Vapnik, Vladimir Naumovich. Statistical learning theory / Vladimir N. Vapnik p. cm (Adaptive and learning systems for signal processing, communications, and. In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition. An Overview of Statistical Learning Theory. Vladimir N. Vapnik. Abstract— Statistical learning theory was introduced in the late. 's. Until the 's it was a.
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Statistical Learning Theory. Fundamentals Learning problem: the problem of choosing the desired . 2 When a p.d.f. F(z) is defined on Z and the functional is. learning theory (Vapnik, , Vapnik, ), a brief overview over statistical Statistical learning theory (SLT) is a theoretical branch of machine learning and. Page 1. Statistics for. Engineering and. Information Science. Vladimir N. Vapnik. The Nature of Statistical. Learning Theory. Second Edition. Springer. Page 2.
The rest of the paper is organized as follows.
Section 2 presents the main idea and concepts in the theory. Section 3 discusses Regularization Networks and Support Vector Machines, two important techniques which produce outputs of the form of equation 1. The relationship is probabilistic because generally an element of X does not??
This can be formalized assuming that an unknown probability distribution P x, y is dened over the set X Y. The problem of learning consists in, given the data set D , providing an estimator, that is a function f : X Y , that can be used, given any value of x X , to predict a value y. Another example is the case where x is a set of parameters, such as pose or facial expressions, y is a motion eld relative to a particular reference image of a face, and f x is a regression function which maps parameters to motion see for example .
In SLT, the standard way to solve the learning problem consists in dening a risk functional, which measures the average amount of error or risk associated with an estimator, and then looking for the estimator with the lowest risk. If V y, f x is the loss function measuring the error we make when we predict y by f x , then the average error, the so called expected risk, is: I [f ] X,Y Straight minimization of the empirical risk in F can be problematic.
First, it is usually an illposed problem , in the sense that there might be many, possibly innitely many, functions minimizing the empirical risk. Second, it can lead to overtting, meaning that although the minimum of the empirical risk can be very close zero, the expected risk which is what we are really interested in can be very large. SLT provides probabilistic bounds on the distance between the empirical and expected risk of any function therefore including the minimizer of the empirical risk in a function space that can be used to control overtting.
Four Periods in the Research of the Learning Problem. Pages Setting of the Learning Problem. Consistency of Learning Processes.
Bounds on the Rate of Convergence of Learning Processes.
Controlling the Generalization Ability of Learning Processes. Methods of Pattern Recognition. Methods of Function Estimation.
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