Related papers: On the Theoretical Properties of the Exchange Algo…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
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…
Density functional theory is the standard theory for computing the electronic structure of materials, which is based on a functional that maps the electron density to the energy. However, a rigorous form of the functional is not known and…
We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g.…
Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…
We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange…
We consider the application of active subspaces to inform a Metropolis-Hastings algorithm, thereby aggressively reducing the computational dimension of the sampling problem. We show that the original formulation, as proposed by Constantine,…
Metropolis algorithms are classical tools for sampling from target distributions, with broad applications in statistics and scientific computing. Their convergence speed is governed by the spectral gap of the associated Markov operator.…
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…
A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
I show how Markov chain sampling with the Metropolis-Hastings algorithm can be modified so as to take bigger steps when the distribution being sampled from has the characteristic that its density can be quickly recomputed for a new point if…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
The general applicability and ease of use of the pseudo-marginal Metropolis--Hastings (PMMH) algorithm, and particle Metropolis--Hastings in particular, makes it a popular method for inference on discretely observed Markovian stochastic…
In this paper, we introduce a new approach for integrating score-based models with the Metropolis-Hastings algorithm. While traditional score-based diffusion models excel in accurately learning the score function from data points, they lack…
Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly…