Alex V Kotlar | Searcharxiv

arXiv2026

scikit-covtest: Covariance Matrix Hypothesis Testing in Python

Covariance matrices play a central role across diverse domains such as finance, machine learning, neuroscience, and genetics, where they are used for tasks including dimensionality reduction, connectivity inference, and risk estimation. Many of these applications require testing whether a covariance matrix follows a specific structure. While several R packages provide partial coverage of such tests, Python, an important language in machine learning, lacks a comprehensive, well-tested implementation. To address this gap, we introduce scikit-covtest, a Python package implementing a variety of hypothesis tests for covariance matrices spanning four categories: identity, sphericity, proportionality, and two-sample equality. The package provides a consistent SciPy-style API, extensive documentation, and supporting functionality for multiple testing correction, synthetic data generation, and diagnostic evaluation. scikit-covtest is open source, available through PyPI, and lowers the barrier to applying modern covariance-testing methods in scientific applications.

stat.CO↗

arXiv2024

Generative Principal Component Regression via Variational Inference

The ability to manipulate complex systems, such as the brain, to modify specific outcomes has far-reaching implications, particularly in the treatment of psychiatric disorders. One approach to designing appropriate manipulations is to target key features of predictive models. While generative latent variable models, such as probabilistic principal component analysis (PPCA), is a powerful tool for identifying targets, they struggle incorporating information relevant to low-variance outcomes into the latent space. When stimulation targets are designed on the latent space in such a scenario, the intervention can be suboptimal with minimal efficacy. To address this problem, we develop a novel objective based on supervised variational autoencoders (SVAEs) that enforces such information is represented in the latent space. The novel objective can be used with linear models, such as PPCA, which we refer to as generative principal component regression (gPCR). We show in simulations that gPCR dramatically improves target selection in manipulation as compared to standard PCR and SVAEs. As part of these simulations, we develop a metric for detecting when relevant information is not properly incorporated into the loadings. We then show in two neural datasets related to stress and social behavior in which gPCR dramatically outperforms PCR in predictive performance and that SVAEs exhibit low incorporation of relevant information into the loadings. Overall, this work suggests that our method significantly improves target selection for manipulation using latent variable models over competitor inference schemes.

stat.ML↗