f {NORMA}

Predictor Function

Description

Computes the predictor function of a general noise SVR based on NORMA optimization.

Usage

f(point, t, x, alpha, beta, f_0, kernel = function(x, y, gamma) {    
  exp(-gamma * (norm(x - y, type = "2")^2)) }, gamma, no_beta)

Arguments

point

numeric with the value of the point where we want to evaluate the predictor function.

t

time parameter value indicating the iteration we want to consider.

x

matrix containing training points. Each row must be a point.

alpha

matrix representing \alpha parameters of NORMA optimization in each iteration, one per row.

beta

numeric representing \beta parameter of NORMA optimization in each iteration.

f_0

initial hypothesis.

kernel

kernel function to use.

gamma

gaussian kernel parameter \gamma.

no_beta

boolean indicating if an offset b is used (FALSE) or not (TRUE).

Value

Returns a numeric representing the prediction value.

Author(s)

Jesus Prada, [e-mail]

References

Link to the scientific paper

Kivinen J., Smola A. J., Williamson R.C.: Online learning with kernels. In: IEEE transactions on signal processing, vol. 52, pp. 2165-2176, IEEE (2004).

with theoretical background for NORMA optimization is provided below.

http://realm.sics.se/papers/KivSmoWil04(1).pdf

Examples

f(c(1,2,3),2,matrix(c(1,2,3,4,5,6),nrow=2,ncol=3,byrow=TRUE),
matrix(c(1,2,3,4,5,6),nrow=2,ncol=3,byrow=TRUE),
c(1,2),0,function(x,y,gamma=0){x%*%y},0.1,FALSE)