foba (version 0.1)

predict.foba: Make predictions or extract coefficients from a fitted foba model

Description

foba() returns a path of variable addition and deletion. predict.foba() allows one to extract a prediction, or coefficients at any desired sparsity level.

Usage

predict.foba(object, newx, k, type=c("fit","coefficients"),...)

Arguments

object

A fitted foba object.

newx

If type="fit", then newx should be the x values at which the fit is required. If type="coefficients", then newx can be omitted.

k

The sparsity level. That is, the number of selected variables for the fitted model.

type

If type="fit", predict returns the fitted values. If type="coefficients", predict returns the coefficients. Abbreviations allowed.

...

further arguments passed to or from other methods.

Value

Return either a "coefficients" object or a "fitted value" object, at the desired sparsity level.A coefficients object is a list containing the following components:

coefficients

coefficients of ridge regression solution using selected.variables

intercept

the intercept value

selected.variables

variables with non-zero coefficients

A "fitted value" object contains the following additional component:

fit

the predicted response for the data newx

Details

FoBa for least squares regression is described in [Tong Zhang (2008)]. This implementation supports ridge regression.

References

Tong Zhang (2008) "Adaptive Forward-Backward Greedy Algorithm for Learning Sparse Representations", Rutgers Technical Report (long version).

Tong Zhang (2008) "Adaptive Forward-Backward Greedy Algorithm for Sparse Learning with Linear Models", NIPS'08 (short version).

See Also

print.foba and foba

Examples

data(boston)

model <- foba(boston$x,boston$y,s=20,nu=0.9)

### make predictions at the values in x, at sparsity level 5

py <- predict(model, boston$x, k=5, type="fit")

print(paste("mean squared error =", mean((py$fit-boston$y)^2)))

### extract the coefficient vector at sparsity level 5
coef <- predict(model, k=5, type="coef")
print("top five variables:")
coef$selected.variables