Skip to content

Latest commit

 

History

History
37 lines (30 loc) · 1.84 KB

README.md

File metadata and controls

37 lines (30 loc) · 1.84 KB

Wild bootstrap Kernel Tests

Two kernel test are implemented in this package

  • MMD Maximum mean discrepancy kernel two-sample test.
  • HSIC Hilbert Schmidt Independence Criterion - independence test.

The wild bootstrap MMD test verifies the hypothesis that X has the same distribution as Y. The wild bootstrap HSIC test verifies the hypothesis that X and Y are independent. For the details see 'A Wild Bootstrap for Degenerate Kernel Tests' http://arxiv.org/abs/1408.5404. See example.m for the sample code.

Syntax

Both tests share the same syntax

RESULTS = wildMMD(X,Y)
RESULTS = wildMMD(X,Y,Name,Value)

RESULTS = wildHSIC(X,Y)
RESULTS = wildHSIC(X,Y,Name,Value)

Arguments

X and Y are arrays of the observations. Each row contains a single observation, each column contains single dimension of all observations. X and Y must have the same number of observations.

The named arguments can be any of:

  • 'Test' : if 1 the first flavor of the test is used, if 2 the second flavor is used - the differences between flavors are described in 'A Wild Bootstrap for Degenerate Kernel Tests'. The default is value is 1.
  • 'Alpha' : test level, default value is 0.05.
  • 'Kernel': function that takes two arrays X,Y, both of dimension m by d, and returns kernel matrix K of size m by m such that K(i,j) = k(X(i,:),Y(j,:)) where k is a kernel function. See rbf_dot for the default implementation.
  • 'WildBootstrap': function that returns wild bootstrap process. See bootstrap_series function in util directory for the default implementation.
  • 'NumBootstrap' : number of bootstrap re-sampling. Default value is 300.

Output The Output RESULTS contains the following fields:

  • testStat : the value of test statistic.
  • quantile : test critical value.
  • reject : 1 iff null hypothesis is rejected by the test.