The Generic Chaining

By Michel Talagrand. 2005

400 citations recorded by the source corpus.

Subfields: Finance, Management Information Systems, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/385690a1e0276d063bab960d3c7b16121d67f3e1

How researchers see this paper

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

In Finance

In Management Information Systems

In Molecular Biology

Citations in the corpus

Empirical Processes with a Bounded Ψ1 Diameter (2010, background): “Note that if T ⊂ Rn, (gi)ni=1 are standard, independent gaussians and Gt = ∑n i=1 giti then d(s, t) = ‖s− t‖2, and therefore c1γ2(T, ‖ · ‖2) ≤ E sup t∈T n∑ i=1 giti ≤ c2γ2(T, ‖ · ‖2).”
Probability and moment inequalities for sums of weakly dependent random variables, with applications (2007, methodology): “According to the course of Michel Talagrand on Generic Chaining (ENS-Paris, 2005) and Talagrand (2005), this implies for some universal constant L, that”
Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees (2011, background): “The asymptotic identity (1) arose in a recent work of Ding, Lee and Peres [17], where a useful connection between cover times, Gaussian processes, and Fernique-Talagrand majorizing measure theory [26, 41, 42] was discovered.”
Parametric estimation. Finite sample theory (2011, methodology): “We, however, follow the more recent approach inspired by the notions of generic chaining and majorizing measures due to M. Talagrand; see e.g. Talagrand (1996, 2001, 2005).”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, background): “1) that also leads to more refined generic chaining bounds (see Talagrand [88]).”
Regularization in kernel learning (2010, methodology): “, [11, 34]), used in the study of Gaussian processes.”
Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks (2019, neutral): “We write ∣f(W0, x̃) − f(W0,x)∣ ≤ ∣f(W0,c) − f(W0,x)∣ + ∣f(W0, x̃) − f(W0,c)∣ To proceed, since Xx = f(W0,x) is a Gaussian process, applying standard chaining bounds [51], we find sup ∥x−c∥`2≤ε0 ∣f(W0,c) − f(W0,x)∣ ≤ c′Γε0√d (10.”