Collaborative Research: Elements: Software and algorithms to advance likelihood-based inference for partially observed dynamic systems via differentiation and parallelization

Automatic differentiation is a powerful computational technique that has driven recent advances in artificial intelligence and machine learning. This project will develop automatic differentiation methods for partially observed Markov process (POMP) models, which are widely used by scientists to investigate nonlinear stochastic dynamic systems such as infectious disease transmission, ecological dynamics, and other complex noisy dynamic systems. POMP models have previously proved resistant to automatic differentiation techniques. The project will develop new algorithms and a new open-source software environment, a Python library called Pypomp, that makes the methods available to scientists. In addition to automatic differentiation, Pypomp will incorporate just-in-time compilation and graphics processing unit acceleration through the JAX Python library. The project will extend Pypomp to accommodate high-dimensional collections of time series and spatiotemporal models. The investigators will develop, document, disseminate, and support Pypomp for use by the scientific community. They will demonstrate Pypomp through scientific investigations of the temporal and spatiotemporal transmission dynamics of cholera and measles. Open-source code for case studies, together with online tutorials, will help scientists use this cyberinfrastructure to develop their own analyses. The investigators will also provide guidance on best practices for using AI tools to support data analysis with Pypomp. The new methodologies will be incorporated into a full-semester time series course for master’s and PhD students, with all class materials made openly available online. The results will also be disseminated through a textbook on dynamic data analysis. Automatic differentiation for particle-filter log-likelihood estimates is technically challenging: although a particle filter often provides a good estimate of the log-likelihood, the derivative of this estimate is generally not a good estimate of the derivative of the log-likelihood. Previous approaches to this difficulty have struggled with several issues: bias if the discontinuous nature of particle resampling is ignored; high Monte Carlo variance if continuity corrections lead to numerical instability; high computational cost for algorithms that involve pairwise interactions between particles; and reduced applicability for algorithms that lose the simulation-based structure of the basic particle filter. Pypomp builds on a methodological advance called differentiated off-parameter (DOP) particle filtering which addresses these concerns. Preliminary work shows that DOP can solve the bias and variance problems while its structure avoids the high computational cost and reduced applicability of some earlier approaches. Development of Pypomp will be carried out in parallel with continued development of DOP algorithms and statistical inference methods that take advantage of these algorithms. Pypomp is designed as a general probabilistic programming framework that will implement existing methods and models while enabling new developments. The project focuses on DOP algorithms because preliminary results show that they extend current capabilities for likelihood-based inference in nonlinear, non-Gaussian, partially observed dynamic systems. Successful cyberinfrastructure requires high-quality software as well as support for the communities that adopt it. The project’s core innovations—DOP methodology and JAX-based parallelization—will therefore be combined with best practices for software engineering, documentation, benchmarking, and community support. This award by the Office of Advanced Cyberinfrastructure is jointly supported by the Section for Mathematical Sciences in the Directorate for Mathematical and Physical Sciences, and the Section for Civil, Mechanical, and Manufacturing Innovation in the Directorate for Engineering. This award reflects NSF's statutory mission and has been deemed worthy of NSF Award ID: 2607870 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Giles Hooker | Institution: University of Pennsylvania, PHILADELPHIA, PA | Award Amount: $297,157 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2607870 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2607870.html