Statistical learning theory
A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
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The Problem ol lnductlon and Statlstlcal
THEORY OF LEARNING AND GENERALIZAIION
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algorithm approximation bounded functions Chapter classical coefﬁcients consider construct converges in probability decision rules deﬁned deﬁnition denote density estimation described empirical distribution function empirical risk functional empirical risk minimization equality equivalence classes estimation problem exists ﬁnd ﬁnite number ﬁrst ﬁxed fulﬁlled func function F functions Q(z given set growth function holds true hyperplane ill-posed problems indicator functions inequality inference inﬁnite kemel leaming machine lemma linear loss function method metric minimize the functional minimizes the empirical necessary and sufﬁcient number of elements number of observations obtain operator equation parameters polynomial probability measure problem of estimating prove random variable rate of convergence real-valued functions right-hand side risk functional satisﬁes Section sequence set of functions set of indicator set of real-valued solution speciﬁc SRM principle structural risk minimization subset sufﬁcient conditions support vectors SV machine Theorem tion uniform convergence valid VC dimension zero