Graduation Year

2020

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Nicholas Pippenger

Reader 2

Michael Orrison

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2020 Nicholas J Richardson

Abstract

Probabilistic graphical models present an attractive class of methods which allow one to represent the world in terms of a joint distribution comprised of component distributions; these models tend to be modular and interpretable. Traditionally, making queries (inference) on the most interesting joint distributions is hard; this limits our ability to construct models to represent the structure present in complex natural data like images and speech. On the other end of the spectrum, adaptive basis methods like kernel machines and neural networks can flexibly capture useful patterns in more complex data. Unfortunately, they offer less toward discovering interpretable components of the process/system being studied. This thesis is concerned with shedding light on the limits and abilities of the emerging practice of model composition; a marrying of probabilistic models with adaptive basis methods in pursuit of models with the modularity of probabilistic methods and the musculature of massively parametric (often approaching nonparametric) nonlinear maps. The automatic discovery of structure in data has applications in genetics, computational neuroscience, signal processing, and machine learning.

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