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Explore mathematical foundations for approximating high-dimensional functions through this comprehensive workshop featuring leading researchers in multivariate approximation theory, high-dimensional integration, and non-parametric regression. Discover how modern approaches overcome the curse of dimensionality by leveraging structural assumptions such as low intrinsic dimensionality, partial separability, and sparse representations in basis functions. Learn about multilevel weighted least squares polynomial approximation, tensor train algorithms for stochastic PDE problems, and approximation of generalized ridge functions in high dimensions. Examine ridge functions and their sums, sparse additive functions, and optimal sampling techniques in weighted least-squares methods for high-dimensional approximation. Delve into concentration properties of tempered posteriors and their variational approximations, recovery of ridge functions in uniform norm, and score estimation with infinite-dimensional exponential families. Understand isotonic regression applications in general dimensions and gain insights into the rich theoretical framework that has emerged over the past decade for addressing complex problems in science and engineering involving unknown processes dependent on numerous parameters.
