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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 ...
In statistics, originally in geostatistics, kriging or Kriging (/ ˈkriːɡɪŋ /), also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. [1]
A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. [1][2][3][4][5][6][7][8] The concept constitutes an intensional definition ...
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. [1] The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings ...
The converged ensemble is a Gaussian process whose mean is the ridgeless kernel regression estimator and whose variance vanishes on the training points. Here, the neural network is a scalar function trained on inputs drawn from the unit circle.
Kernel regression. In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y. In any nonparametric regression, the conditional expectation of a variable relative to a variable may be written:
The hyperparameters typically specify a prior covariance kernel. In case the kernel should also be inferred nonparametrically from the data, the critical filter can be used. Smoothing splines have an interpretation as the posterior mode of a Gaussian process regression.
In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of vectors while the output space is a space of scalars.