CRII: RI: Anytime Inference with Confidence Bounds for Graphical Models

CRII：RI：图形模型的随时推理与置信界限

• 批准号: 1565796
• 负责人: Qiang Liu
• 金额: $ 15.77万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-04-01 至 2018-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1565796&HistoricalAwards=false
• 关键词: CRII; RI; Anytime; Inference; Confidence

Probabilistic graphical models are widely used throughout science and engineering to solve difficult problems, understand large data sets, or make predictions about complex phenomena. Making predictions or decisions out of graphical models involves challenging #P-hard computational problems, and efficient approximation methods are highly demanded. The most useful approximations should give not only accurate estimates, but also (1) come with tight and conservative error bounds and (2) can be improved continuously to trade time for increased accuracy in a memory efficient and predictable way (an "anytime" property). Such algorithms should allow us to solve easy problems with strong certificates of accuracy, and also identify harder problems together with clear guidance for further improvement. Unfortunately, most state-of-the-art methods, including deterministic variational methods and Monte Carlo-based methods, often do not fully satisfy these criteria. This project aims to develop a new generation of inference tools with tight non-asymptotic confidence bounds and anytime property. Based on several key insights that connect variational inference with non-asymptotic bounds of Monte Carlo, the PI derives a spectrum of powerful methods that naturally integrate and combine the advantages of these two approaches, providing a new foundation for more reliable inference. The project also develops novel non-asymptotic error bounds for advanced Monte Carlo methods such as annealed importance sampling (AIS), based on which the researchers construct highly efficient estimates and bounds built on the state-of-the-art AIS. The approaches are tested extensively on various application domains, and provide practical guidance and open source packages for practitioners. The new powerful anytime, error-aware inference tools will lead much more reliable use of graphical models across different application domains, greatly expanding our ability of reasoning over large datasets and complex phenomena.

概率图模型广泛应用于整个科学和工程领域，以解决难题、理解大型数据集或对复杂现象进行预测。利用图形模型进行预测或决策涉及具有挑战性的#P-hard 计算问题，并且非常需要有效的近似方法。最有用的近似值不仅应该给出准确的估计，而且（1）具有严格且保守的误差范围，并且（2）可以不断改进，以内存有效和可预测的方式（“随时”属性）以时间换取更高的准确性。 ）。这样的算法应该让我们能够解决简单的问题，并具有强大的准确性证明，并且还可以识别更困难的问题，并为进一步改进提供明确的指导。不幸的是，大多数最先进的方法，包括确定性变分方法和基于蒙特卡罗的方法，通常不能完全满足这些标准。 该项目旨在开发具有严格的非渐进置信界和随时属性的新一代推理工具。基于将变分推理与蒙特卡洛非渐进界限联系起来的几个关键见解，PI 推导出一系列强大的方法，这些方法自然地集成和结合了这两种方法的优点，为更可靠的推理提供了新的基础。该项目还为先进的蒙特卡洛方法（例如退火重要性采样（AIS））开发了新颖的非渐近误差界限，研究人员在此基础上构建了基于最先进的 AIS 的高效估计和界限。这些方法在各个应用领域进行了广泛的测试，并为从业者提供实用指导和开源包。新的强大的随时错误感知推理工具将在不同的应用领域中更可靠地使用图形模型，从而极大地扩展我们对大型数据集和复杂现象的推理能力。