Gaussian Process
Synopsis
This operator is an implementation of Gaussian Process (GP) which is a probabilistic method both for classification and regression.
Description
A Gaussian process is a stochastic process whose realizations consist of random values associated with every point in a range of times (or of space) such that each such random variable has a normal distribution. Moreover, every finite collection of those random variables has a multivariate normal distribution. Gaussian processes are important in statistical modeling because of properties inherited from the normal. For example, if a random process is modeled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include: the average value of the process over a range of times; the error in estimating the average using sample values at a small set of times.
Gaussian processes (GPs) extend multivariate Gaussian distributions to infinite dimensionality. Formally, a Gaussian process generates data located throughout some domain such that any finite subset of the range follows a multivariate Gaussian distribution. Gaussian Process is a powerful non-parametric machine learning technique for constructing comprehensive probabilistic models of real world problems. They can be applied to geostatistics, supervised, unsupervised and reinforcement learning, principal component analysis, system identification and control, rendering music performance, optimization and many other tasks.
Input
training set
This input port expects an ExampleSet. This operator cannot handle nominal attributes; it can be applied on data sets with numeric attributes. Thus often you may have to use the Nominal to Numerical operator before the application of this operator.
Output
model
The Gaussian Process is applied and the resultant model is delivered from this output port. This model can now be applied on unseen data sets.
example set
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.
Parameters
Kernel type
The type of the kernel function is selected through this parameter. Following kernel types are supported:rbf, cauchy, laplace, poly, sigmoid, Epanechnikov, gaussian combination, multiquadric.
Kernel lengthscale
This parameter specifies the lengthscale to be used in all kernels.
Kernel degree
这是内核parameter degree. This is only available when thekernel typeparameter is set topolynomialorepachnenikov.
Kernel bias
This parameter specifies the bias to be used in the poly kernel.
Kernel sigma1
这是内核parameter sigma1. This is only available when thekernel typeparameter is set toepachnenikov,gaussian combinationormultiquadric.
Kernel sigma2
这是内核parameter sigma2. This is only available when thekernel typeparameter is set togaussian combination.
Kernel sigma3
这是内核parameter sigma3. This is only available when thekernel typeparameter is set togaussian combination.
Kernel shift
这是内核parameter shift. This is only available when thekernel typeparameter is set tomultiquadric.
Kernel a
这是内核parameter a. This is only available when thekernel typeparameter is set tosigmoid
Kernel b
这是内核parameter b. This is only available when thekernel typeparameter is set tosigmoid
Max basis vectors
This parameter specifies the maximum number of basis vectors to be used.
Epsilon tol
This parameter specifies the tolerance for gamma induced projections.
Geometrical tol
This parameter specifies the tolerance for geometry induced projections.