# Robust Independence Tests with Finite Sample Guarantees for Synchronous Stochastic Linear Systems

arXiv: https://arxiv.org/abs/2308.02054 · HTML: https://mlsanity.com/paper/2308.02054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 3 Aug 2023.

## Builds on (most cited first, 6 of 6)

- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [A Kernel Independence Test for Random Processes](https://mlsanity.com/paper/1402.4501/) (2014)
- [Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models](https://mlsanity.com/paper/1807.08216/) (2018)
- [Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets](https://mlsanity.com/paper/1412.2352/) (2014)
- [Sign-Perturbed Sums (SPS) with Instrumental Variables for the Identification of ARX Systems - Extended Version](https://mlsanity.com/paper/1509.04774/) (2015)
- [Semi-Parametric Uncertainty Bounds for Binary Classification](https://mlsanity.com/paper/1903.09790/) (2019)

## Abstract (arXiv)

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven by jointly i.i.d. noises. Our method provides bounds for the type I error probabilities that are distribution-free, i.e., the innovations can have arbitrary distributions. The algorithm combines confidence region estimates with permutation tests and general dependence measures, such as the Hilbert-Schmidt independence criterion and the distance covariance, to detect any nonlinear dependence between the observed systems. We also prove the consistency of our hypothesis tests under mild assumptions and demonstrate the ideas through the example of autoregressive systems.