kernlab (version 0.9-7)

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 containg the training data or a kernel matrix of class kernelMatrix of the training data or a list of character vectors (for use w

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 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<

...

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 :
• 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)
• ...

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 [object Object],[object Object],[object Object]

ksvm # 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") regression nonlinear