A wide range of machine learning problems, including astronomical inference about galaxy clusters, scene classification, parametric statistical inference, and predictions of public opinion, can be well-modeled as learning a function on (samples from) distributions. This project explores problems in learning such functions via kernel methods, particularly for large-scale problems. 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. We investigate the approach of approximate embeddings into Euclidean spaces such that inner products in the embedding space approximate kernel values between the source distributions. We first improve the understanding of the workhorse methods of random Fourier features: we show that of the two approaches in common usage, one is strictly superior. We then present a new embedding for a class of information-theoretic distribution distances, and evaluate it and existing embeddings on several real-world applications.
Critical infrastructures underpin the domestic security, health, safety and economic well being of the United States. They are large, widely dispersed, mostly privately owned systems operated under a mixture of federal, state and local government departments, laws and regulations. While there currently are enormous pressures to secure all aspects of all critical infrastructures immediately, budget realities limit available options. The purpose of this study is to provide a clear framework for systematically analyzing and prioritizing resources to most effectively secure US critical infrastructures from terrorist threats. It is a scalable framework (based on the interplay of consequences, threats and vulnerabilities) that can be applied at the highest national level, the component level of an individual infrastructure, or anywhere in between. This study also provides a set of key findings and a recommended approach for framework application. In addition, this study develops three laptop computer-based tools to assist with framework implementation-a Risk Assessment Credibility Tool, a Notional Risk Prioritization Tool, and a County Prioritization tool. This study's tools and insights are based on Sandia National Laboratories' many years of experience in risk, consequence, threat and vulnerability assessments, both in defense- and critical infrastructure-related areas.