Dougal Sutherland

A wide range of machine learning problems, including astronomical inference about galaxy clusters, natural image scene classification, parametric statistical inference, and detection of potentially harmful sources of radiation, can be well-modeled as learning a function on (samples from) distributions. This thesis explores problems in learning such functions via kernel methods, and applies the framework to yield state-of-the-art results in several novel settings.

One major challenge with this approach is one of computational efficiency when learning from large numbers of distributions: the computation of typical methods scales between quadratically and cubically, and so they are not amenable to large datasets. As a solution, we investigate approximate embeddings into Euclidean spaces such that inner products in the embedding space approximate kernel values between the source distributions. We provide a greater understanding of the standard existing tool for doing so on Euclidean inputs, random Fourier features. We also present a new embedding for a class of information-theoretic distribution distances, and evaluate it and existing embeddings on several real-world applications.

The next challenge is that the choice of distance is important for getting good practical performance, but how to choose a good distance for a given problem is not obvious. We study this problem in the setting of two-sample testing, where we attempt to distinguish two distributions via the maximum mean divergence, and provide a new technique for kernel choice in these settings, including the use of kernels defined by deep learning-type models.

In a related problem setting, common to physical observations, autonomous sensing, and electoral polling, we have the following challenge: when observing samples is expensive, but we can choose where we would like to do so, how do we pick where to observe? We give a method for a closely related problem where we search for instances of patterns by making point observations. Throughout, we combine theoretical results with extensive empirical evaluations to increase our understanding of the methods.