"KernelDensityEstimation" (Machine Learning Method)
- Method for LearnDistribution.
- Models probability density with a mixture of simple distributions.
Details & Suboptions
- "KernelDensityEstimation" is a nonparametric method that models the probability density of a numeric space with a mixture of simple distributions (called kernels) centered around each training example, as in KernelMixtureDistribution.
- The probability density function for a vector is given by for a kernel function , kernel size and a number of training examples m.
- The following options can be given:
Method "Fixed" kernel size method "KernelSize" Automatic size of the kernels when Method"Fixed" "KernelType" "Gaussian" type of kernel used "NeighborsNumber" Automatic kernel size expressed as a number of neighbors
- Possible settings for "KernelType" include:
"Gaussian" each kernel is a Gaussian distribution "Ball" each kernel is a uniform distribution on a ball
- Possible settings for Method include:
"Adaptive" kernel sizes can differ from each other "Fixed" all kernels have the same size
- When "KernelType""Gaussian", each kernel is a spherical Gaussian (product of independent normal distributions ), and "KernelSize" h refers to the standard deviation of the normal distribution.
- When "KernelType""Ball", each kernel is a uniform distribution inside a sphere, and "KernelSize" refers to the radius of the sphere.
- The value of "NeighborsNumber"k is converted into kernel size(s), so that a kernel centered around a training example typically "contains" k other training examples. If "KernelType""Ball", "contains" refers to examples that are inside the ball. If "KernelType""Gaussian", "contains" refers to examples that are inside a ball of radius h where n is the dimension of the data.
- When Method"Fixed" and "NeighborsNumber"k, a unique kernel size is found such that training examples contain on average k other examples.
- When Method"Adaptive" and "NeighborsNumber"k, each training example adapts its kernel size such that it contains about k other examples.
- Because of preprocessing, the "NeighborsNumber" option is typically a more convenient way to control kernel sizes than "KernelSize". When Method"Fixed", the value of "KernelSize" supersedes the value of "NeighborsNumber".
- Information[LearnedDistribution[…],"MethodOption"] can be used to extract the values of options chosen by the automation system.
- LearnDistribution[…,FeatureExtractor"Minimal"] can be used to remove most preprocessing and directly access the method.
Examplesopen allclose all
Basic Examples (3)
Look at the distribution Information:
Use SynthesizeMissingValues to impute missing values using the learned distribution:
Use ComputeUncertainty to obtain the uncertainty on the result:
Increase MaxIterations to improve the estimation precision: