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

"rvm"(x, data=NULL, ..., subset, na.action = na.omit)
"rvm"(x, ...)
"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$double.eps, minmaxdiff = 1e-3, cross = 0, fit = TRUE, ... , subset, na.action = na.omit) 
"rvm"(x, y, type = "regression", kernel = "stringdot", kpar = list(length = 4, lambda = 0.5), alpha = 5, var = 0.1, var.fix = FALSE, iterations = 100, verbosity = 0, tol = .Machine$double.eps, minmaxdiff = 1e-3, cross = 0, fit = TRUE, ..., subset, na.action = na.omit)

Arguments

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 with the string kernel). Note, that the intercept is always excluded, whether given in the formula or not.

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.

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 "Gaussian"
polydot Polynomial kernel
vanilladot Linear kernel
tanhdot Hyperbolic tangent kernel
laplacedot Laplacian kernel
besseldot Bessel kernel
anovadot ANOVA RBF kernel
splinedot Spline kernel
stringdot String 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".

length, lambda, normalized for the "stringdot" kernel where length is the length of the strings considered, lambda the decay factor and normalized a logical parameter determining if the kernel evaluations should be normalized.

Hyper-parameters for user defined kernels can be passed through the kpar parameter as well. In the case of a Radial Basis kernel function (Gaussian) kpar can also be set to the string "automatic" which uses the heuristics in sigest to calculate a good sigma value for the Gaussian RBF or Laplace kernel, from the data. (default = "automatic").

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, which causes an error if NA cases are found. (NOTE: If given, this argument must be named.)

...

additional parameters

Value

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

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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