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Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…
The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint,…
Standard Markov chain Monte Carlo (MCMC) admits three fundamental control parameters: the number of chains, the length of the warmup phase, and the length of the sampling phase. These control parameters play a large role in determining the…
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…
We propose a fast potential splitting Markov Chain Monte Carlo method which costs $O(1)$ time each step for sampling from equilibrium distributions (Gibbs measures) corresponding to particle systems with singular interacting kernels. We…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
Monte Carlo dropout may effectively capture model uncertainty in deep learning, where a measure of uncertainty is obtained by using multiple instances of dropout at test time. However, Monte Carlo dropout is applied across the whole network…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…
Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets for problems with intractable or {unavailable} likelihood function. It uses synthetic data drawn from the simulation model to approximate the…
This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is…
Parallel tempering is a meta-algorithm for Markov Chain Monte Carlo that uses multiple chains to sample from tempered versions of the target distribution, enhancing mixing in multi-modal distributions that are challenging for traditional…