Pilot Project 1

Contemporary Optimal Recovery

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)

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

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)