Fast and Robust Gaussian Process Inference for Bayesian Nonparametric Learning

用于贝叶斯非参数学习的快速且稳健的高斯过程推理

基本信息

批准号：
1907316
负责人：
Yun Yang
金额：
$ 12万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-05-17 至 2022-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907316&HistoricalAwards=false
关键词：
Fast Robust Gaussian Process Inference

项目摘要

Advances in modern technology have empowered researchers to collect massive data to conduct inference and making predictions. With the abundance of available observations, traditional statistical methods under the parametric assumption that a model can be characterized by a pre-specified number of parameters become inadequate and less attractive. Bayesian nonparametric models are attractive in this context which allow the resolution level of the analysis to be determined in a data-driven manner, and provide automatic characterization of uncertainty. The goal of this project is to develop new theory, methodology and computational tools for Bayesian nonparametric inference via Gaussian process priors. Given the availability of massive data, nonparametric inference offers an attractive framework for flexibly modeling the underlying structure and extracting useful information. For instance, such challenges occur in chemical physics, computational biology, computer vision, engineering, and meteorology. This project aims to lay down a solid methodological, algorithmic, and theoretical foundation for nonparametric inference based on Gaussian processes. In particular, Gaussian process-based approaches tend to be vulnerable to data contamination and have heavy computational costs. To alleviate the high-computational cost of Gaussian process inference procedures, the investigator puts forward two novel computational frameworks which differ at their respective approximating targets as being either the prior or the posterior. To enhance the robustness of Gaussian process inference against data contamination, the investigator proposes a novel class of Bayesian hierarchical models for incorporating this extra measurement error structure, leading to a class of robust Gaussian process inference procedures. The new theoretical development offers valuable insight to experiment-design practitioners into the impact of measurement errors upon prediction and estimation, and provides evidence on the deep connection between computational complexity and statistical learnability. These computational and theoretical frameworks also benefit other disciplines such as applied mathematics, computer science and finance where stochastic processes such as Gaussian processes are routinely used.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

现代技术的进步使研究人员有能力收集大量数据以进行推理和做出预测。有了丰富的可用观测，在参数假设下的传统统计方法可以通过预先指定的参数来表征模型的特征是不充分且吸引人的。在这种情况下，贝叶斯非参数模型具有吸引力，可以以数据驱动的方式确定分析的分辨率水平，并提供不确定性的自动表征。该项目的目的是通过高斯工艺先验开发用于贝叶斯非参数推断的新理论，方法论和计算工具。鉴于大量数据的可用性，非参数推理为灵活地建模基础结构并提取有用的信息提供了一个有吸引力的框架。例如，这种挑战发生在化学物理学，计算生物学，计算机视觉，工程和气象学中。该项目旨在基于高斯过程，为非参数推断提供一个可靠的方法论，算法和理论基础。特别是，基于高斯的方法的方法往往容易受到数据污染的影响，并且具有沉重的计算成本。为了减轻高斯工艺推理程序的高计算成本，研究人员提出了两个新型的计算框架，它们各自的近似目标有所不同，为先验或后部。为了增强高斯工艺对数据污染的鲁棒性，研究者提出了一类新型的贝叶斯分层模型，以结合这种额外的测量误差结构，从而导致一类强大的高斯工艺推理程序。新的理论发展为实验设计的实践者提供了宝贵的见解，以了解测量错误对预测和估计的影响，并提供了有关计算复杂性和统计学可学习性之间深厚联系的证据。这些计算和理论框架还受益于其他学科，例如应用数学，计算机科学和金融，在这些学科，计算机科学和金融上，常规使用随机过程（例如高斯流程）。该奖项反映了NSF的法定使命，并被认为是值得通过基金会的知识分子优点和知识分子的优点和评估来支持的。更广泛的影响审查标准。

项目成果

期刊论文数量（18）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Bayesian regression tree ensembles that adapt to smoothness and sparsity

DOI：
10.1111/rssb.12293
发表时间：
2017-07
期刊：
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
影响因子：
0
作者：
A. Linero;Yun Yang
通讯作者：
A. Linero;Yun Yang

Diffusion K-means clustering on manifolds: Provable exact recovery via semidefinite relaxations