Random variable objects in the Pattern Recognition Toolbox

The Pattern Recognition Toolbox offers a set of random variable objects with a wide range of functionality. prtRv objects can compute pdf or cdf values of a random variable, be used as a random variable generator, or perform a maximum likelihood fit of a random variable from a data set.

Contents

Specifying a random variable object

If you wish to specify the parameters of the random variable, you can do so in the following manner.

 % Create a multi-variate normal random variable object
rv = prtRvMvn;
rv.mu = [1 1];         % Set the mean to be the coordinates [1 1]
rv.sigma = [1 0; 0 1]; % Specify the covariance matrix

rv.plotPdf;            % Plot the pdf

randomDraw = rv.draw(1)       % Draw one sample from this distribution

pdfVal = rv.pdf([1.5 1])      % Evaluate the pdf of this random variable
                              % at the point [1.5 1]

randomDraw =
    2.4473    1.4084
pdfVal =
    0.1405

Maximum likelihood estimation of the parameters of a prtRv

If you have a dataset that you would like to fit to a prtRv object, you can use the mle method to find the parameters. For example:

data = randn(1000,2);   % Create a zero mean 2 dimensional Normal vector

rv = rv.mle(data)       % Call the MLE function to estimate the
                        % parameters of this data set

rv = 
  prtRvMvn

  Properties:
                    name: 'Multi-Variate Normal'
        nameAbbreviation: 'RVMVN'
            isSupervised: 0
    isCrossValidateValid: 1
     covarianceStructure: 'full'
                      mu: [-0.0066 0.0440]
                   sigma: [2x2 double]
             plotOptions: [1x1 prtOptions.prtOptionsRvPlot]
          verboseStorage: 1
         showProgressBar: 1
               isTrained: 0
          dataSetSummary: []
                 dataSet: []
                userData: [1x1 struct]

You can fit any data set to any prtRv object. For example, you could fit a uniform random variable to the same set of data in the following manner:

rvUni = prtRvUniform;    % Create a uniform random variable object
rvUni = rvUni.mle(data)  % Call the MLE function

rvUni = 
  prtRvUniform

  Properties:
                    name: 'Uniform Random Variable'
        nameAbbreviation: 'RVUnif'
            isSupervised: 0
    isCrossValidateValid: 1
             upperBounds: [3.1655 2.9978]
             lowerBounds: [-3.3042 -4.1145]
             plotOptions: [1x1 prtOptions.prtOptionsRvPlot]
          verboseStorage: 1
         showProgressBar: 1
               isTrained: 0
          dataSetSummary: []
                 dataSet: []
                userData: [1x1 struct]

Note, now the parameters of rvUni are set, and you can call any of the other prtRv functions, such as plotPdf or draw:

rvUni.plotPdf;              % Plot the pdf
randomDraw = rvUni.draw(2)  % Draw 2 samples

randomDraw =
   -3.0211   -1.9934
    0.1665   -2.0092

For a list of other functions related to to prtRv objects, see prtRv. All random variable objects in the Pattern Recognition Toolbox have the same API as discussed above. For a list of all the different random variables supported, and links to their individual help entries, A list of commonly used functions

Published with MATLAB® R2012b