Related papers: Dimension-independent likelihood-informed MCMC
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…
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…
Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…
In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…
We consider the theoretical analysis of Multiscale Sampling Methods, which are a new class of gradient-free Markov chain Monte Carlo (MCMC) methods for high dimensional inverse differential equation problems. A detailed presentation of…
This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and…
Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that…
This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte…
The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…
MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently,…
Markov Chain Monte Carlo (MCMC) algorithms are standard approaches to solve imaging inverse problems and quantify estimation uncertainties, a key requirement in absence of ground-truth data. To improve estimation quality, Plug-and-Play MCMC…
Markov chain Monte Carlo (MCMC) algorithms are widely used to sample from complicated distributions, especially to sample from the posterior distribution in Bayesian inference. However, MCMC is not directly applicable when facing the doubly…