CAREER: Theory and Methods for Nonparametric Estimation with Neural Networks

Modern science, industry, and public decision-making increasingly depend on the ability to learn from large, complex data. Neural networks are now widely used to support decisions in areas such as health care, scientific discovery, finance, engineering, and language technologies. These tools can be powerful, but their predictions are often difficult to understand, and it is not always clear when they can be trusted. This project addresses a fundamental challenge: how to make modern data-driven methods more reliable and efficient. By developing stronger statistical foundations for neural network methods, the project will help improve the quality of data-driven decisions in settings where accuracy and uncertainty matter. These advances serve the national interest by promoting progress in science, supporting innovation, and strengthening the responsible use of artificial intelligence in applications that affect health, prosperity, and public welfare. The project will also contribute to education and workforce development by training graduate and undergraduate students in modern statistical learning. Outreach activities for high school and college students will broaden participation in data science and help prepare the future workforce. This project develops new theory and methodology for nonparametric statistical estimation using neural networks. The research will establish rigorous foundations for pretraining, a widely used strategy in machine learning, by characterizing when it improves statistical efficiency in multi-population and high-dimensional settings. It will introduce novel methods for regression and inference when data lie in complex spaces, including non-Euclidean domains and general metric spaces. The project will also develop principled approaches for uncertainty quantification and causal inference with neural networks, including methods for estimating distributional treatment effects. Theoretical guarantees will be derived for all developed methods, and their performance will be validated through simulations and real-world applications. Software implementations will be developed to facilitate the broad adoption of the developed techniques. 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. NSF Award ID: 2541747 | Program: 01002930DB NSF RESEARCH & RELATED ACTIVIT,01002627DB NSF RESEARCH & RELATED ACTIVIT,01003031DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: OSCAR HERNAN MADRID PADILLA | Institution: University of California-Los Angeles, LOS ANGELES, CA | Award Amount: $270,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2541747 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2541747.html