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

• 批准号: 1810831
• 负责人: Yun Yang
• 金额: $ 12万
• 依托单位: Florida State University
• 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: 2018-06-01 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1810831&HistoricalAwards=false
• 关键词: Fast; Robust; Gaussian; Process; Inference

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能够收集大量数据来进行推理和预测。随着观测数据的丰富，传统的统计方法的参数假设下，一个模型可以被预先指定的参数数量的特点变得不够，不那么有吸引力。在这种情况下，贝叶斯非参数模型很有吸引力，它允许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。这个项目的目标是发展新的理论，方法和计算工具，通过高斯过程先验的贝叶斯非参数推断。由于大量数据的可用性，非参数推理提供了一个有吸引力的框架，灵活地建模的基础结构和提取有用的信息。例如，这样的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。该项目旨在为基于高斯过程的非参数推断奠定坚实的方法论、算法和理论基础。特别是，基于高斯过程的方法往往容易受到数据污染，并具有沉重的计算成本。为了减轻高斯过程推理程序的高计算成本，研究者提出了两种新的计算框架，它们在各自的近似目标上不同，无论是先验还是后验。为了提高高斯过程推理对数据污染的鲁棒性，研究者提出了一类新的贝叶斯分层模型，将这种额外的测量误差结构，导致一类强大的高斯过程推理程序。新的理论发展为实验设计从业者提供了有价值的洞察力，测量误差对预测和估计的影响，并提供了计算复杂性和统计可学习性之间的深层联系的证据。这些计算和理论框架也有利于其他学科，如应用数学，计算机科学和金融，其中随机过程，如高斯过程是经常使用的。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。