Likelihood-Free Inference for Discrete Time Series Data Using Machine Learning
Date
2023
Authors
O'Loughlin, Luke Phillip
Editors
Advisors
Black, Andrew
Maclean, John
Maclean, John
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
Statement of Responsibility
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Abstract
Mechanistic models are ubiquitous across many scientific domains, for example the
susceptible-infectious-removed (SIR) model in epidemiology. Of great interest are
the parameters of the mechanistic model, which often determine the specific behaviour
that the system of interest displays. The parameters of mechanistic models
are usually unobservable, hence they must be inferred from observed data. In particular,
the Bayesian inference framework is popular when working with mechanistic
models due to the conceptually simple way in which it allows one to marry prior
information with data. Unfortunately, for many mechanistic models, performing
Bayesian inference is computationally expensive due to unobserved latent variables
in the model. In this thesis we develop a procedure to perform (approximate)
Bayesian inference for models yielding a time series of discrete observations, using
machine learning to address the scalability issues with traditional approaches such
as particle marginal Metropolis Hastings (PMMH). We approach this problem by
constructing a convolutional neural network based surrogate likelihood model which
can evaluate the likelihood of the entire time series using a single neural network
evaluation. This is in contrast to similar surrogate likelihood approaches to inference,
which usually require one to additionally design/learn informative summary
statistics from the time series data. We test our methods on a series of inference
experiments using simulated data from epidemiological models, obtaining accurate
results compared to the exact inference algorithm PMMH. Furthermore, we demonstrate
that the runtime of our inference methods scale significantly better than
PMMH with increasing dataset sizes, and with increasing model complexity. We
also show how to extend our methods such that they work with multidimensional
(discrete) time series data, and we demonstrate this by performing inference experiments
on simulated data from a two-dimensional predator-prey model. Our
methods obtain accurate results and significantly better runtimes than PMMH on
the predator-prey experiments.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2023
Provenance
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