2010/08/01 by Guillaume Lecué, Shahar Mendelson · 1 citation
Computer Science · Mathematics · #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques #math.ST #stat.TH
paper · pdf · doi:10.3150/09-bej225
published as Bernoulli 2010, Vol. 16, No. 3, 605-613 · Published in at http://dx.doi.org/10.3150/09-BEJ225 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2010/08/01 · arxiv created 2011/02/24 · arxiv updated 2011/02/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function T and the learning class F, the excess risk of the empirical risk minimization algorithm is lower bounded by \frac𝔼supq∈ QGq√(n)δ where (Gq)q∈Q is a canonical Gaussian process associated with Q (a well chosen subset of F) and δ is a parameter governing the oscillations of the empirical excess risk function over a small ball in F.