gelnet.lin.obj: Linear regression objective function value
In gelnet: Generalized Elastic Nets

gelnet.lin.obj

R Documentation

Linear regression objective function value

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

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))
)

`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

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)

The objective function value.