THIS IS A CONTINUATION OF N00014-14-1-0245 Bayesian Learning for High-Dimensional Low Sample Size Data
Abstract
Project Summary/Statement of Work Fundamental research is proposed in theory, methods, computations and applications of learning from high-dimensional low sample size data. Such data arise routinely in broad applications of interest in national security and defense. Due to the lack of sufficient sample size, it is impossible to rely entirely on the data at hand in conducting inferences and making decisions; it is crucial to incorporate carefully-structured prior information. With this motivation, we focus on Bayesian probability models, which provide a natural framework for combining prior information with current data, while characterizing uncertainty in inferences and decision making. The proposed research is divided into two broad thrust areas. Thrust 1: Bayesian Aggregation will develop fundamentally new frameworks for accommodating model uncertainty in Bayesian inferences avoiding standard assumptions that the true model belongs to a pre-specified list. Thrust 2: Robust and Scalable Bayesian Inference will develop new classes of approximations to Bayesian inference, which are robust to contaminated or corrupted data and facilitate rapid computation in high-dimensions. Within both areas, we aim to develop broad frameworks that can be applied in essentially any application area, with a particular motivation to challenging high-dimensional low sample size problems. Strong theoretical support will be developed providing a precise handle on learning rates in terms of the dimension of the problem and sample size. In addition, scalable algorithms for efficient computation will be developed and assessed theoretically and in terms of practical performance. Real world applications, involving classification and regression from massive-dimensional features and structured learning in multivariate, time series and network applications, provide concrete motivation. Methods will be tested on synthetic and real world applications of DoD interest.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 03, 2016
- Source ID
- N000141612147
Entities
People
- David A. Duncan
Organizations
- Duke University
- Office of Naval Research
- United States Navy