English
Related papers

Related papers: Faster Sampling from Log-Concave Densities over Po…

200 papers

We study the problem of parallelizing sampling from distributions related to determinants: symmetric, nonsymmetric, and partition-constrained determinantal point processes, as well as planar perfect matchings. For these distributions, the…

Data Structures and Algorithms · Computer Science 2023-05-01 Nima Anari , Callum Burgess , Kevin Tian , Thuy-Duong Vuong

We consider the Random Walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. It is well known (see Roberts et al. (Ann. Appl. Probab. 7…

Methodology · Statistics 2014-10-22 Benjamin Jourdain , Tony Lelièvre , Błażej Miasojedow

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

In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…

Machine Learning · Statistics 2022-10-19 Abhishek Shetty , Raaz Dwivedi , Lester Mackey

Motivated by recent Linear Programming solvers, we design dynamic data structures for maintaining the inverse of an $n\times n$ real matrix under $\textit{low-rank}$ updates, with polynomially faster amortized running time. Our data…

Data Structures and Algorithms · Computer Science 2020-04-17 Shunhua Jiang , Zhao Song , Omri Weinstein , Hengjie Zhang

Collecting the most informative data from a large dataset distributed over a network is a fundamental problem in many fields, including control, signal processing and machine learning. In this paper, we establish a connection between…

Systems and Control · Electrical Eng. & Systems 2024-06-05 Xu Zhang , Marcos M. Vasconcelos

In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…

Computation · Statistics 2023-12-22 Björn Sprungk , Simon Weissmann , Jakob Zech

A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…

Data Structures and Algorithms · Computer Science 2018-08-09 Bernhard Haeupler , Jason Li

We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…

Data Structures and Algorithms · Computer Science 2024-11-21 Yunbum Kook , Santosh S. Vempala

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…

Machine Learning · Statistics 2020-10-20 Difan Zou , Pan Xu , Quanquan Gu

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

Markov decision processes (MDP) are useful to model optimisation problems in concurrent systems. To verify MDPs with efficient Monte Carlo techniques requires that their nondeterminism be resolved by a scheduler. Recent work has introduced…

Data Structures and Algorithms · Computer Science 2016-11-15 Pedro D'Argenio , Axel Legay , Sean Sedwards , Louis-Marie Traonouez

Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…

Probability · Mathematics 2022-02-01 Laurent Saloff-Coste , Sophie Uluatam

It is common to subsample Markov chain output to reduce the storage burden. Geyer (1992) shows that discarding $k-1$ out of every $k$ observations will not improve statistical efficiency, as quantified through variance in a given…

Computation · Statistics 2017-04-12 Art B. Owen

While one-dimensional Markov processes are well understood, going to higher dimensions there are only a few analytically solved Ising-like models, in practice requiring to use relatively costly, uncontrollable and inaccurate Monte-Carlo…

Information Theory · Computer Science 2021-04-20 Jarek Duda

Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in…

Computer Vision and Pattern Recognition · Computer Science 2024-07-04 Shuchen Xue , Zhaoqiang Liu , Fei Chen , Shifeng Zhang , Tianyang Hu , Enze Xie , Zhenguo Li

We consider convex optimization problems which are widely used as convex relaxations for low-rank matrix recovery problems. In particular, in several important problems, such as phase retrieval and robust PCA, the underlying assumption in…

Optimization and Control · Mathematics 2022-06-22 Dan Garber

State inference and parameter learning in sequential models can be successfully performed with approximation techniques that maximize the evidence lower bound to the marginal log-likelihood of the data distribution. These methods may be…

Machine Learning · Computer Science 2026-03-10 Helena Calatrava , Ricardo Augusto Borsoi , Tales Imbiriba , Pau Closas

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

Data Structures and Algorithms · Computer Science 2016-08-18 Themistoklis Gouleakis , Christos Tzamos , Manolis Zampetakis

Several recent publications investigated Markov-chain modelling of linear optimization by a $(1,\lambda)$-ES, considering both unconstrained and linearly constrained optimization, and both constant and varying step size. All of them assume…

Numerical Analysis · Computer Science 2014-06-19 Alexandre Chotard , Martin Holena