kernlab (version 0.9-13)

gausspr: Gaussian processes for regression and classification

Description

gausspr is an implementation of Gaussian processes for classification and regression.

Usage

## S3 method for class 'formula':
gausspr(x, data=NULL, ..., subset, na.action = na.omit, scaled = TRUE)
## S3 method for class 'vector':
gausspr(x,...)
## S3 method for class 'matrix':
gausspr(x, y, scaled = TRUE, type= NULL, kernel="rbfdot", kpar="automatic",
          var=1, tol=0.0005, cross=0, fit=TRUE, ... , subset, na.action = na.omit)

Arguments

x

a symbolic description of the model to be fit or a matrix or vector when a formula interface is not used. When not using a formula x is a matrix or vector containing 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 `gausspr' 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

Type of problem. Either "classification" or "regression". Depending on whether y is a factor or not, the default setting for type is classification or regression, respectively, but can be ove

scaled

A logical vector indicating the variables to be scaled. If scaled is of length 1, the value is recycled as many times as needed and all non-binary variables are scaled. Per default, data are scaled internally (both x

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. Valid parameters for existing kernels are :

• sigmainverse kernel width for the Radial Basis

var

the initial noise variance, (only for regression) (default : 0.001)

tol

tolerance of termination criterion (default: 0.001)

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, whi

...

additional parameters

Value

• An S4 object of class "gausspr" containing the fitted model along with information. Accessor functions can be used to access the slots of the object which include :
• alpha
  The resulting model parameters
• error
  Training error (if fit == TRUE)

Details

A Gaussian process is specified by a mean and a covariance function. The mean is a function of $x$ (which is often the zero function), and the covariance is a function $C(x,x')$ which expresses the expected covariance between the value of the function $y$ at the points $x$ and $x'$. The actual function $y(x)$ in any data modeling problem is assumed to be a single sample from this Gaussian distribution. Laplace approximation is used for the parameter estimation in gaussian processes for classification. The predict function can return class probabilities for classification problems by setting the type parameter to "probabilities".

References

C. K. I. Williams and D. Barber Bayesian classification with Gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(12):1342-1351, 1998 http://www.dai.ed.ac.uk/homes/ckiw/postscript/pami_final.ps.gz

See Also

predict.gausspr, rvm, ksvm, gausspr-class, lssvm

Examples

# train model
data(iris)
test <- gausspr(Species~.,data=iris,var=2)
test
alpha(test)

# predict on the training set
predict(test,iris[,-5])
# class probabilities 
predict(test, iris[,-5], type="probabilities")

# create regression data
x <- seq(-20,20,0.1)
y <- sin(x)/x + rnorm(401,sd=0.03)

# regression with gaussian processes
foo <- gausspr(x, y)
foo

# predict and plot
ytest <- predict(foo, x)
plot(x, y, type ="l")
lines(x, ytest, col="red")