CAREER: Efficient Algorithms for Learning and Testing Structured Probabilistic Models

近年来，科学和技术领域的可用数据量呈爆炸式增长，目前正以前所未有的速度扩大。在大型复杂数据集上进行准确推理的一般任务已成为各个学科的主要瓶颈。这种推理任务的自然形式化涉及将数据视为从概率模型中提取的随机样本-我们认为该模型描述了生成数据的过程。这个项目的首要目标是从统计和计算的角度来获得这些推理任务的精确理解。在这个项目中解决的问题来自现代数据分析所面临的紧迫挑战。该项目的一个关键组成部分是促进不同社区之间的合作。此外，PI将指导高中和本科生，并设计几个新的理论课程，将研究和教学结合在一起，在本科和研究生阶段。PI将研究无监督学习和测试中的几个基本算法问题，我们目前的理解存在惊人的差距。这些包括设计有效的算法，在存在偏离假设模型的情况下保持稳定，规避分布学习中的维数灾难，以及测试高维概率模型。这组方向可能导致新的算法和概率技术，并提供深入了解无监督估计中结构和效率之间的相互作用。这项研究与计算机科学、概率论、统计学和信息论等更广泛的工作联系在一起。

In recent years, the amount of available data in science and technology has exploded and is currently expanding at an unprecedented rate. The general task of making accurate inferences on large and complex datasets has become a major bottleneck across various disciplines. A natural formalization of such inference tasks involves viewing the data as random samples drawn from a probabilistic model -- a model that we believe describes the process generating the data. The overarching goal of this project is to obtain a refined understanding of these inference tasks from both statistical and computational perspectives. The questions addressed in this project arise from pressing challenges faced in modern data analysis. A crucial component of the project involves fostering collaboration between different communities. Furthermore, the PI will mentor high-school and undergraduate students, and design several new theory courses integrating research and teaching at the undergraduate and graduate levels.The PI will investigate several fundamental algorithmic questions in unsupervised learning and testing for which there is an alarming gap in our current understanding. These include designing efficient algorithms that are stable in the presence of deviations from the assumed model, circumventing the curse of dimensionality in distribution learning, and testing high-dimensional probabilistic models. This set of directions could lead to new algorithmic and probabilistic techniques, and offer insights into the interplay between structure and efficiency in unsupervised estimation. This research ties into a broader range of work across computer science, probability, statistics, and information theory.