glmpath {glmpath} | R Documentation |
This algorithm uses predictor-corrector method to compute the entire regularization path for generalized linear models with L1 penalty.
glmpath(x, y, data, family = binomial, weight = rep(1,length(y)), lambda2 = 1e-5, max.steps = NULL, max.norm = 100*ncol(x), min.lambda = 0, max.arclength = Inf, add.newvars = 1, bshoot.threshold = 0.1, relax.lambda = 1e-8, eps = .Machine$double.eps, trace = FALSE)
x |
matrix of features |
y |
response |
data |
a list consisting of x: a matrix of features and y:
response. data is not needed if above x and y are
input separately.
|
family |
name of a family function that represents the distribution of y to be
used in the model. It must be binomial , gaussian , or
poisson . For each one, the canonical link function is used;
logit for binomial, identity for gaussian, and
log for poisson distribution. Default is binomial.
|
weight |
an optional vector of weights for observations |
lambda2 |
regularization parameter for the L2 norm of the coefficients. Default
is 1e-5.
|
max.steps |
an optional bound for the number of steps to be taken. Default is
10 * min{nrow(x), ncol(x)}.
|
max.norm |
an optional bound for the L1 norm of the coefficients. Default is
100 * ncol(x).
|
min.lambda |
an optional (lower) bound for the size of λ. Default is
0 for ncol(x) < nrow(x) cases and 1e-6 otherwise.
|
max.arclength |
an optional bound for arc length (L1 norm) of a step. If
max.arclength is extremely small, an exact nonlinear path is
produced. Default is Inf.
|
add.newvars |
add.newvars candidate variables (that are currently not in
the active set) are used in the corrector step as potential active
variables. Default is 1.
|
bshoot.threshold |
If the absolute value of a coefficient is larger than
bshoot.threshold at the first corrector step it becomes nonzero
(therefore when λ is considered to have been decreased too
far), λ is increased again. i.e. A backward distance in
λ that makes the coefficient zero is computed. Default is
0.1.
|
relax.lambda |
A variable joins the active set if |l'(β)| >
λ(1-relax.lambda ). Default is 1e-8. If no
variable joins the active set even after many (>20) steps, the user
should increase relax.lambda to 1e-7 or 1e-6, but
not more than that. This adjustment is sometimes needed because of the
numerical precision/error propagation problems. In general, the paths
are less accurate with relaxed lambda.
|
eps |
an effective zero |
trace |
If TRUE, the algorithm prints out its progress.
|
This algorithm implements the predictor-corrector method to determine the entire path of the coefficient estimates as the amount of regularization varies; it computes a series of solution sets, each time estimating the coefficients with less regularization, based on the previous estimate. The coefficients are estimated with no error at the knots, and the values are connected, thereby making the paths piecewise linear.
We thank Michael Saunders of SOL, Stanford University for providing the solver used for the convex optimization in corrector steps of glmpath.
A glmpath
object is returned.
lambda |
vector of λ values for which exact coefficients are computed |
lambda2 |
λ_2 used |
step.length |
vector of step lengths in λ |
corr |
matrix of l'(β) values (derivatives of the log-likelihood) |
new.df |
vector of degrees of freedom (to be used in the plot function) |
df |
vector of degrees of freedom at each step |
deviance |
vector of deviance computed at each step |
aic |
vector of AIC values |
bic |
vector of BIC values |
b.predictor |
matrix of coefficient estimates from the predictor steps |
b.corrector |
matrix of coefficient estimates from the corrector steps |
actions |
actions taken at each step |
meanx |
means of the columns of x |
sdx |
standard deviations of the columns of x |
xnames |
column names of x |
family |
family used |
weight |
weights used |
Mee Young Park and Trevor Hastie
Mee Young Park and Trevor Hastie (2006) L1 Regularization Path Algorithm for Generalized Linear Models - available at the authors' websites, http://www.stanford.edu/~mypark or http://stat.stanford.edu/~hastie/pub.htm.
cv.glmpath, plot.glmpath, predict.glmpath
data(heart.data) attach(heart.data) fit.a <- glmpath(x, y, family=binomial) fit.b <- glmpath(x, y, family=gaussian) detach(heart.data)