Entropy and "-capacity of sets in func-tional spaces

By A. Kolmogorov, V. Tikhomirov. 1961

Subfields: Statistical Learning Theory, Information Theory

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In Statistical Learning Theory

1. Stefan Wager
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Citations in the corpus

• Analysis of a Random Forests Model (2010, methodology): “It is well known that the ε -entropy as ε ↓ 0 (Kolmogorov and Tihomirov [31]), where Here we have an interesting interpretation of the dimension reduction phenomenon: Working with Lipschitz functions on S (that is, s = 0) is roughly equivalent to working with functions on R d for which all [( d/S )…”
• Additive models with trend filtering (2017, methodology): “Some nice contributions are given in Lin and Zhang [2006], Ravikumar et al. [2009], Meier et al. [2009], all primarily focused on fitting splines for component functions and achieving sparsity through a group lasso type penalty. In other even more recent and interesting work sparse additive models, ”
• Optimal rates of statistical seriation (2016, background): “First recall some standard definitions that date back at least to [KT61].”
• Unsupervised Risk Estimation with only Structural Assumptions (2016, methodology): “…Bayesian hypothesis test whose performance is justified via a novel notion of identifiability index, using classical tools such as metric entropy (Kolmogorov & Tikhomirov, 1959; Lorentz, 1966), fractional covering numbers (Lovász, 1975), and Lipschitz concentration of Gaussians (Tsirelson et…”
• The Riemann boundary value problem on non-rectifiable curves and related questions (2014, background): “This characteristic of sets in a metric space was introduced first by Kolmogorov and Tikhomirov [14].”
• Covering Numbers for Convex Functions (2012, background): “…Guntuboyina is with the Department of Statistics, University of California, Berkeley, CA 94720 USA e-mail: aditya@stat.berkeley.du B. Sen is with the Department of Statistics, Columbia University, New York, NY 10027 USA e-mail: bodhi@stat.columbia.edu. characterize optimal rates of convergence.”
• The spatial distribution in infinite dimensional spaces and related quantiles and depths (2014, unknown): “, [19]).”