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The spaces of multivariate functions that can be implemented by a network are determined by the structure of the network, the set of simple functions, and its multiplicative parameters. A great deal of theoretical work has gone into characterizing these function spaces. Most universal approximation theorems are in one of two classes.
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 ]
Aside from their empirical performance, activation functions also have different mathematical properties: Nonlinear When the activation function is non-linear, then a two-layer neural network can be proven to be a universal function approximator. [6] This is known as the Universal Approximation Theorem. The identity activation function does not ...
2 Network properties. 3 Network theory applications. 4 Networks with certain properties. 5 Other terms. ... Network theorems. Max flow min cut theorem; Menger's theorem;
Linear regression plays an important role in the subfield of artificial intelligence known as machine learning. The linear regression algorithm is one of the fundamental supervised machine-learning algorithms due to its relative simplicity and well-known properties. [34]
The standard softmax function is often used in the final layer of a neural network-based classifier. Such networks are commonly trained under a log loss (or cross-entropy ) regime, giving a non-linear variant of multinomial logistic regression.
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.
VC theory covers at least four parts (as explained in The Nature of Statistical Learning Theory [1]): Theory of consistency of learning processes What are (necessary and sufficient) conditions for consistency of a learning process based on the empirical risk minimization principle? Nonasymptotic theory of the rate of convergence of learning ...