arXiv subjects

Tom Szwagier

Publications and source records attributed to Tom Szwagier.

6 recordsLinked to original sources

arXiv2025

Nested subspace learning with flags

Many machine learning methods look for low-dimensional representations of the data. The underlying subspace can be estimated by first choosing a dimension $q$ and then optimizing a certain objective function over the space of $q$-dimensional subspaces (the Grassmannian). Trying different $q$ yields in general non-nested subspaces, which raises an important issue of consistency between the data representations. In this paper, we propose a simple and easily implementable principle to enforce nestedness in subspace learning methods. It consists in lifting Grassmannian optimization criteria to flag manifolds (the space of nested subspaces of increasing dimension) via nested projectors. We apply the flag trick to several classical machine learning methods and show that it successfully addresses the nestedness issue.

stat.ML↗

arXiv2025

Parsimonious Gaussian mixture models with piecewise-constant eigenvalue profiles

Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs (with isotropic covariance matrices) certainly lack flexibility to fit certain anisotropic distributions. Connecting these two extremes, we introduce a new family of parsimonious GMMs with piecewise-constant covariance eigenvalue profiles. These extend several low-rank models like the celebrated mixtures of probabilistic principal component analyzers (MPPCA), by enabling any possible sequence of eigenvalue multiplicities. If the latter are prespecified, then we can naturally derive an expectation-maximization (EM) algorithm to learn the mixture parameters. Otherwise, to address the notoriously-challenging issue of jointly learning the mixture parameters and hyperparameters, we propose a componentwise penalized EM algorithm, whose monotonicity is proven. We show the superior likelihood-parsimony tradeoffs achieved by our models on a variety of unsupervised experiments: density fitting, clustering and single-image denoising.

stat.ML↗

arXiv2025

The curse of isotropy: from principal components to principal subspaces

Principal component analysis is a ubiquitous tool in exploratory data analysis. It is widely used by applied scientists for visualization and interpretability purposes. We raise an important issue (the curse of isotropy) about the interpretation of principal components with close eigenvalues. They may indeed suffer from an important rotational variability, which is a pitfall for interpretation. Through the lens of a probabilistic covariance model parameterized with flags of subspaces, we show that the curse of isotropy cannot be overlooked in practice. In this context, we propose to transition from ill-defined principal components to more-interpretable principal subspaces. The final methodology (principal subspace analysis) is extremely simple and shows promising results on a variety of datasets from different fields.

stat.ME↗

arXiv2025

Eigengap Sparsity for Covariance Parsimony

Covariance estimation is a central problem in statistics. An important issue is that there are rarely enough samples $n$ to accurately estimate the $p (p+1) / 2$ coefficients in dimension $p$. Parsimonious covariance models are therefore preferred, but the discrete nature of model selection makes inference computationally challenging. In this paper, we propose a relaxation of covariance parsimony termed "eigengap sparsity" and motivated by the good accuracy-parsimony tradeoffs of eigenvalue-equalization in covariance matrices. This penalty can be included in a penalized-likelihood framework that we propose to solve with a projected gradient descent on a monotone cone. The algorithm turns out to resemble an isotonic regression of mutually-attracted sample eigenvalues, drawing an interesting link between covariance parsimony and shrinkage.

stat.ME↗

arXiv2022

Generalizable and Robust Deep Learning Algorithm for Atrial Fibrillation Diagnosis Across Ethnicities, Ages and Sexes

To drive health innovation that meets the needs of all and democratize healthcare, there is a need to assess the generalization performance of deep learning (DL) algorithms across various distribution shifts to ensure that these algorithms are robust. This retrospective study is, to the best of our knowledge, the first to develop and assess the generalization performance of a deep learning (DL) model for AF events detection from long term beat-to-beat intervals across ethnicities, ages and sexes. The new recurrent DL model, denoted ArNet2, was developed on a large retrospective dataset of 2,147 patients totaling 51,386 hours of continuous electrocardiogram (ECG). The models generalization was evaluated on manually annotated test sets from four centers (USA, Israel, Japan and China) totaling 402 patients. The model was further validated on a retrospective dataset of 1,730 consecutives Holter recordings from the Rambam Hospital Holter clinic, Haifa, Israel. The model outperformed benchmark state-of-the-art models and generalized well across ethnicities, ages and sexes. Performance was higher for female than male and young adults (less than 60 years old) and showed some differences across ethnicities. The main finding explaining these variations was an impairment in performance in groups with a higher prevalence of atrial flutter (AFL). Our findings on the relative performance of ArNet2 across groups may have clinical implications on the choice of the preferred AF examination method to use relative to the group of interest.

cs.LG↗

arXiv2022

ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results

This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learning". The competition asked participants to provide implementations of machine learning algorithms on manifolds that would respect the API of the open-source software Geomstats (manifold part) and Scikit-Learn (machine learning part) or PyTorch. The challenge attracted seven teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.CG↗