Related papers: Polynomial Time Algorithms for Dual Volume Samplin…

We consider Ising models on the hypercube with a general interaction matrix $J$, and give a polynomial time sampling algorithm when all but $O(1)$ eigenvalues of $J$ lie in an interval of length one, a situation which occurs in many models…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

Magnetic resonance imaging (MRI) is mainly limited by long scanning time and vulnerable to human tissue motion artifacts, in 3D clinical scenarios. Thus, k-space undersampling is used to accelerate the acquisition of MRI while leading to…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

Markov Chain Monte Carlo (MCMC) techniques have long been studied in computational geometry subjects whereabouts the problems to be studied are complex geometric objects which by their nature require optimized techniques to be deployed or…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…

Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than…

For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…

With the growing availability of large-scale biomedical data, it is often time-consuming or infeasible to directly perform traditional statistical analysis with relatively limited computing resources at hand. We propose a fast subsampling…

We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…

We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…

We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…

We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…