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For supervised learning applications in machine learning and statistical learning theory, generalization error[1] (also known as the out-of-sample error[2] or the risk) is a measure of how accurately an algorithm is able to predict outcome values for previously unseen data. Because learning algorithms are evaluated on finite samples, the ...
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however, this ...
e. 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] In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions.
Using cross-validation, we can obtain empirical estimates comparing these two methods in terms of their respective fractions of misclassified characters. In contrast, the in-sample estimate will not represent the quantity of interest (i.e. the generalization error). [35] Cross-validation can also be used in variable selection. [36]
k. -nearest neighbors algorithm. In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, [1] and later expanded by Thomas Cover. [2] It is used for classification and regression. In both cases, the input consists of the k closest training ...
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. [1] This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application ...
Individual values that are larger than this indicate GARCH errors. To estimate the total number of lags, use the Ljung–Box test until the value of these are less than, say, 10% significant. The Ljung–Box Q-statistic follows χ 2 {\displaystyle \chi ^{2}} distribution with n degrees of freedom if the squared residuals ϵ t 2 {\displaystyle ...
Gaussian process. In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those ...