Related papers: Exact Discrete Stochastic Simulation with Deep-Lea…

Algorithms for decentralized optimization and learning rely on local optimization steps coupled with combination steps over a graph. Recent works have demonstrated that using a time-varying sequence of matrices that achieves finite-time…

In this work we propose an accelerated stochastic learning system for very large-scale applications. Acceleration is achieved by mapping the training algorithm onto massively parallel processors: we demonstrate a parallel, asynchronous GPU…

Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…

Bayesian deep learning offers a principled way to address many issues concerning safety of artificial intelligence (AI), such as model uncertainty,model interpretability, and prediction bias. However, due to the lack of efficient Monte…

We study the estimation of policy gradients for continuous-time systems with known dynamics. By reframing policy learning in continuous-time, we show that it is possible construct a more efficient and accurate gradient estimator. The…

Convergence rate analysis for general state-space Markov chains is fundamentally important in areas such as Markov chain Monte Carlo and algorithmic analysis (for computing explicit convergence bounds). This problem, however, is notoriously…

Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…

Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of…

We study a variation of vanilla stochastic gradient descent where the optimizer only has access to a Markovian sampling scheme. These schemes encompass applications that range from decentralized optimization with a random walker (token…

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space,…

Accurately detecting symbols transmitted over multiple-input multiple-output (MIMO) wireless channels is crucial in realizing the benefits of MIMO techniques. However, optimal MIMO detection is associated with a complexity that grows…

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has been increasingly popular in Bayesian learning due to its ability to deal with large data. A standard SG-MCMC algorithm simulates samples from a discretized-time Markov chain to…

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…

In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…