Related papers: Quantization of Probability Distributions via Divi…
Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel,…
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Approximate inference techniques are the cornerstone of probabilistic methods based on Gaussian process priors. Despite this, most work approximately optimizes standard divergence measures such as the Kullback-Leibler (KL) divergence, which…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
We build and study a recursive algorithm based on the occupation measure of an Euler scheme with decreasing step for the numerical approximation of the quasistationary distribution (QSD) of an elliptic diffusion in a bounded domain. We…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
This paper studies the problem of distribution matching (DM), which is a fundamental machine learning problem seeking to robustly align two probability distributions. Our approach is established on a relaxed formulation, called partial…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…