gelnet.lin.obj: 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
Value
The objective function value.
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
$$R(w) = \lambda_1 \sum_j d_j |w_j| + \frac{\lambda_2}{2} (w-m)^T P (w-m)$$