rvm {kernlab}R Documentation

Relevance Vector Machine

Description

The Relevance Vector Machine is a Bayesian model for regression and classification of identical functional form to the support vector machine. The rvm function currently supports only regression.

Usage

## S4 method for signature 'formula':
rvm(x, data=NULL, ..., subset, na.action = na.omit)

## S4 method for signature 'vector':
rvm(x, ...)

## S4 method for signature 'matrix':
rvm(x, y, type="regression", kernel="rbfdot", kpar=list(sigma=0.1),
alpha=1, var=0.1, var.fix=FALSE, iterations=100, verbosity=0, tol=
.Machine$double.eps,minmaxdiff = 1e-3, cross = 0, fit =TRUE, subset,
na.action = na.omit,...) 

Arguments

x a symbolic description of the model to be fit. Note, that an intercept is always included, whether given in the formula or not. When not using a formula x is a matrix or vector containg the variables in the model.
data an optional data frame containing the variables in the model. By default the variables are taken from the environment which `rvm' is called from.
y a response vector with one label for each row/component of x. Can be either a factor (for classification tasks) or a numeric vector (for regression).
type rvm can only be used for regression at the moment.
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 be used by setting the kernel parameter to the following strings:
  • rbfdot Radial Basis kernel function "Gaussian"
  • polydot Polynomial kernel function
  • vanilladot Linear kernel function
  • tanhdot Hyperbolic tangent kernel function
  • laplacedot Laplacian kernel function
  • besseldot Bessel kernel function
  • anovadot ANOVA RBF kernel function
  • splinedot Spline kernel
The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument.
kpar the list of hyper-parameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. For valid parameters for existing kernels are :
  • sigma inverse kernel width for the Radial Basis kernel function "rbfdot" and the Laplacian kernel "laplacedot".
  • degree, scale, offset for the Polynomial kernel "polydot"
  • scale, offset for the Hyperbolic tangent kernel function "tanhdot"
  • sigma, order, degree for the Bessel kernel "besseldot".
  • sigma, degree for the ANOVA kernel "anovadot".

Hyper-parameters for user defined kernels can be passed through the kpar parameter as well.
alpha The initial alpha vector. Can be either a vector of length equal to the number of data points or a single number.
var the initial noise variance
var.fix Keep noise variance fix during iterations (default: FALSE)
iterations Number of iterations allowed (default: 100)
tol tolerance of termination criterion
minmaxdiff termination criteria. Stop when max difference is equall to this parameter (default:1e-3)
verbosity print information on algorithm convergence (default = FALSE)
fit indicates whether the fitted values should be computed and included in the model or not (default: TRUE)
cross if a integer value k>0 is specified, a k-fold cross validation on the training data is performed to assess the quality of the model: the Mean Squared Error for regression
subset An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
na.action A function to specify the action to be taken if NAs are found. The default action is na.omit, which leads to rejection of cases with missing values on any required variable. An alternative is na.fail, which causes an error if NA cases are found. (NOTE: If given, this argument must be named.)
... additional parameters

Details

The Relevance Vector Machine typically leads to sparser models then the SVM. It also performs better in many cases (specially in regression).

Value

An S4 object of class "rvm" containing the fitted model. Accessor functions can be used to access the slots of the object which include :

alpha The resulting relevance vectors
alphaindex The index of the resulting relevance vectors in the data matrix
nRV Number of relevance vectors
RVindex The indexes of the relevance vectors
error Training error (if fit == TRUE)


...

Author(s)

Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at

References

  • Tipping, M. E.
    Sparse Bayesian learning and the relevance vector machine
    Journal of Machine Learning Research 1, 211-244
    http://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf

    See Also

    ksvm

    Examples

    # create data
    x <- seq(-20,20,0.1)
    y <- sin(x)/x + rnorm(401,sd=0.05)
    
    # train relevance vector machine
    foo <- rvm(x, y)
    foo
    # print relevance vectors
    alpha(foo)
    RVindex(foo)
    
    # predict and plot
    ytest <- predict(foo, x)
    plot(x, y, type ="l")
    lines(x, ytest, col="red")
    

    [Package kernlab version 0.6-2 Index]