Related papers: On the Theoretical Properties of the Exchange Algo…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically,…
The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant…
We consider Metropolis Hastings MCMC in cases where the log of the ratio of target distributions is replaced by an estimator. The estimator is based on m samples from an independent online Monte Carlo simulation. Under some conditions on…
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…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…
In this paper we shall consider optimal scaling problems for high-dimensional Metropolis--Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the…
We consider the problem of distributed learning, where a network of agents collectively aim to agree on a hypothesis that best explains a set of distributed observations of conditionally independent random processes. We propose a…
Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler…
We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…