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.
