arXiv:2607. 21847v1 Announce Type: cross Abstract: We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
arXiv:2405. 15768v2 Announce Type: replace-cross Abstract: In this paper, we address the classification of instances represented by distributions on a vector space rather than single points.
The paper introduces a multivariate pseudo‑Voigt mixture model, combining Gaussian and Cauchy components with shared location and scale parameters, for robust clustering and outlier detection. Parameter estimation is performed using an EM algorithm that leverages latent variables for efficient likelihood inference. The authors evaluate the model through simulations and real data, comparing it to established robust mixtures such as contaminated normals, and demonstrate its effectiveness on heavy‑tailed datasets.
arXiv:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.
arXiv:2606. 19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations.
arXiv:2607. 14880v1 Announce Type: cross Abstract: We propose a novel measure of the discrepancy between two probability distributions $f$ and $g$ on a graph - which we call the diffusion distance - that measures the rate of convergence of $f$ to $g$ under a graph-constrained Markov chain with stationary distribution $g$.
arXiv:2608. 13418v1 Announce Type: cross Abstract: Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution.
arXiv:2609.16622v1 Announce Type: cross Abstract: Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated sub...
Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution. To this end, we propose Wasserstein Filtering (WF), a novel sample selection framework that discards a fraction of suspicious samples and estimates the target distribution using the empirical measure of the remaining data.
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.
arXiv:2609.36911v1 Announce Type: new Abstract: In this thesis I develop methods for statistical inference when the distributions arising from complex biological systems are multi-modal, geometricall...