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.
Diffeomorphism-based fea- ture learning using Poincaré inequalities on augmented input space.Journal of Machine Learning Research, 26(139):1–31, June 2025
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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.