Related papers: Large sample scaling analysis of the Zig-Zag algor…
Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational…
Novel Monte Carlo methods to generate samples from a target distribution, such as a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs),…
Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition…
Piecewise deterministic Markov processes are an important new tool in the design of Markov Chain Monte Carlo algorithms. Two examples of fundamental importance are the Bouncy Particle Sampler (BPS) and the Zig-Zag process (ZZ). In this…
We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…
Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics, and as datasets grow larger and models grow more complex, many popular MCMC algorithms become too computationally expensive to be practical. Recent progress has…
Piecewise Deterministic Markov Processes (PDMPs) such as the Bouncy Particle Sampler and the Zig-Zag Sampler, have gained attention as continuous-time counterparts of classical Markov chain Monte Carlo. We study their transient regime under…
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event…
We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic…
Whereas the ability of deep networks to produce useful predictions has been amply demonstrated, estimating the reliability of these predictions remains challenging. Sampling approaches such as MC-Dropout and Deep Ensembles have emerged as…
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
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…
Piecewise deterministic Markov processes (PDMPs) are a class of continuous-time Markov processes that were recently used to develop a new class of Markov chain Monte Carlo algorithms. However, the implementation of the processes is…
This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…
Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel,…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable…
We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge…