Approximate Manifold Sampling
: Robust Bayesian Inference for Machine Learning

  • Mauro Camara Escudero

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)

Abstract

Efficient sampling from probability densities concentrated around a lower-dimensional
submanifold is crucial in numerous applications arising in machine learning, statistics,
and statistical physics. This task is particularly challenging due to the extreme anisotropy
and high-dimensionality of the problem, and the correlation between the variables. We propose a
novel family of bespoke MCMC algorithms designed to sample efficiently from these densities and
show their computational superiority to general purpose and specialized samplers. Furthermore,
we contribute to the development of integrator and Markov snippets, which are a particular
class of general-purpose sequential algorithms for Bayesian inference and machine learning
that can leverage the geometry of the space with integrators, is highly robust to the choice of
the step size and the number of integration steps, and naturally lends itself to parallelisation.
Building on these foundations, we present a sequential algorithm that is particularly well-suited
to approximate manifold sampling.
Date of Award18 Jun 2024
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorChristophe Andrieu (Supervisor), Mark A Beaumont (Supervisor) & Oliver T Johnson (Supervisor)

Keywords

  • Approximate Manifold Sampling
  • Sampling
  • Integrator Snippets
  • Bayesian Inference
  • Robust
  • Machine Learning
  • Computational Statistics
  • Data Science
  • Manifold Sampling
  • Constrained HMC
  • Hamiltonian Monte Carlo
  • Monte Carlo
  • Hamiltonian
  • Tangential Hug
  • Tangential
  • Ghums
  • filamentary distributions
  • filamentary
  • mcmc
  • smc
  • markov snippets
  • markov
  • snippets

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