Statistical learning theory and stochastic optimization

By Olivier Catoni, Jean Picard. 2004

348 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0bbc4b35701cc3d0984f0dd0572e8bb0bd676fba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Aggregation for Gaussian regression (2007, background): “4) in regression problems have been obtained by many authors mainly for the model selection case; see, for example, [4, 5, 7, 8, 9, 10, 11, 12, 15, 23, 28, 30, 32, 42] and the references cited in these works.”
Optimal Rates of Aggregation (2003, methodology): “A sequence of positive numbers ψn is called optimal rate of aggregation for (H,F ,F ′) if – for any family of Borel functions {fλ, λ ∈ H} indexed by H and contained in F ′ there exists an estimator f̃n of f (aggregate) such that sup f∈F [ R(f̃n, f)− inf λ∈H ‖fλ − f‖2 ] ≤ Cψn, (3) for some constant C”
Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators (2006, background): “The aggregation framework considered, among others, by [34], [54], [13],[46], [49], [5], [6] is the following: take F0 a finite subset of F , our aim is to mimic (up to an 6”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, background): “, McAllester [75], Catoni [31], Audibert [4], Zhang [99, 100, 101] and references therein).”
User-friendly introduction to PAC-Bayes bounds (2021, methodology): “Many aggregates share a formal similarity with the EWA of online learning and with the Gibbs posterior of the PAC-Bayes approach, we refer the reader to [144, 106, 202, 139, 203, 42, 206, 119, 116, 64, 40, 183, 65, 60, 63, 59, 62, 126, 61].”
Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity (2008, background): “In particular, (Catoni 1999) and (Catoni 2004) establish a sharp oracle inequality, i.”
On the properties of variational approximations of Gibbs posteriors (2015, methodology): “We refer the reader to Chapter 1 in Catoni [2007] for such assumption-free bounds.”
Theory of classification : a survey of some recent advances (2005, methodology): “Other classifiers based on weighted voting schemes have been considered by Freund, Mansour, and Schapire [88], Catoni [53–55], Yang [231].”
Aggregation via empirical risk minimization (2009, methodology): “Indeed, in [4,10], optimal inequalities of the same flavor as Theorem B have been obtained (in expectation), as well as in [2], where the results are optimal up to a logarithm factor, while in [5], PAC-Bayesian bounds [4] have been obtained with respect to the empirical risk R̄n( f ) = (1/n)∑n i=1 f”
Learning by mirror averaging (2005, methodology): “This result for Gaussian regression model is more general than that of [9], page 89, because we do not assume that f and all fj , j = 1, .”
ROBUST EMPIRICAL MEAN ESTIMATORS (2011, methodology): “Catoni [12, 14] has recently developed a Pac-Bayesian approach that has applied in several problems of non parametric statistics including linear regression and classiﬁcation [1, 2, 13].”
Linear and convex aggregation of density estimators (2006, methodology): “The study of convergence properties of aggregation methods has been pioneered in [15], [6], [7] and [29].”
ℓ1-regularized linear regression: persistence and oracle inequalities (2011, neutral): “Mathematics Subject Classification (2000) 62G08 · 62J07”
Model selection for regression on a random design (2002, background): “Consequently, the procedures proposed by Barron et al. [2], Kohler [15], Wegkamp [19], Yang [21] and Catoni [9] fail to provide an adaptive estimator over such classes.”
PAC-Bayesian bounds for randomized empirical risk minimizers (2007, methodology): “Note that PAC-Bayesian bounds given by Catoni [6, 7, 8] usually apply to ”randomized estimators”.”