kernlab (version 0.9-7)

kmmd: Kernel Maximum Mean Discrepancy.

Description

The Kernel Maximum Mean Discrepancy kmmd performs a non-parametric distribution test.

Usage

## S3 method for class 'matrix':
kmmd(x, y, kernel="rbfdot",kpar="automatic", alpha = 0.05, asymptotic = FALSE,  replace = TRUE, ntimes = 150, frac = 1,  ...)
## S3 method for class 'kernelMatrix':
kmmd(x, y, Kxy, alpha = 0.05, asymptotic = FALSE,  replace = TRUE, ntimes = 100, frac = 1,  ...)
## S3 method for class 'list':
kmmd(x, y, kernel="rbfdot",kpar="automatic", alpha = 0.05, asymptotic = FALSE,  replace = TRUE, ntimes = 150, frac = 1,  ...)

Arguments

x

data values, in a matrix, list, or kernelMatrix

y

data values, in a matrix, list, or kernelMatrix

Kxy

kernlMatrix between $x$ and $y$ values (only for the kernelMatrix interface)

kernel

the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a dot product between two vector arguments. kernlab provides the most popular kernel functions which can

kpar

the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. Valid parameters for existing kernels are :

• sigmainverse kernel width for the Radial Basis

alpha

the confidence level of the test (default: 0.05)

asymptotic

calculate the bounds asymptotically (suitable for smaller datasets) (default: FALSE)

replace

use replace when sampling for computing the asymptotic bounds (default : TRUE)

ntimes

number of times repeating the sampling procedure (default : 150)

frac

fraction of points to sample (frac : 1)

...

additional parameters.

Value

• An S4 object of class kmmd containing the results of whether the H0 hypothesis is rejected or not. H0 being that the samples $x$ and $y$ come from the same distribution. The object contains the following slots :
• H0
  is H0 rejected (logical)
• AsympH0
  is H0 rejected according to the asymptotic bound (logical)
• kernelf
  the kernel function used.
• mmdstats
  the test statistics (vector of two)
• Radbound
  the Rademacher bound
• Asymbound
  the asymptotic bound
• see kmmd-class for more details.

Details

kmmd calculates the kernel maximum mean discrepancy for samples from two distributions and conducts a test as to whether the samples are from different distributions with level alpha.

References

Gretton, A., K. Borgwardt, M. Rasch, B. Schoelkopf and A. Smola A Kernel Method for the Two-Sample-Problem Neural Information Processing Systems 2006, Vancouver http://www.kyb.mpg.de/publications/attachments/mmd_final_4193[1].pdf

See Also

ksvm

Examples

# create data
x <- matrix(runif(300),100)
y <- matrix(runif(300)+1,100)


mmdo <- kmmd(x, y)

mmdo