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We develop a forward-reverse EM (FREM) algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the FREM method…
The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a…
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be…
The article examines in some detail the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are…
Mirror Descent (MD) is a well-known method of solving non-smooth convex optimization problems. This paper analyzes the stochastic variant of MD with adaptive stepsizes. Its convergence on average is shown to be faster than with the fixed…
This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state.…
To determine the effect of nonradiative excitation energy transfer on the fluorescence of a rigid multicomponent solution, a new analytical method was developed by treating this transfer as a time-resolved Markov chain (TRMC). In the TRMC…
Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…
For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we…
The prediction of wind speed is very important when dealing with the production of energy through wind turbines. In this paper, we show a new nonparametric model, based on semi-Markov chains, to predict wind speed. Particularly we use an…
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…
Efficient sampling of many-dimensional and multimodal density functions is a task of great interest in many research fields. We describe an algorithm that allows parallelizing inherently serial Markov chain Monte Carlo (MCMC) sampling by…
Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…
The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo…
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively…