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Automatic model construction with Gaussian processes 10.17863/CAM.14087 Duvenaud, David This thesis develops a method for automatically constructing, visualizing and describing a large class of models, useful for forecasting and finding structure in domains such as time series, geological formations, and physical dynamics. These models, based on Gaussian processes, can capture many types of statistical structure, such as periodicity, changepoints, additivity, and symmetries. Such structure can be encoded through kernels, which have historically been hand-chosen by experts. We show how to automate this task, creating a system that explores an open-ended space of models and reports the structures discovered. To automatically construct Gaussian process models, we search over sums and products of kernels, maximizing the approximate marginal likelihood. We show how any model in this class can be automatically decomposed into qualitatively different parts, and how each component can be visualized and described through text. We combine these results into a procedure that, given a dataset, automatically constructs a model along with a detailed report containing plots and generated text that illustrate the structure discovered in the data. The introductory chapters contain a tutorial showing how to express many types of structure through kernels, and how adding and multiplying different kernels combines their properties. Examples also show how symmetric kernels can produce priors over topological manifolds such as cylinders, toruses, and Möbius strips, as well as their higher-dimensional generalizations. This thesis also explores several extensions to Gaussian process models. First, building on existing work that relates Gaussian processes and neural nets, we analyze natural extensions of these models to deep kernels and deep Gaussian processes. Second, we examine additive Gaussian processes, showing their relation to the regularization method of dropout. Third, we combine Gaussian processes with the Dirichlet process to produce the warped mixture model: a Bayesian clustering model having nonparametric cluster shapes, and a corresponding latent space in which each cluster has an interpretable parametric form. University of Cambridge 2014-11-11 Thesis Doctoral Doctor of Philosophy (PhD) en This work was supported by the National Sciences and Engineering Research Council of Canada, the Cambridge Commonwealth Trust, Pembroke College, a grant from the Engineering and Physical Sciences Research Council, and a grant from Google. https://www.repository.cam.ac.uk/handle/1810/247281 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7baac148-8518-4895-9348-85d89980a462/download d31eae2f2861c263f46b35b82c09d04d https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/460b1c3f-6c8f-4efc-9688-c4cc479bae87/download 835269bda140c10400fe0606a14c3d21 Machine learning Statistics Forecasting Model building Gaussian processes Time series