Related papers: A Non-asymptotic Analysis for Learning and Applyin…

The task of choosing a preconditioner $\boldsymbol{M}$ to use when solving a linear system $\boldsymbol{Ax}=\boldsymbol{b}$ with iterative methods is difficult. For instance, even if one has access to a collection…

Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…

We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model. These methods range from principal component analysis to…

We introduce adaptive, tuning-free step size schedules for gradient-based sampling algorithms obtained as time-discretizations of Wasserstein gradient flows. The result is a suite of tuning-free sampling algorithms, including tuning-free…

Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…

It is widely known that the performance of Markov chain Monte Carlo (MCMC) can degrade quickly when targeting computationally expensive posterior distributions, such as when the sample size is large. This has motivated the search for MCMC…

In the case of a linear state space model, we implement an MCMC sampler with two phases. In the learning phase, a self-tuning sampler is used to learn the parameter mean and covariance structure. In the estimation phase, the parameter mean…

Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a…

Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…

Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…

The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis-Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the…

The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem…

This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown…

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and…

We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the…

We derive and analyze learning algorithms for apprenticeship learning, policy evaluation, and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on…