Bayesian approaches to distribution regression

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the groups. This effectively assumes that small and large groups are estimated equally well, and should have equal weight in the final regression. We account for this uncertainty with a Bayesian distribution regression formalism, improving the robustness and performance of the model when group sizes vary. We frame our models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. We demonstrate our approach on illustrative toy datasets, as well as on a challenging problem of predicting age from images

Automating Active Learning for Gaussian Processes

In many problems in science, technology, and engineering, unlabeled data is abundant but acquiring labeled observations is expensive -- it requires a human annotator, a costly laboratory experiment, or a time-consuming computer simulation. Active learning is a machine learning paradigm designed to minimize the cost of obtaining labeled data by carefully selecting which new data should be gathered next. However, excessive machine learning expertise is often required to effectively apply these techniques in their current form. In this dissertation, we propose solutions that further automate active learning. Our core contributions are active learning algorithms that are easy for non-experts to use but that deliver results competitive with or better than human-expert solutions. We begin introducing a novel active search algorithm that automatically and dynamically balances exploration against exploitation --- without relying on a parameter to control this tradeoff. We also provide a theoretical investigation on the hardness of this problem, proving that no polynomial-time policy can achieve a constant factor approximation ratio for the expected utility of the optimal policy. Next, we introduce a novel information-theoretic approach for active model selection. Our method is based on maximizing the mutual information between the output variable and the model class. This is the first active-model-selection approach that does not require updating each model for every candidate point. As a result, we successfully developed an automated audiometry test for rapid screening of noise-induced hearing loss, a widespread and preventable disability, if diagnosed early. We proceed by introducing a novel model selection algorithm for fixed-size datasets, called Bayesian optimization for model selection (BOMS). Our proposed model search method is based on Bayesian optimization in model space, where we reason about the model evidence as a function to be maximized. BOMS is capable of finding a model that explains the dataset well without any human assistance. Finally, we extend BOMS to active learning, creating a fully automatic active learning framework. We apply this framework to Bayesian optimization, creating a sample-efficient automated system for black-box optimization. Crucially, we account for the uncertainty in the choice of model; our method uses multiple and carefully-selected models to represent its current belief about the latent objective function. Our algorithms are completely general and can be extended to any class of probabilistic models. In this dissertation, however, we mainly use the powerful class of Gaussian process models to perform inference. Extensive experimental evidence is provided to demonstrate that all proposed algorithms outperform previously developed solutions to these problems