Related papers: On Mixing Times of Metropolized Algorithm With Opt…
Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence…
The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis-Hastings (MH)…
We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of…
Given a target distribution $\mu \propto e^{-\mathcal{H}}$ to sample from with Hamiltonian $\mathcal{H}$, in this paper we propose and analyze new Metropolis-Hastings sampling algorithms that target an alternative distribution…
Sampling from high dimensional distributions is a computational bottleneck in many scientific applications. Hamiltonian Monte Carlo (HMC), and in particular the No-U-Turn Sampler (NUTS), are widely used, yet they struggle on problems with a…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
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…
This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on…
This article presents MAPS$^2$ : a distributed algorithm that allows multi-robot systems to deliver coupled tasks expressed as Signal Temporal Logic (STL) constraints. Classical control theoretical tools addressing STL constraints either…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…
We make two closely related theoretical contributions to the use of importance sampling schemes. First, for independent sampling, we prove that the minimax optimal trial distribution coincides with the target if and only if the target…
Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…
Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition…
We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the…
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…
We propose a weighting scheme for the proposals within Markov chain Monte Carlo algorithms and show how this can improve statistical efficiency at no extra computational cost. These methods are most powerful when combined with…
A number of problems in a variety of fields are characterised by target distributions with a multimodal structure in which the presence of several isolated local maxima dramatically reduces the efficiency of Markov Chain Monte Carlo…