gelnet.lin.obj {gelnet}

Linear regression objective function value

Description

Evaluates the linear regression objective function value for a given model. See details.

Usage

gelnet.lin.obj(w, b, X, z, l1, l2, a = rep(1, nrow(X)), d = rep(1, ncol(X)),
  P = diag(ncol(X)), m = rep(0, ncol(X)))

Arguments

w

p-by-1 vector of model weights

b

the model bias term

X

n-by-p matrix of n samples in p dimensions

z

n-by-1 response vector

l1

L1-norm penalty scaling factor \lambda_1

l2

L2-norm penalty scaling factor \lambda_2

a

n-by-1 vector of sample weights

d

p-by-1 vector of feature weights

P

p-by-p feature-feature penalty matrix

m

p-by-1 vector of translation coefficients

Details

Computes the objective function value according to

\frac{1}{2n} \sum_i a_i (z_i - (w^T x_i + b))^2 + R(w)

where

R(w) = \lambda_1 \sum_j d_j |w_j| + \frac{\lambda_2}{2} (w-m)^T P (w-m)

Value

The objective function value.

See Also

gelnet