Doctoral Degrees (Statistics and Actuarial Science)

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Browsing Doctoral Degrees (Statistics and Actuarial Science) by browse.metadata.advisor "Du Preez, J. A."

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    Regularised Gaussian belief propagation
    (Stellenbosch : Stellenbosch University, 2018-12) Kamper, Francois; Steel, S. J.; Du Preez, J. A.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : Belief propagation (BP) has been applied as an approximation tool in a variety of inference problems. BP does not necessarily converge in loopy graphs and, even if it does, is not guaranteed to provide exact inference. Even so, BP is useful in many applications due to its computational tractability. On a high level this dissertation is concerned with addressing the issues of BP when applied to loopy graphs. To address these issues we formulate the principle of node regularisation on Markov graphs (MGs) within the context of BP. The main contribution of this dissertation is to provide mathematical and empirical evidence that the principle of node regularisation can achieve convergence and good inference quality when applied to a MG constructed from a Gaussian distribution in canonical parameterisation. There is a rich literature surrounding BP on Gaussian MGs (labelled Gaussian belief propagation or GaBP), and this is known to suffer from the same problems as general BP on graphs. GaBP is known to provide the correct marginal means if it converges (this is not guaranteed), but it does not provide the exact marginal precisions. We show that our regularised BP will, with sufficient tuning, always converge while maintaining the exact marginal means. This is true for a graph where nodes are allowed to have any number of variables. The selection of the degree of regularisation is addressed through the use of heuristics. Our variant of GaBP is tested empirically in a variety of settings. We show that our method outperforms other variants of GaBP available in the literature, both in terms of convergence speed and quality of inference. These improvements suggest that the principle of node regularisation in BP should be investigated in other inference problems. A by-product of GaBP is that it can be used to solve linear systems of equations; the same is true for our variant and in this context we make an empirical comparison with the conjugate gradient (CG) method.