February 2026

arXiv:2504.11304v2 Announce Type: replace Abstract: In statistical applications it has become increasingly common to encounter data structures that live on non-linear spaces such as manifolds. Classical linear regression, one of the most fundamental methodologies of statistical learning, captures the relationship between an independent variable and a response variable which both are assumed to live in Euclidean space. Thus, geodesic regression emerged as an extension where the response variable lives on a Riemannian manifold. The parameters of geodesic regression, […]

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arXiv:2504.06477v2 Announce Type: replace Abstract: Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse learning framework tailored to high-dimensional heavy-tailed locally stationary time series (LSTS). The data-generating mechanism incorporates a regression function that changes smoothly over time and is observed under noise belonging to the class of sub-Weibull and regularly […]

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arXiv:2502.03792v2 Announce Type: replace Abstract: We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures that the resulting network exhibits a high degree of Lipschitz regularity, that is, a small Lipschitz constant. Moreover, we show that this decay does not hinder the convergence rate of the empirical risk, now […]

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arXiv:2408.06525v4 Announce Type: replace Abstract: This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex quadratic nature for any instance of an input data. We further illustrate the non-convexity of the problem with several explicit examples.

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arXiv:2406.19958v2 Announce Type: replace Abstract: Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory, comprising guarantees that its posterior distribution concentrates around the true regression function at optimal rates under various data generative settings and for appropriate prior choices. However, the computational properties of the widely-used BART sampler proposed by Chipman et al. (2010) are yet […]

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arXiv:2406.03628v3 Announce Type: replace Abstract: Imbalanced classification and spurious correlation are common challenges in data science and machine learning. Both issues are linked to data imbalance, with certain groups of data samples significantly underrepresented, which in turn would compromise the accuracy, robustness and generalizability of the learned models. Recent advances have proposed leveraging the flexibility and generative capabilities of large language models (LLMs), typically built on transformer architectures, to generate synthetic samples and to augment the observed data. […]

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arXiv:2405.16958v3 Announce Type: replace Abstract: We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalises earlier work, in which bounded and continuous activation functions were considered. In practice, linearly growing activation functions such as ReLU are most commonly used. We furthermore simplify previous expressions for the rate function and provide a power-series expansions for the ReLU case.

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arXiv:2105.13440v5 Announce Type: replace Abstract: In an effort to develop topic modeling methods that can be quickly applied to large data sets, we revisit the problem of maximum-likelihood estimation in topic models. It is known, at least informally, that maximum-likelihood estimation in topic models is closely related to non-negative matrix factorization (NMF). Yet, to our knowledge, this relationship has not been exploited previously to fit topic models. We show that recent advances in NMF optimization methods can be […]

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arXiv:2006.06618v3 Announce Type: replace Abstract: We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically using synthetic and real-world datasets — showing that their asymptotic error rates match the state-of-the-art theoretical bounds, and that they concretely outperform all previous methods. Specifically, previous estimators either have weak empirical accuracy at small sample sizes, perform poorly for […]

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arXiv:2602.08980v1 Announce Type: cross Abstract: Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size or structure than encountered during training. We study neural ODEs ($mathtt{nODE}$s) with vector fields following the Barab’asi-Barzel form, trained on synthetic data from five common dynamical systems on graphs. Using the $mathbb{S}^1$-model to generate graphs with realistic and tunable structure, we […]

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