Papers

Differentiable Particle Filtering

Published:

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.

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Masked Bouncy Particle Sampler

Published:

Piecewise deterministic Markov Processes (PDMP) provide the foundation for a promising class of non-reversible, continuous-time Markov Chain Monte Carlo (MCMC) procedures and have been shown experimentally to enjoy attractive scaling properties in high-dimensional settings. This work introduces the Masked Bouncy Particle Sampler (BPS), a flexible MCMC procedure within the PDMP framework that exploits model structure and modern parallel computing resources using chromatic spatial partitioning ideas from the discrete-time MCMC literature (\cite{gonzalez2011parallel}). We extend the basic procedure by introducing a dynamic factorisation scheme of the target distribution to reduce boundary effects commonly associated to fixed partitioning. The validity of the proposed method is theoretically justified and we provide experimental evidence that the Masked Bouncy Particle Sampler delivers significant efficiency gains over other state-of-the-art sampling schemes for certain high-dimensional sparse models.

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MCMC for Bayesian Non-Parametric Mixture Models

Published:

This dissertation concerns the use of Markov Chain Monte Carlo (MCMC) procedures in performing Bayesian inference on non-parametric mixture models. In particular, this report will focus on Dirichlet Process Mixture Models.

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