Related papers: Limit Distribution for Smooth Total Variation and …
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
Motivated by questions of manifold learning, we study a sequence of random manifolds, generated by embedding a fixed, compact manifold $M$ into Euclidean spheres of increasing dimension via a sequence of Gaussian mappings. One of the…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be…
We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either…
We consider versions of the FIND algorithm where the pivot element used is the median of a subset chosen uniformly at random from the data. For the median selection we assume that subsamples of size asymptotic to $c \cdot n^\alpha$ are…
We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…
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…
We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…
Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…
In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…