CIF: Small: Advancing Adaptive Importance Sampling for Signal Processing

点击翻译按钮获取中文摘要

There are many applications where the interest is in learning about unknowns from observed data. The goals range from predicting future data to learning about scientific or societal truths. Bayesian signal processing allows for explicit incorporation of all available information about an addressed task. It amounts to optimally combining common-sense knowledge and observational evidence. Due to its strength and appeal, Bayesian modeling and analysis has been embraced by all of science and engineering. However, the main current problems are those with large numbers of unknowns (complex systems) and/or large amounts of data (big data). This raises the concern that Bayesian inference may become computationally incapable of handling them because of the sheer size and complexity of the studied systems. The goal of this project is to advance the theory and practice of a class of Bayesian methods, adaptive importance sampling (AIS), for dealing with problems where the numbers of unknowns and/or data are large.This project focuses on building a novel framework for AIS that will extend its use for Bayesian inference to problems with large amounts of unknowns and/or data. The research involves investigating in greatest detail the intricacies of AIS on several areas including (a) novel schemes for AIS with emphasis on new strategies for adaptive learning and for stable weight computation, and on advanced approaches for dealing with high dimensional models and big data, (b) model selection and machine learning, (c) global optimization, and (d) application to a case-study where understanding the progression of cancer from cancer stem cells is of interest.