Related papers: Sampling from Log-Concave Distributions over Polyt…
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity,…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
Frank-Wolfe methods are popular for optimization over a polytope. One of the reasons is because they do not need projection onto the polytope but only linear optimization over it. To understand its complexity, Lacoste-Julien and Jaggi…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods.…
We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…
Langevin diffusions are rapidly convergent under appropriate functional inequality assumptions. Hence, it is natural to expect that with additional smoothness conditions to handle the discretization errors, their discretizations like the…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
We study function estimation in the empirical Bayes setting for Poisson and normal means. Specifically, given observations $Y_i\sim f(\cdot; \theta_i)$ with latent parameters $\theta_i\sim \pi$, the goal is to estimate…
This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
Most prior results on differentially private stochastic gradient descent (DP-SGD) are derived under the simplistic assumption of uniform Lipschitzness, i.e., the per-sample gradients are uniformly bounded. We generalize uniform…
A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…
We provide new results for noise-tolerant and sample-efficient learning algorithms under $s$-concave distributions. The new class of $s$-concave distributions is a broad and natural generalization of log-concavity, and includes many…
We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another…
We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related…
Most approximation algorithms for #P-complete problems (e.g., evaluating the permanent of a matrix or the volume of a polytope) work by reduction to the problem of approximate sampling from a distribution $\pi$ over a large set $\S$. This…