This three-year, $260,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund research towards designing optimal statistical learning procedures through precise medium-dimensional asymptotic analysis. The grantee, Columbia University, will develop a novel analytical framework to quantitatively characterize the performance of diverse learning algorithms and provide guidance on designing optimal learning procedures. This work aims to fill gaps in theoretical understanding of ubiquitous statistical models, with a focus on scenarios where the number of parameters (P) scales linearly with the number of observations (N). Outcomes will include determining performance limits of broad learning method classes and evaluating gaps between information-theoretic bounds and existing algorithm performance. Insights gained from this research are expected to inform the development of next-generation data science and artificial intelligence technologies.
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