Generic Chaining Upper And Lower Bounds For Stochastic Processes

By Florian Nadel. 2016

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How researchers see this paper

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The Theory of Quantum Information (2018, methodology): “The proof makes essential use of Talagrand’s chaining method [199].”
Sequential complexities and uniform martingale laws of large numbers (2015, background): “The structure and “richness” of the index set S (as given by covering numbers or, more generally, via the chaining technique [31, 33]) yield precise control on the supremum of the stochastic process.”
Learning Compact Neural Networks with Regularization (2018, methodology): “This is done by combining Mendelson’s small-ball argument with tools from generic chaining (Mendelson, 2014; Talagrand, 2006).”
Finite-sample Analysis of M-estimators using Self-concordance (2018, methodology): “On the other hand, the first step (localization of the estimate) is done via the control of the event {θ̂n / ∈ Θ1(θ∗)}, by bounding the uniform deviations of the empirical risk Ln(θ) − Ln(θ∗) via advanced tools from empirical process theory such as generic chaining [52].”
Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path? (2018, background): “Some common notions of intrinsic dimension include Vapnik–Chervonenkis (VC) Dimension (Vapnik & Chervonenkis, 2015), Rademacher/Gaussian complexity (Bartlett & Mendelson, 2002; Mohri et al., 2018; Talagrand, 2006), as well as naive parameter counting.”