate Gaussian Data](https://mlsanity.com/paper/1509.05453/) (2015)
- [Testing separability of space--time functional processes](https://mlsanity.com/paper/1509.07017/) (2015)
- [A Normality Test for High-dimensional Data based on a Nearest Neighbor Approach](https://mlsanity.com/paper/1904.05289/) (2019)
- [Covariance Estimation for Matrix-valued Data](https://mlsanity.com/paper/2004.05281/) (2020)
- [Substitution principle for CLT of linear spectral statistics of high-dimensional sample covariance matrices with applications to hypothesis testing](https://mlsanity.com/paper/1404.6633/) (2014)
- [Hypothesis Testing of Matrix Graph Model with Application to Brain Connectivity Analysis](https://mlsanity.com/paper/1511.00718/) (2015)
- [Joint mean and covariance estimation with unreplicated matrix-variate data](https://mlsanity.com/paper/1611.04208/) (2016)
- [A Test for Separability in Covariance Operators of Random Surfaces](https://mlsanity.com/paper/1710.08388/) (2017)
- [A Locally Adaptive Algorithm for Multiple Testing with Network Structure](https://mlsanity.com/paper/2203.11461/) (2022)
- [Inference for High-dimensional Differential Correlation Matrices](https://mlsanity.com/paper/1408.5907/) (2014)
- [Incorporation of Sparsity Information in Large-scale Multiple Two-sample t Tests](https://mlsanity.com/paper/1410.4282/) (2014)
- [Testing and Support Recovery of Correlation Structures for Matrix-Valued Observations with an Application to Stock Market Data](https://mlsanity.com/paper/2006.16501/) (2020)
- [NAPA: Neighborhood-Assisted and Posterior-Adjusted Two-sample Inference](https://mlsanity.com/paper/2201.10043/) (2022)

## Abstract (arXiv)

Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.