Optimal rates and adaptation in the single-index model using aggregation

By St'ephane Gaiffas, Guillaume Lecué. 2007

52 citations recorded by the source corpus.

We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to the second part of Question 2 from Stone (1982) on the optimal convergence rate. The procedure constructed here has strong adaptation properties: it adapts both to the smoothness of the link function and to the unknown index. Moreover, the procedure locally adapts to the distribution of the design. We propose new upper bounds for the local polynomial estimator (which are results of independent interest) that allows a fairly general design. The behavior of this algorithm is studied through numerical simulations. In particular, we show empirically that it improves strongly over empirical risk minimization.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/60472a132fa2bd2cefe1d5fe93373fb6ee3b7d3e

Citations in the corpus

• Aggregation via empirical risk minimization (2009, unknown): “minimizes the empirical risk, and this choice turns out to be a rather efficient one, as shown by some empirical studies in [7].”
• NONPARAMETRIC ESTIMATION OF COMPOSITE FUNCTIONS (2009, unknown): “, [7, 9, 11, 26]).”
• User-friendly introduction to PAC-Bayes bounds (2021, unknown): “• single-index regression, in small dimension [77], and in high-dimension (with sparsity) [4].”