Related papers: Sampling via Rejection-Free Partial Neighbor Searc…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a…
In this paper we study the Metropolis algorithm in connection with two mean--field spin systems, the so called mean--field Ising model and the Blume--Emery--Griffiths model. In both this examples the naive choice of proposal chain gives…
Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and…
The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
We consider the combined use of resampling and partial rejection control in sequential Monte Carlo methods, also known as particle filters. While the variance reducing properties of rejection control are known, there has not been (to the…
The supervised learning problem to determine a neural network approximation $\mathbb{R}^d\ni x\mapsto\sum_{k=1}^K\hat\beta_k e^{{\mathrm{i}}\omega_k\cdot x}$ with one hidden layer is studied as a random Fourier features algorithm. The…
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by…
We study the computational complexity of a Metropolis-Hastings algorithm for Bayesian community detection. We first establish a posterior strong consistency result for a natural prior distribution on stochastic block models under the…
GNM: The MCMC Jagger. A rocking awesome sampler. This python package is an affine invariant Markov chain Monte Carlo (MCMC) sampler based on the dynamic Gauss-Newton-Metropolis (GNM) algorithm. The GNM algorithm is specialized in sampling…
Traditional image detail enhancement is local filter-based or global filter-based. In both approaches, the original image is first divided into the base layer and the detail layer, and then the enhanced image is obtained by amplifying the…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
Approximate nearest neighbor search (ANNS) constitutes an important operation in a multitude of applications, including recommendation systems, information retrieval, and pattern recognition. In the past decade, graph-based ANNS algorithms…
This work considers black-box Bayesian inference over high-dimensional parameter spaces. The well-known adaptive Metropolis (AM) algorithm of (Haario etal. 2001) is extended herein to scale asymptotically uniformly with respect to the…
The popularity of Adaptive MCMC has been fueled on the one hand by its success in applications, and on the other hand, by mathematically appealing and computationally straightforward optimisation criteria for the Metropolis algorithm…
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in…
Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…