This algorithm uses predictor-corrector method to compute the entire regularization path for Cox proportional hazards model with L1 penalty.
coxpath(data, nopenalty.subset = NULL, method = c("breslow", "efron"),
lambda2 = 1e-5, max.steps = 10 * min(n, m), max.norm = 100 * m,
min.lambda = (if (m >= n) 1e-3 else 0), max.vars = Inf,
max.arclength = Inf, frac.arclength = 1, add.newvars = 1,
bshoot.threshold = 0.1, relax.lambda = 1e-7,
approx.Gram = FALSE, standardize = TRUE,
eps = .Machine$double.eps, trace = FALSE)a list consisting of x: a matrix of features, time:
the survival time, and status: censor status with 1 if died
and 0 if censored.
a set of indices for the predictors that are not subject to the L1 penalty
approximation method for tied survival times. Approximations derived
by Breslow (1974) and Efron (1977) are available. Default is
breslow.
regularization parameter for the L2 norm of the
coefficients. Default is 1e-5.
an optional bound for the number of steps to be taken. Default is
10 * min{nrow(x), ncol(x)}.
an optional bound for the L1 norm of the coefficients. Default is
100 * ncol(x).
an optional (lower) bound for the size of \(\lambda\). When
ncol(x) is relatively large, the coefficient estimates are
prone to numerical precision errors at extremely small
\(\lambda\). In such cases, early stopping is recommended. Default
is 0 for ncol(x) < nrow(x) cases and 1e-3
otherwise.
an optional bound for the number of active variables. Default is
Inf.
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.
Under the default setting, the next step size is computed so that
the active set changes right at the next value of lambda. When
frac.arclength is assigned some fraction between 0 and 1, the
step size is decreased by the factor of frac.arclength in arc
length. If frac.arclength=0.2, the step length is adjusted so
that the active set would change after five smaller steps. Either
max.arclength or frac.arclength can be used to force
the path to be more accurate. Default is 1.
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.
If the absolute value of a coefficient is larger than
bshoot.threshold at the first corrector step it becomes
nonzero (therefore when \(\lambda\) is considered to have been
decreased too far), \(\lambda\) is increased again. i.e. A
backward distance in \(\lambda\) that makes the coefficient zero
is computed. Default is 0.1.
A variable joins the active set if \(|l'(\beta)| >
\lambda\)*(1-relax.lambda). Default is 1e-7. If no
variable joins the active set even after many (>20) steps, the user
should increase relax.lambda to 1e-6 or 1e-5,
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.
If TRUE, an approximated Gram matrix is used in predictor
steps; each step takes less number of computations, but the total
number of steps usually increases. This might be useful when the
number of features is large.
If TRUE, predictors are standardized to have a unit variance.
an effective zero
If TRUE, the algorithm prints out its progress.
A coxpath object is returned.
vector of \(\lambda\) values for which the exact coefficients are computed
\(\lambda_2\) used
vector of step lengths in \(\lambda\)
matrix of \(l'(\beta)\) values (derivatives of the log-partial-likelihood)
vector of degrees of freedom (to be used in the plot function)
vector of degrees of freedom at each step
vector of log-partial-likelihood computed at each step
vector of AIC values
vector of BIC values
matrix of coefficient estimates from the predictor steps
matrix of coefficient estimates from the corrector steps
vector of boolean values indicating the steps at which the active set changed (to be used in the plot/predict functions)
actions taken at each step
means of the columns of x
standard deviations of the columns of x
column names of x
method used
nopenalty.subset used
TRUE if the predictors were standardized before fitting
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.
Mee Young Park and Trevor Hastie (2007) L1 regularization path algorithm for generalized linear models. J. R. Statist. Soc. B, 69, 659-677.
cv.coxpath, plot.coxpath, predict.coxpath, summary.coxpath
# NOT RUN {
data(lung.data)
attach(lung.data)
fit.a <- coxpath(lung.data)
fit.b <- coxpath(lung.data, method="efron")
detach(lung.data)
# }
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