Related papers: Quantitative spectral gap estimate and Wasserstein…

We propose a new class of Markov chain Monte Carlo methods, called $k$-polar slice sampling ($k$-PSS), as a technical tool that interpolates between and extrapolates beyond uniform and polar slice sampling. By examining Wasserstein…

Polar slice sampling, a Markov chain construction for approximate sampling, performs, under suitable assumptions on the target and initial distribution, provably independent of the state space dimension. We extend the aforementioned result…

We present a framework that allows for the non-asymptotic study of the $2$-Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation and the distribution of its numerical approximation in the…

This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…

Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic…

It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…

In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…

We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying…

Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this…

The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space…

Let $X_1,\dots,X_n$ be i.i.d. log-concave random vectors in $\mathbb R^d$ with mean 0 and covariance matrix $\Sigma$. We study the problem of quantifying the normal approximation error for $W=n^{-1/2}\sum_{i=1}^nX_i$ with explicit…

The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…

The exponential contraction in $L^1$-Wasserstein distance and exponential convergence in $L^q$-Wasserstein distance ($q\geq 1$) are considered for stochastic differential equations with irregular drift. When the irregular drift drift is…

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…

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 prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional…

Let $X_t$ be the (reflecting) diffusion process generated by $L:=\Delta+\nabla V$ on a complete connected Riemannian manifold $M$ possibly with a boundary $\partial M$, where $V\in C^1(M)$ such that $\mu(d x):= e^{V(x)}d x$ is a probability…

Statistical inference based on optimal transport offers a different perspective from that of maximum likelihood, and has increasingly gained attention in recent years. In this paper, we study univariate nonparametric shape-constrained…