rvm function

Relevance Vector Machine

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.

## 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="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) 

## S4 method for signature '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 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.

• 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 "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

Details

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

Returns

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)

...

References

Tipping, M. E.

Sparse Bayesian learning and the relevance vector machine

Journal of Machine Learning Research 1, 211-244

https://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf

Author(s)

Alexandros Karatzoglou

alexandros.karatzoglou@ci.tuwien.ac.at

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")