arXiv research

The paper shows how heat flows and Wasserstein distances relate to space rigidity.

The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat semigroup, and quadratic Wasserstein distance contraction properties at different times.…

In this article, exponential contraction in Wasserstein distance for heat semigroups of diffusion processes on Riemannian manifolds is established under curvature conditions where Ricci curvature is not necessarily required to be non-negative. Compared to the results of Wang (2016), we focus on explicit estimates for t…

Algorithm improves variational inference in Wasserstein distance.

Nonnegative sectional curvature linked to matrix displacement convexity.

Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.

New method improves sampling efficiency in complex stochastic systems.

We study contractivity properties of gradient flows for functions on normed spaces or, more generally, on Finsler manifolds. Contractivity of the flows turns out to be equivalent to a new notion of convexity for the functions. This is different from the usual convexity along geodesics in non-Riemannian Finsler manifold…

In this paper we will give a new proof of the monotonicity of Wasserstein distances of two diffusions under super Ricci flow. Our proof is based on the coupling method of B.Andrew and J.Clutterbuck. The same method can also be applied to the contractivity of normalized L-Wasserstein distance under backward Ricci flow.

The paper analyzes insurance contracts under distributional uncertainty using Bregman-Wasserstein divergence.

New approach to quantify posterior concentration rates using Wasserstein dynamics.

SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal targ…

New bounds for SGLD show error decreases with more data.

Study non-negative curvature Markov chains, proving entropy contraction.

New method for variational inference without conjugacy constraints.

Paper analyzes Hit-and-Run's convergence rates and applies similar methods to randomized Kaczmarz.

Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.

Study on nonsmooth contractive SA with constant stepsize and Q-learning.

New methods improve stability of Sinkhorn algorithm in machine learning.

Unified framework for analyzing convergence of RSAs using Wasserstein divergence.

Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.

Accelerates sampling from Gibbs distributions using ARWP method.

LMC achieves sqrt(d) dependence in sampling error, improving previous bounds.

New algorithms improve sampling from constrained distributions.

In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(κ,N)$-convex functions on metric spaces where $κ$ is a lower semi-continuous function, and gradient flow curves in the sense of a new evolution variational inequality that captures the information that …

Paper analyzes convergence of ODE samplers in Wasserstein distances.

Researchers establish bounds for SGMs' KL and Wasserstein divergences under various noise schedules.

DCDC calculates convergence rates for Markov chains using neural networks.

The paper proves a conjecture about manifold limits and characterizes their structure.

New stability theory for Sinkhorn semigroups with explicit decay rates.

We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality, gradient estimates and Wa…

Improved KLMC for sampling under various conditions.

We prove the equivalence of the curvature-dimension bounds of Lott-Sturm-Villani (via entropy and optimal transport) and of Bakry--Émery (via energy and Γ_2$-calculus) in complete generality for infinitesimally Hilbertian metric measure spaces. In particular, we establish the full Bochner inequality on such metric meas…

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.

SGD with constant stepsize converges to a non-Gaussian limit near flat minima.

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from t…

SGD handles label noise with bounds improving over SGLD.

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein d…

The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.

Bayesian histograms achieve optimal distribution estimation with minimal memory usage.

Enhances privacy in machine learning through Rényi Pufferfish mechanisms.

Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth Itô diffusions exhibiting fast Wasserstein-$2$ contraction, based on local deviat…

New method improves sampling from non-convex distributions using HFHR dynamics.

Batch normalization makes deep neural networks' representations increasingly orthogonal.

Unified analysis of KL divergence using shifted composition for sampling.

SIMPOL solves complex economic models using numerical methods.

Robust VB framework for large datasets with outliers.