KernelModelFit [data]
fits the given dataset data using a default local kernel.
KernelModelFit [data,bw]
uses bandwidth bw for the kernel function.
KernelModelFit [data,bw,f]
uses the specified local kernel f.
KernelModelFit
KernelModelFit [data]
fits the given dataset data using a default local kernel.
KernelModelFit [data,bw]
uses bandwidth bw for the kernel function.
KernelModelFit [data,bw,f]
uses the specified local kernel f.
Details
- The KernelModelFit function performs localized data fitting using a specified kernel function.
- KernelModelFit uses fixed basis expansion, which is commonly used in data analysis fields like signal processing and financial modeling, where capturing local variations is essential.
- Possible forms of data are:
-
{y1,y2,…} equivalent to the form {{1,y1},{2,y2},…}{{x11,x12,…,y1},…} a list of independent values xij and the responses yi{{x11,x12,…}y1,…} a list of rules between input values and responses{{x11,x12,…},…}{y1,y2,…} a rule between a list of input values and a list of responses{{x11,…,y1,…},…}n fit the n^(th) column of a matrix
- The following bandwidth specifications bw can be given:
-
Automatic automatically computed bandwidth (default)h bandwidth to use{bw1,bw2,…} use a bandwidth bwi in dimension i{{n1, bw1},…} use ni kernel functions in dimension i
- With multivariate data such as {{x_(11),x_(12),... ,y_(1)},{x_(21),x_(22),... ,y_(2)},...}, the number of coordinates xi1, xi2, … should equal the number of input arguments of f.
- The kernel function f can be an arbitrary expression or one of the following values:
-
Automatic automatically pick the basis function (default)"Cauchy" 1/(1+x)2 fit a Cauchy mixture model"Constant" TemplateBox[{{x, /, 4}}, UnitBoxSeq] fit a piecewise constant combination"Gaussian" -2 x2 fit a Gaussian mixture model"Linear" TemplateBox[{{x, /, 2}}, HeavisideLambdaSeq] fit a linear piecewise combinationfun explicit function
- If an explicit kernel function f is specified, this function will receive arguments r of the form dist[x,x0]/d, with dist a distance metric, x the prediction point, x0 the central point of the local kernel function and d a scaling factor. Typically, the function f[r] should be positive for 0<=r<=1 to work well. For example, the "Gaussian" mixture model corresponds to f[r]== Exp [-2r2].
- KernelModelFit has the following options:
-
-
ConfidenceLevel 95/100 confidence level to use for parameters and predictions
Examples
open all close allBasic Examples (2)
Fit a random dataset with a mixture of Gaussians:
Add a piecewise linear approximation to a plot:
Fit a linear kernel model:
Plot the fit together with the original data:
Scope (8)
Data (2)
Fit univariate data:
Fit a function with two independent variables:
Bandwidth (2)
Specify a bandwidth:
Specify a number of kernels and a bandwidth:
Kernel (4)
Fit a Gaussian kernel:
Fit a Cauchy kernel:
Fit a linear kernel:
Fit a constant kernel:
See Also
FittedModel LocalModelFit Fit LinearModelFit SmoothKernelDistribution
Methods: GaussianMixture
Related Guides
History
Text
Wolfram Research (2025), KernelModelFit, Wolfram Language function, https://reference.wolfram.com/language/ref/KernelModelFit.html.
CMS
Wolfram Language. 2025. "KernelModelFit." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/KernelModelFit.html.
APA
Wolfram Language. (2025). KernelModelFit. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KernelModelFit.html
BibTeX
@misc{reference.wolfram_2025_kernelmodelfit, author="Wolfram Research", title="{KernelModelFit}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/KernelModelFit.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_kernelmodelfit, organization={Wolfram Research}, title={KernelModelFit}, year={2025}, url={https://reference.wolfram.com/language/ref/KernelModelFit.html}, note=[Accessed: 05-December-2025]}