Statistical and numerical algorithms

Latest papers

• Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions

  Emile Pierret, Bruno Galerne · 28 July 2026

  Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as inpainting, super-resolution, and deblurring. However, there is st…

• Entropic Mirror Descent for Linear Systems: Polyak's Stepsize and Implicit Bias

  Yura Malitsky, Alexander Posch · 9 March 2026

  This paper focuses on applying entropic mirror descent to solve linear systems, where the main challenge for the convergence analysis stems from the unboundedness of the domain. To overcome this without imposing restrictive assumptions, we introduce a variant of Polyak-type stepsizes. Along the way,…

• Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain

  Jacek Karwowski, Frank Nielsen · 4 March 2026

  Symmetric positive-definite (SPD) matrix datasets play a central role across numerous scientific disciplines, including signal processing, statistics, finance, computer vision, information theory, and machine learning among others. The set of SPD matrices forms a cone which can be viewed as a global…

• Kernel Embeddings and the Separation of Measure Phenomenon

  Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos · 26 January 2026

  We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic (Borel) probability measures on a locally compact Polish space i…