CIF: Small: Advancing Adaptive Importance Sampling for Signal Processing

有许多应用的兴趣在于从观测数据中了解未知。目标从预测未来数据到了解科学或社会真相不等。贝叶斯信号处理允许显式地合并有关寻址任务的所有可用信息。它相当于将常识性知识和观察证据最佳地结合起来。由于它的强大和吸引力，贝叶斯建模和分析已经被所有的科学和工程所接受。然而，当前的主要问题是那些具有大量未知数（复杂系统）和/或大量数据（大数据）的问题。这引起了人们的担忧，即由于所研究系统的庞大规模和复杂性，贝叶斯推理可能在计算上无法处理它们。该项目的目标是推进一类贝叶斯方法的理论和实践，自适应重要性抽样（AIS），用于处理未知数量和/或数据量很大的问题。该项目的重点是为AIS构建一个新的框架，将其用于贝叶斯推理的应用扩展到具有大量未知和/或数据的问题。该研究涉及最详细地调查AIS在几个领域的复杂性，包括(a) AIS的新方案，重点是自适应学习和稳定权重计算的新策略，以及处理高维模型和大数据的先进方法，(b)模型选择和机器学习，(c)全局优化，以及(d)应用于案例研究，其中了解癌症干细胞的癌症进展是感兴趣的。

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.