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The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
Target tracking faces the challenge in coping with large volumes of data which requires efficient methods for real time applications. The complexity considered in this paper is when there is a large number of measurements which are required…
We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…
A sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers separate the configuration space into distinct sectors and can lead…
A system to update estimates from a sequence of probability distributions is presented. The aim of the system is to quickly produce estimates with a user-specified bound on the Monte Carlo error. The estimates are based upon weighted…
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Inferring directed acyclic graphs (DAGs) from data via Markov chain Monte Carlo (MCMC) is computationally challenging in moderate-to-high dimensional settings because their discrete sampling space grows super-exponentially with the number…
Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic…
Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit improved mixing properties. The recently introduced magnetic HMC,…
In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…
Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…