MATLAB File Help: prtRvKde
  prtRvKde - Gaussian Kernel Density Estimation Random Variable 
    Assumes independence between each of the dimensions.
    RV = prtRvKde creates a prtRvKde object with empty trainingData and
    bandwidths parameters. The trainingData must be set either directly
    or by calling the MLE method.
    RV = prtRvKde('bandwidthMode', VALUE) enforces the bandwidths to be 
    determined either using 'manual' or 'diffusion'. Setting this
    property to 'manual' requires that the bandwidths also be
    sepecified. The default, 'diffusion', uses the automatic bandwidth
    selection method discussed in
    Botev et al., Kernel density estimation via diffusion,
    Ann. Statist. Volume 38, Number 5 (2010), 2916-2957.
    RV = prtRvKde(PROPERTY1, VALUE1,...) creates a prtRvKde object RV
    with properties as specified by PROPERTY/VALUE pairs.
    A prtRvKde object inherits all properties from the prtRv class. In
    addition, it has the following properties:
    bandwidthMode    - A string specifying the method by which the
                       bandwidths are determined. Possibilities
                       {'diffusion'}, 'manual'
    bandwidths       - The bandwidths of the kernels used in each
                       dimension of the kernel density estimate. These
                       are the diagonal values of the covariance matrix
                       for the RBF kernels.
    trainingData     - The training data used to determined the kernel
                       density estimate
    minimumBandwidth - Minium bandwidth that is aloud to be estimated.
                       Diffusion based estimation can correctly 
                       identify a discrete density and infer a very
                       small bandwidth. This is sometimes undesirable
                       and causes stability issues. The default value
                       is []. If this value is empty it is estimated
                       during MLE as max(std(X)/size(X,1),eps);.
   A prtRvKde object inherits all methods from the prtRv class. The MLE
   method can be used to estimate the distribution parameters from
    % Plot a 2D density 
    ds = prtDataGenOldFaithful;
    % or using the static method
    % Diffusion bandwidth estimation can identify discrete densities
    plotPdf(mle(prtRvKde,[0; 0; 0; 1; 1; 1; 2; 2;]))
    % Comparison to ksdensity (Statistics toolbox required)
    % ksdensity() is only for 1D data
    ds = prtDataGenUnimodal;
    xlim([-5 5]), ylim([0 0.2])
    xlim([-5 5]), ylim([0 0.2])
    % Classification comparison on multi-modal data
    % We use a MAP classifier with three different RVs
    ds = prtDataGenBimodal;
    outputKde = kfolds(prtClassMap('rvs',prtRvKde),ds,5);
    outputMvn = kfolds(prtClassMap('rvs',prtRvMvn),ds,5);
    outputGmm = kfolds(prtClassMap('rvs',prtRvGmm('nComponents',2)),ds,5);
    [pfKde,pdKde] = prtScoreRoc(outputKde);
    [pfMvn,pdMvn] = prtScoreRoc(outputMvn);
    [pfGmm,pdGmm] = prtScoreRoc(outputGmm);
    grid on
    title('Comparison of MAP Classification With Different RVs')
    legend({'MAP - MVN','MAP - GMM(2)','MAP - KDE'},'Location','SouthEast')
See also
Class Details
Superclasses prtRv
Sealed false
Construct on load false
Constructor Summary
prtRvKde Gaussian Kernel Density Estimation Random Variable  
Property Summary
bandwidths Will be estimated 
dataSet The training prtDataSet, only stored if verboseStorage is true.  
dataSetSummary Structure that summarizes prtDataSet. 
isTrained Indicates if prtAction object has been trained. 
trainingData Locations of kernels 
userData User specified data 
verboseStorage Specifies whether or not to store the training prtDataset. 
Method Summary
  cdf Output the cdf of the random variable evaluated at the points specified 
  crossValidate Cross validate prtAction using prtDataSet and cross validation keys. 
  draw Draw random samples from the distribution described by the prtRv object 
Static   ezPlotPdf  
  get get the object properties 
  kfolds Perform K-folds cross-validation of prtAction 
  logPdf Output the log pdf of the random variable evaluated at the points specified 
  mle Compute the maximum likelihood estimate  
  optimize Optimize action parameter by exhaustive function maximization. 
  pdf Output the pdf of the random variable evaluated at the points specified 
  plotCdf Plot the cdf of the prtRv 
  plotLogPdf Plot the pdf of the prtRv 
  plotPdf Plot the pdf 
  run Run a prtAction object on a prtDataSet object. 
  set set the object properties 
  train Train a prtAction object using training a prtDataSet object.