kernlab (version 0.9-13)

rvm: 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

## S3 method for class 'formula':
rvm(x, data=NULL, ..., subset, na.action = na.omit)

## S3 method for class 'vector': rvm(x, ...)

## S3 method for class 'matrix': rvm(x, y, type="regression", kernel="rbfdot", kpar="automatic", alpha= ncol(as.matrix(x)), 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)

## S3 method for class 'list': rvm(x, y, type = "regression", kernel = "stringdot", kpar = list(length = 4, lambda = 0.5), alpha = 5, 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. When not using a formula x can be a matrix or vector containing the training data or a kernel matrix of class kernelMatrix of the training data or a list of character vectors (for use
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
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 :

  • sigmainverse kernel width for the Radial

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 equal 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<
...
additional parameters

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 :
  • alphaThe resulting relevance vectors
  • alphaindexThe index of the resulting relevance vectors in the data matrix
  • nRVNumber of relevance vectors
  • RVindexThe indexes of the relevance vectors
  • errorTraining error (if fit = TRUE)
  • ...

Details

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

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

Run this code
# 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")

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