RI: Small: Frontiers in Monte Carlo and Variational Inference

RI：小：蒙特卡罗和变分推理的前沿

基本信息

批准号：
1908577
负责人：
Justin Domke
金额：
$ 44.96万
依托单位：
University of Massachusetts Amherst
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2023-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1908577&HistoricalAwards=false
关键词：
RI Small Frontiers Monte Carlo

项目摘要

Probabilistic inference allows humans to gain insight and make predictions from data. There is an ever-growing need in business, government, and science to answer questions using data. Often, these questions are best answered by phrasing them as probability calculations. As data sets grow larger and more complex, probability calculations are increasingly difficult and often cannot be performed exactly within reasonable time budgets. This project will promote science and technology by providing new theoretical results, algorithms, and empirical knowledge about how to compute approximate answers to probabilistic queries in a way that achieves good tradeoffs between accuracy and efficiency. In particular, the project will study how to best combine the strengths of two different strategies for calculating probabilities. This work will provide new techniques that are practical, have tunable accuracy, and scale to very large data sets.To meet these goals, this project will combine two different approaches to probabilistic inference: variational inference (VI), and Monte Carlo (MC). MC algorithms are general-purpose and are asymptotically exact, but may fail to give good answers in reasonable time or scale large data sets. In contrast, VI is a way to get a "pretty good answer, quickly" by restricting the approximate posterior to tractable family. This project will combine these in a principled way to derive algorithms that are general-purpose, practical, have tunable accuracy, and scale to very large data sets. The new algorithms are expected to achieve time-accuracy tradeoffs that dominate Monte Carlo methods for a wide range of problems and time budgets. The proposed methods will 1) incorporate strengths of Monte Carlo methods into variational inference by designing approximating families based on Monte Carlo estimators; and 2) improve the usefulness of variational inference for downstream tasks by adapting divergences and approximating families to the needs of a downstream Monte Carlo estimator. The project will result in a comprehensive evaluation benchmark as well as a set of practical techniques to make the method more effective. A novel application in ecology will demonstrate the project's real-world potential.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.

概率推论允许人类获得洞察力并从数据中做出预测。商业，政府和科学的需求不断增长，可以使用数据回答问题。通常，最好通过将它们作为概率计算来回答这些问题。随着数据集变得更大且更复杂的情况，概率计算越来越困难，并且通常无法在合理的时间预算内进行精确执行。该项目将通过提供有关如何以在准确性和效率之间实现良好权衡的方式来计算概率查询的近似答案的新理论结果，算法以及经验知识来促进科学和技术。特别是，该项目将研究如何最好地结合两种不同策略来计算概率的优势。这项工作将提供实用的新技术，具有可调的准确性，并扩展到非常大的数据集。为了实现这些目标，该项目将结合两种不同的概率推断方法：变异推理（VI）和Monte Carlo（MC）。 MC算法是通用的，并且在合理的时间或规模大数据集中可能无法给出良好的答案。相比之下，VI是通过限制可牵引家庭后方的大概限制“很快的答案”的一种方式。该项目将以一种原则性的方式结合这些项目，以得出通用，实用，具有可调节精度的算法，并扩展到非常大的数据集。预计新算法将实现时间准确性的权衡，该算法在各种问题和时间预算方面主导了蒙特卡洛方法。所提出的方法将通过设计基于蒙特卡洛估计量的近似族来将蒙特卡洛方法的强度纳入变异推理； 2）通过调整分歧和近似家庭满足下游蒙特卡洛估计量的需求，提高了下游任务的变异推断的有用性。该项目将产生全面的评估基准以及一组实用技术，以使该方法更有效。生态学上的新应用将证明该项目的现实世界潜力。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更广泛影响的评论标准来评估值得支持的。