Generative Models for Complex Data: Inference, Sensing, and Repair

该项目的研究处于统计学和机器学习的边界，重点是研究新的统计模型家族。生成模型是一种算法，它将随机输入转换为合成数据，以模仿自然发生的数据集中的数据，例如图像数据库。该研究将探索生成模型的理论，算法和应用，以深入了解在实践中观察到的现象，但在数学原理方面知之甚少。这项工作还将追求生成模型在计算神经科学中的新应用，从细胞水平到人类认知的宏观水平。该研究的预期成果包括开发实现新方法的软件，培养跨传统学科的研究生，以及通过基于这项工作的研究项目向本科生介绍现代统计和机器学习。该项目的技术目标包括四个相互关联的目标。首先是研究在深度学习中广泛使用的变分程序的统计特性，并开发新的方法来为新的数据类型构建生成模型。第二个目标是探索基于生成模型的反问题求解新算法。第三，将研究一种新形式的鲁棒估计，其中模型在数据上构建后被破坏。模型修复的动机是越来越大的统计模型，包括神经网络，被嵌入到可能会失败的系统中。最后，该项目将开发生成建模和反演算法的应用程序，用于建模大脑成像数据，包括使用不同模式的同步记录。该奖项反映了NSF的法定使命，并被认为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。

The research in this project lies at the boundary of statistics and machine learning, and is focused on studying new families of statistical models. A generative model is an algorithm that transforms random inputs into synthesized data to mimic data found in a naturally occurring dataset, such as a database of images. The research will explore theory, algorithms, and applications of generative models to gain insight into phenomena observed in practice but poorly understood in terms of mathematical principles. The work will also pursue new applications of generative models in computational neuroscience, at scales from the cellular level to the macro level of human cognition. Anticipated outcomes of the research include development of software that implements new methodology, training of graduate students across traditional disciplines, and the introduction of modern statistics and machine learning to undergraduates through research projects based on this work.The technical objectives of the project include four interrelated aims. First is to investigate the statistical properties of variational programs that are widely used in deep learning, and to develop new approaches to building generative models for novel data types. The second aim is to explore new algorithms to solve inverse problems based on generative models. Third, a new form of robust estimation will be studied where a model is corrupted after it has been constructed on data. Model repair is motivated from the fact that increasingly large statistical models, including neural networks, are being embedded in systems that may be subject to failure. Finally, the project will develop applications of generative modeling and inversion algorithms for modeling brain imaging data, including the use of simultaneous recordings in different modalities.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.