Convex surrogates derived via concentration inequalities replace the Poincaré loss J(g) for nonlinear dimension reduction, delivering suboptimality bounds for polynomials and empirical gains over iterative minimization on benchmarks.
Nonlinear dimension reduction for surrogate modeling using gradient information.Information and Inference: A Journal of the IMA, 11(4):1597–1639, December 2022
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Surrogate to Poincar\'e inequalities on manifolds for dimension reduction in nonlinear feature spaces
Convex surrogates derived via concentration inequalities replace the Poincaré loss J(g) for nonlinear dimension reduction, delivering suboptimality bounds for polynomials and empirical gains over iterative minimization on benchmarks.