Related papers: Replica Symmetric Bound for Restricted Isometry Co…
We developed a replica exchange method that is effectively parallelizable even if the computational cost of the Monte Carlo moves in the parallel replicas are considerably different, for instance, because the replicas run on different type…
This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
The study considers the usage of a probabilistic optimization method called Cross-Entropy (CE). This is the version of the Monte Carlo method created by Reuven Rubinstein (1997). It was developed in the context of determining rare events.…
Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated impressive success in many…
Single-particle imaging with X-ray free-electron lasers depends crucially on algorithms that merge large numbers of weak diffraction patterns despite missing measurements of parameters such as particle orientations. The…
The replica-exchange Monte-Carlo (RXMC) method is a powerful Markov-chain Monte-Carlo algorithm for sampling from multi-modal distributions, which are challenging for conventional methods. The sampling efficiency of the RXMC method depends…
Given an undirected graph G, the effective resistance r(s,t) measures the dissimilarity of node pair s,t in G, which finds numerous applications in real-world problems, such as recommender systems, combinatorial optimization, molecular…
A new method based on a Reverse Monte Carlo [RMC] technique and aimed at the inverse problem in the analysis of interstellar (intergalactic) absorption lines is presented. The line formation process in chaotic media with a finite…
Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…
We present a novel approach to reverse Monte Carlo (RMC) modeling, SpecSwap-RMC, which makes use of pre-computed property data from a discrete configuration space replacing atomistic moves with swap moves of contributions to a sample-set…
The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error…
We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…
We analyze Riemannian Hamiltonian Monte Carlo (RHMC) for sampling a polytope defined by $m$ inequalities in $\R^n$ endowed with the metric defined by the Hessian of a convex barrier function. The advantage of RHMC over Euclidean methods…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
This paper studies the estimation of outage probability in GSC/MRC SIMO systems under Rician fading in the rare-event regime. The difficulty arises from the evaluation of the CDF of a partial sum of ordered non-central chi-square random…