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Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. [ 1 ] [ 2 ] [ 3 ] Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data.
Statistical learning is the ability for humans and other animals to extract statistical regularities from the world around them to learn about the environment. Although statistical learning is now thought to be a generalized learning mechanism, the phenomenon was first identified in human infant language acquisition.
VC Theory is a major subbranch of statistical learning theory. One of its main applications in statistical learning theory is to provide generalization conditions for learning algorithms. From this point of view, VC theory is related to stability, which is an alternative approach for characterizing generalization.
In general, the risk () cannot be computed because the distribution (,) is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure:
In order to develop a statistical explanation for the learning phenomena, William Kaye Estes developed the Stimulus Sampling Theory in 1950 which suggested that a stimulus-response association is learned on a single trial; however, the learning process is continuous and consists of the accumulation of distinct stimulus-response pairings.
In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant . [ 1 ]
It is especially used in the context of statistical learning theory, where it is used to study properties of statistical learning methods. The term 'growth function' was coined by Vapnik and Chervonenkis in their 1968 paper, where they also proved many of its properties. [1] It is a basic concept in machine learning. [2] [3]
In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions.