Team: S. Foucart (lead), G. Paouris, N. Veldt

Synopsizing points

• Revisit a venerable Approximation Theory topic through the modern themes of Data Science, e.g. computability, data variety, uncertainties, etc.

• Reinforce algorithm trustworthiness by emphasizing worst-case over average-case scenarios, e.g. via principled hyperparameter selection

• Compare the resulting analytical learning theory to the more popular statistical learning theory

• Removal of any statistical assumption balanced by the need for a priori information (i.e., a model)

Related grants

• NSF CDS&E-MSS: Optimal Recovery in the Age of Data Science, 2021-24 (PI: S. Foucart)

Recent relevant papers 

• S. F., N. Hengartner. Worst-case learning under a multi-fidelity model.

• S. Foucart, C. Liao. Radius of information for two intersected centered hyperellipsoids and implications in optimal recovery from inaccurate data. Journal of Complexity, 83, 101841, 2024. (doi)

• S. Foucart, C. Liao. S-procedure relaxation: a case of exactness involving Chebyshev centers. (arXiv)

• S. Foucart, C. Liao, N. Veldt. On the optimal recovery of graph signals. SampTA 2023. (doi)

• S. Foucart, G. Paouris. Near-optimal estimation of linear functionals with log-concave observation errors. Information and Inference, 2/4, iaad038, 2023. (doi)

• S. Foucart. Full recovery from point values: an optimal algorithm for Chebyshev approximability prior. Advances in Computational Mathematics, 49, 57, 2023. (doi)

• S. Foucart, C. Liao. Optimal recovery from inaccurate data in Hilbert spaces: regularize, but what of the parameter? Constructive Approximation, 57, 489-520, 2023. (doi)

• S. Foucart, C. Liao, S. Shahrampour, Y. Wang. Learning from non-random data in Hilbert spaces: an optimal recovery perspective. Sampling Theory, Signal Processing, and Data Analysis, 20, 5, 2022. (doi)

• M. Ettehad, S. Foucart. Instances of computational optimal recovery: dealing with observation errors. SIAM/ASA Journal on Uncertainty Quantification, 9/4, 1438-1456, 2021. (doi)

• S. Foucart. Instances of computational optimal recovery: refined approximability models. Journal of Complexity, 62, 101503, 2021. (doi)

Additional resources

• GitHub repository: https://github.com/foucart/COR