Search results
Results From The WOW.Com Content Network
Specifically, function classes that ensure the existence of a sequence {^} that satisfies are known as learnable classes. [ 1 ] It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies ( 1 ). [ 2 ]
In statistics, the Matérn covariance, also called the Matérn kernel, [1] is a covariance function used in spatial statistics, geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis on metric spaces. It is named after the Swedish forestry statistician Bertil Matérn. [2]
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.
In the adaptive control literature, the learning rate is commonly referred to as gain. [2] In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that ...
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function 1 / Γ(z) is an entire function.
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:
Proximal gradient methods provide a general framework which is applicable to a wide variety of problems in statistical learning theory. Certain problems in learning can often involve data which has additional structure that is known a priori. In the past several years there have been new developments which incorporate information about group ...
A widely used type of composition is the nonlinear weighted sum, where () = (()), where (commonly referred to as the activation function [3]) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth ...