Explorations in the Mathematics of Data Science
Description
This edited volume reports on the recent activities of the new Center for Approximation and Mathematical Data Analytics (CAMDA) at Texas A&M University. Chapters are based on talks from CAMDA's inaugural conference - held in May 2023 - and its seminar series, as well as work performed by members of the Center. They showcase the interdisciplinary nature of data science, emphasizing its mathematical and theoretical foundations, especially those rooted in approximation theory.
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Content
Preface.- S-Procedure Relaxation: a Case of Exactness Involving Chebyshev Centers.- Neural networks: deep, shallow, or in between?.- Qualitative neural network approximation over R and C.- Linearly Embedding Sparse Vectors from l2 to l1 via Deterministic Dimension-Reducing Maps.- Ridge Function Machines.- Learning Collective Behaviors from Observation.- Provably Accelerating Ill-Conditioned Low-Rank Estimation via Scaled Gradient Descent, Even with Overparameterization.- CLAIRE: Scalable GPU-Accelerated Algorithms for Diffeomorphic Image Registration in 3D.- A genomic tree based sparse solver.- A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces.
