arXiv research

Paper proves generalized Talagrand inequality for Sinkhorn distance.

The paper establishes conditions for strict power concavity in convolutions.

The study provides guarantees for diffusion-based models under log-concave data, offering best-known convergence rates.

A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.

Study Langevin Monte Carlo for sampling non-log-concave distributions.

We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior. This power posterior is known to be non-log-concave and multi-modal, which leads to exponential mixing times for some standard MCMC algorithms. We introduce and study …

In this paper, we prove the concavity of $p$-entropy power of probability densities solving the $p$-heat equation on closed Riemannian manifold with nonnegative Ricci curvature. As applications, we give new proofs of $L^p$-Euclidean Nash inequality and $L^p$-Euclidean Logarithmic Sobolev inequality, moreover, an improv…

The paper proposes a conjecture for a symmetric version of Ehrhard's inequality.

Estimates self- and cross-impact concavity and decay patterns in financial markets.

This work extends stochastic localization to joint probability measures for data analysis.

This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly initialized point. We establish the explicit convergence rates and sample complex…

We prove the concavity of $p$-Rényi entropy power for positive solutions to the doubly nonlinear diffusion equations on $\mathbb{R}^n$ or compact Riemannian manifolds with nonnegative Ricci curvature. As applications, we give new proofs of the sharp $L^p$-Sobolev inequality and $L^p$-Gagliardo-Nirenberg inequalities on…

New lower bounds for sampling from log-concave distributions in higher dimensions.

This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.

Algorithm samples from composite log-concave distributions using gradient evaluations and restricted Gaussian oracles.

Study improves sampling from non-log-concave distributions using Fisher information.

Improves SGM convergence bounds in W2-distance without strict assumptions.

Let $Ω$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(ω(p)-c|p|^2)$, where $c>0$ and $ω$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\partialΩ$. In this work we follow a varia…

This work proposes new methods for variational inference using gradient flows on Gaussian measures.

The paper examines how nonlinear transformations affect ridge sets in manifold learning.

New privacy mechanism reduces error in query results.

By using asymptotic Morse inequalities we give a lower bound for the space of holomorphic sections of high tensor powers in a positive line bundle over a q-concave domain. The curvature of the positive bundle induces a hermitian metric on the manifold. The bound is given explicitely in terms of the volume of the domain…

Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the evaluation of the Cholesky factorization or solving linear systems. Recently, Anit…

Unified study of Brunn-Minkowski conjectures for log-concave measures.

Study concavity of solutions to elliptic equations under conformal deformations.

Gaussian-SVGD dynamics converge to Gaussian distributions under certain conditions.

The study analyzes the evolution of Gaussian measures under a specific gradient flow.

Improved sampling algorithm with state-of-the-art complexity bounds.

In this paper, we study the conjecture of Gardner and Zvavitch from \cite{GZ}, which suggests that the standard Gaussian measure $γ$ enjoys $\frac{1}{n}$-concavity with respect to the Minkowski addition of \textbf{symmetric} convex sets. We prove this fact up to a factor of 2: that is, we show that for symmetric convex…

A new sampling method using log-concave Markov chains.

RHMC accelerates sampling from log-concave distributions.

New bounds for generative models under weaker assumptions.

This paper concerns the evolution of complete noncompact locally uniformly convex hypersurface in Euclidean space by curvature flow, for which the normal speed $Φ$ is given by a power $β\geq 1$ of a monotone symmetric and homogeneous of degree one function $F$ of the principal curvatures. Under the assumption that $F$ …

The unadjusted Langevin algorithm converges faster for some variables in high dimensions.

In this paper, we prove the concavity of the Renyi entropy power for nonlinear diffusion equation (NLDE) associated with the Laplacian and the Witten Laplacian on compact Riemannian manifolds with non-negative Ricci curvature or $CD(0,m)$-condition and on compact manifolds equipped with time dependent metrics and poten…

Non-convex SGD learns halfspaces with adversarial label noise efficiently.

Researchers found counterexamples to conjectures about optimal transport maps on curved spaces.

Efficient algorithm for learning halfspaces in a new model with polynomial time complexity.

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved…

A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have provided "beyond worst-case" guarantees for such settings. For log-c…

Optimal trading strategy under market resistance and concave price impact model.

New sampling algorithm for non-log-concave distributions requires many queries.

Two new methods improve block-sparse signal recovery from noisy data.

The study finds that only round spheres shrink self-similarly under certain curvature flows.

Study shows cliff-learning in transfer learning from foundation models.

Square-root natural-gradient improves variational inference convergence.

New method accelerates Bayesian imaging using Langevin sampling.

Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.