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We give algorithms for sampling several structured logconcave families to high accuracy. We further develop a reduction framework, inspired by proximal point methods in convex optimization, which bootstraps samplers for regularized…

Data Structures and Algorithms · Computer Science 2021-10-25 Yin Tat Lee , Ruoqi Shen , Kevin Tian

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…

Statistics Theory · Mathematics 2024-05-28 Ye He , Alireza Mousavi-Hosseini , Krishnakumar Balasubramanian , Murat A. Erdogdu

We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…

Statistics Theory · Mathematics 2026-05-18 Fan Chen , Sinho Chewi , Constantinos Daskalakis , Alexander Rakhlin

This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the score function in the conventional SGD quantile algorithm, we achieve monotonicity in the quantile…

Machine Learning · Statistics 2025-05-20 Likai Chen , Georg Keilbar , Wei Biao Wu

In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…

Machine Learning · Computer Science 2021-07-07 Abdulrahman Alabdulkareem , Jean Honorio

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…

Machine Learning · Computer Science 2024-12-16 Binxu Wang , John J. Vastola

We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter''…

Astrophysics · Physics 2011-02-11 Guo-Liang Li , S. Mao , Y. P. Jing , X. Kang , M. Bartelmann

We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…

Statistics Theory · Mathematics 2023-06-29 Jiaojiao Fan , Bo Yuan , Yongxin Chen

Gradient Smoothing is an efficient approach to reducing noise in gradient-based model explanation method. SmoothGrad adds Gaussian noise to mitigate much of these noise. However, the crucial hyper-parameter in this method, the variance…

Machine Learning · Computer Science 2025-10-23 Linjiang Zhou , Chao Ma , Zepeng Wang , Libing Wu , Xiaochuan Shi

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove an information theoretic lower bound on the number of stochastic gradient queries of the log density needed. Several popular sampling…

Machine Learning · Statistics 2021-07-06 Niladri S. Chatterji , Peter L. Bartlett , Philip M. Long

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Optimization and Control · Mathematics 2025-02-25 Chenhao Yu , Yusu Hong , Junhong Lin

We consider sampling from composite densities on $\mathbb{R}^d$ of the form $d\pi(x) \propto \exp(-f(x) - g(x))dx$ for well-conditioned $f$ and convex (but possibly non-smooth) $g$, a family generalizing restrictions to a convex set,…

Machine Learning · Computer Science 2020-06-11 Ruoqi Shen , Kevin Tian , Yin Tat Lee

In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation, Gaussian smoothing and smoothing on a sphere. The methods…

Optimization and Control · Mathematics 2021-03-29 Albert S. Berahas , Liyuan Cao , Krzysztof Choromanski , Katya Scheinberg

Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…

Computation · Statistics 2025-07-14 Fuqun Han , Stanley Osher , Wuchen Li

We consider the problem of high-dimensional heavy-tailed statistical estimation in the streaming setting, which is much harder than the traditional batch setting due to memory constraints. We cast this problem as stochastic convex…

Machine Learning · Statistics 2024-10-29 Aniket Das , Dheeraj Nagaraj , Soumyabrata Pal , Arun Suggala , Prateek Varshney

We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…

Machine Learning · Computer Science 2026-02-25 Ilias Diakonikolas , Daniel M. Kane

Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…

Machine Learning · Statistics 2020-05-12 Saeed Saremi , Rupesh Srivastava

In this paper, we consider two distinct challenges in the resolution of nonsmooth stochastic optimization. Of these, the first pertains to the pronounced dependence of dimension in Gaussian smoothing-enabled zeroth-order schemes, impeding…

Optimization and Control · Mathematics 2026-04-20 Mingrui Wang , Prakash Chakraborty , Uday V. Shanbhag

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…

Optimization and Control · Mathematics 2023-07-03 Akash Mondal , Prashanth L. A. , Shalabh Bhatnagar
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