Hussain, MS; (2014) Real-coded genetic algorithm particle filters for high-dimensional state spaces. Doctoral thesis , UCL (University College London).

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Abstract

This thesis successfully addresses the issues faced by particle filters in high-dimensional state-spaces by comparing them with genetic algorithms and then using genetic algorithm theory to address these issues. Sequential Monte Carlo methods are a class of online posterior density estimation algorithms that are suitable for non-Gaussian and nonlinear environments, however they are known to suffer from particle degeneracy; where the sample of particles becomes too sparse to approximate the posterior accurately. Various techniques have been proposed to address this issue but these techniques fail in high-dimensions. In this thesis, after a careful comparison between genetic algorithms and particle filters, we posit that genetic algorithm theoretic arguments can be used to explain the working of particle filters. Analysing the working of a particle filter, we note that it is designed similar to a genetic algorithm but does not include recombination. We argue based on the building-block hypothesis that the addition of a recombination operator would be able to address the sample impoverishment phenomenon in higher dimensions. We propose a novel real-coded genetic algorithm particle filter (RGAPF) based on these observations and test our hypothesis on the stochastic volatility estimation of financial stocks. The RGAPF successfully scales to higher-dimensions. To further strengthen our argument that whether building-block-hypothesis-like effects are due to the recombination operator, we compare the RGAPF with a mutation-only particle filter with an adjustable mutation rate that is set to equal the population-to-population variance of the RGAPF. The latter significantly and consistently performs better, indicating that recombination is having a subtle and significant effect that may be theoretically explained by genetic algorithm theory. After two successful attempts at validating our hypothesis we compare the performance of the RGAPF using different real-recombination operators. Observing the behaviour of the RGAPF under these recombination operators we propose a mean-centric recombination operator specifically for high-dimensional particle filtering. This recombination operator is successfully tested and compared with benchmark particle filters and a hybrid CMA-ES particle filter using simulated data and finally on real end-of-day data of the securities making up the FTSE-100 index. Each experiment is discussed in detail and we conclude with a brief description of the future direction of research.

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