"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:
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- Possible settings for "KernelType" include:
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"Gaussian" each kernel is a Gaussian distribution"Ball" each kernel is a uniform distribution on a ball
- Possible settings for Method include:
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"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.
Examples
open all close allBasic Examples (3)
Train a "KernelDensityEstimation" distribution on a numeric dataset:
Look at the distribution Information :
Obtain options information:
Obtain an option value directly:
Compute the probability density for a new example:
Plot the PDF along with the training data:
Generate and visualize new samples:
Train a "KernelDensityEstimation" distribution on a two-dimensional dataset:
Plot the PDF along with the training data:
Use SynthesizeMissingValues to impute missing values using the learned distribution:
Train a "KernelDensityEstimation" distribution on a nominal dataset:
Because of the necessary preprocessing, the PDF computation is not exact:
Use ComputeUncertainty to obtain the uncertainty on the result:
Increase MaxIterations to improve the estimation precision:
Options (4)
"KernelSize" (1)
Train a kernel mixture distribution with a kernel size of 0.2:
Evaluate the PDF of the distribution at a specific point:
Visualize the PDF obtained after training a kernel mixture distribution with various kernel sizes:
"KernelType" (1)
Train a "KernelDensityEstimation" distribution with a "Ball" kernel:
Evaluate the PDF of the distribution at a specific point:
Visualize the PDF obtained after training a kernel mixture distribution with a "Ball" and a "Gaussian" kernel:
Method (1)
Train a "KernelDensityEstimation" distribution with the "Adaptive" method:
Evaluate the PDF of the distribution at a specific point:
Visualize the PDF obtained after training a kernel mixture distribution with a "Ball" and a "Gaussian" kernel:
"NeighborsNumber" (1)
Train a kernel mixture distribution with a kernel size of about 10 neighbors:
Evaluate the PDF of the distribution at a specific point:
Visualize the PDF obtained after training a kernel mixture distribution with various kernel sizes expressed as neighbors numbers: