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.
Sliced Inverse Regression for Dimension Reduction.Journal of the American Statistical Association, 86(414):316–327, June 1991
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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.