Regularization in kernel learning
Shahar Mendelson,Joe Neeman +1 more
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In this article, the authors used Australian Research Council Discovery Grant DP0559465 and by the Israel Science Foundation Grant 666/06 to investigate the effect of genetic mutations on cancer.Abstract:
Supported in part by Australian Research Council Discovery Grant DP0559465 and by Israel
Science Foundation Grant 666/06.read more
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Quasi-Oracle Estimation of Heterogeneous Treatment Effects
Xinkun Nie,Stefan Wager +1 more
TL;DR: This paper develops a general class of two-step algorithms for heterogeneous treatment effect estimation in observational studies that have a quasi-oracle property, and implements variants of this approach based on penalized regression, kernel ridge regression, and boosting, and find promising performance relative to existing baselines.
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Oracle inequalities in empirical risk minimization and sparse recovery problems
TL;DR: The main tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds) as discussed by the authors.
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Mercer’s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs
Ingo Steinwart,Clint Scovel +1 more
TL;DR: In this paper, the authors show that the spectral decomposition of a positive self-adjoint integral operator T>>\sk€�€€ Þ→L>>\s€ € Þ of a continuous k yields a series representation of k in terms of the eigenvalues and -functions of ǫ k€  Þ, where Þ is the difference of two reproducing kernels.
Journal Article
On the equivalence between kernel quadrature rules and random feature expansions
TL;DR: In this paper, the authors show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels.
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Estimating conditional quantiles with the help of the pinball loss
TL;DR: This work establishes inequalities that describe how close approximate pinball risk minimizers are to the corresponding conditional quantile, and uses them to establish an oracle inequality for support vector machines that use the pinball loss.
References
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Book
The concentration of measure phenomenon
TL;DR: Concentration functions and inequalities isoperimetric and functional examples Concentration and geometry Concentration in product spaces Entropy and concentration Transportation cost inequalities Sharp bounds of Gaussian and empirical processes Selected applications References Index
Journal ArticleDOI
On the mathematical foundations of learning
TL;DR: A main theme of this report is the relationship of approximation to learning and the primary role of sampling (inductive inference) and relations of the theory of learning to the mainstream of mathematics are emphasized.
Book
Concentration Inequalities and Model Selection
TL;DR: In this article, Gaussian Processes and Gaussian Model Selection are used to estimate density estimation via model selection via statistical learning.Exponential and Information Inequalities, Gaussian processes and model selection.
Book
The volume of convex bodies and Banach space geometry
TL;DR: In this paper, the authors present a proof of the QS theorem for weak Hilbert spaces and weak cotype for weak type 2... and weak Hilbert space for weak Cotype.
Journal ArticleDOI
Local Rademacher complexities
TL;DR: New bounds on the error of learning algorithms in terms of a data-dependent notion of complexity are proposed and some applications to classification and prediction with convex function classes, and with kernel classes in particular are presented.