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We present a novel method for drawing samples from Gibbs distributions with densities of the form $\pi(x) \propto \exp(-U(x))$. The method accelerates the unadjusted Langevin algorithm by introducing an inertia term similar to Polyak's…

Numerical Analysis · Mathematics 2025-10-09 Alexander Falk , Andreas Habring , Christoph Griesbacher , Thomas Pock

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

Machine Learning · Computer Science 2024-10-14 Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Sebastian Reich , Andrew M. Stuart

In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…

Numerical Analysis · Mathematics 2019-12-17 Ben Adcock , Juan M. Cardenas

We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…

Probability · Mathematics 2007-05-23 Elchanan Mossel , Dror Weitz , Nicholas Wormald

Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…

Numerical Analysis · Mathematics 2019-01-21 Kevin W. Aiton , Tobin A. Driscoll

We suppose that a L\'evy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a…

Statistics Theory · Mathematics 2020-12-01 Katerina Papagiannouli

We construct an estimator of the L\'evy density of a pure jump L\'evy process, possibly of infinite variation, from the discrete observation of one trajectory at high frequency. The novelty of our procedure is that we directly estimate the…

Probability · Mathematics 2020-04-06 Céline Duval , Ester Mariucci

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

Computation · Statistics 2013-10-15 Alexis Roche

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…

Machine Learning · Computer Science 2022-04-25 Khashayar Gatmiry , Santosh S. Vempala

In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…

Machine Learning · Statistics 2025-05-27 Yifeng Yu , Lu Yu

We revisit the problem of sampling from a target distribution that has a smooth strongly log-concave density everywhere in $\mathbb R^p$. In this context, if no additional density information is available, the randomized midpoint…

Statistics Theory · Mathematics 2023-06-19 Lu Yu , Avetik Karagulyan , Arnak Dalalyan

We give a Markov chain based perfect sampler for uniform sampling solutions of constraint satisfaction problems (CSP). Under some mild Lov\'asz local lemma conditions where each constraint of the CSP has a small number of forbidden local…

Data Structures and Algorithms · Computer Science 2021-07-09 Kun He , Xiaoming Sun , Kewen Wu

In large-data applications, such as the inference process of diffusion models, it is desirable to design sampling algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of sampling, which is the…

Data Structures and Algorithms · Computer Science 2025-05-21 Huanjian Zhou , Baoxiang Wang , Masashi Sugiyama

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…

Probability · Mathematics 2018-12-27 Arnak S. Dalalyan , Lionel Riou-Durand

Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…

Computation · Statistics 2012-03-09 James M. Flegal , Radu Herbei

We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather than…

Machine Learning · Computer Science 2023-02-21 Jiaming Liang , Yongxin Chen

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…

Machine Learning · Computer Science 2019-09-13 Ruoqi Shen , Yin Tat Lee

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…

Statistics Theory · Mathematics 2024-02-26 Arnak S. Dalalyan , Avetik G. Karagulyan

Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution \(\pi\) by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential…

Probability · Mathematics 2023-03-15 David Oechsler

Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty by introducing adaptive biasing potentials to facilitate…

Numerical Analysis · Mathematics 2026-05-06 Liyao Lyu , Siyu Guo , Huan Lei