proximal_gradient_descent: Proximal Gradient Descent Algorithm

In hreed7/SemiCompRisksPen: Penalized Models for Semi-Competing Risks

Proximal Gradient Descent Algorithm

Description

This function runs a proximal gradient descent algorithm with backtracking similar to that presented by Wang et al. (2014).

Usage

proximal_gradient_descent(
  para,
  y1,
  y2,
  delta1,
  delta2,
  Xmat1 = matrix(nrow(length(y1)), ncol = 0),
  Xmat2 = matrix(nrow(length(y1)), ncol = 0),
  Xmat3 = matrix(nrow(length(y1)), ncol = 0),
  hazard,
  frailty,
  model,
  basis1 = NULL,
  basis2 = NULL,
  basis3 = NULL,
  basis3_y1 = NULL,
  dbasis1 = NULL,
  dbasis2 = NULL,
  dbasis3 = NULL,
  penalty,
  lambda,
  a,
  penalty_fusedcoef,
  lambda_fusedcoef,
  penalty_fusedbaseline,
  lambda_fusedbaseline,
  penweights_list,
  mu_smooth_fused,
  step_size_init = 1,
  step_size_min = 1e-06,
  step_size_max = 1e+06,
  step_size_scale = 1/2,
  ball_L2 = Inf,
  maxit = 300,
  select_tol = 1e-04,
  conv_crit = "nll_pen_change",
  conv_tol = if (lambda > 0) lambda/4 else 1e-06,
  verbose
)

Arguments

para	A numeric vector of parameters, arranged as follows: the first k_1+k_2+k_3 elements correspond to the baseline hazard parameters, then the k_1+k_2+k_3+1 element corresponds to the gamma frailty log-variance parameter, then the lastq_1+q_2+q_3 elements correspond with the regression parameters.
y1, y2	Numeric vectors of length n with (possibly censored) non-terminal and terminal event times
delta1, delta2	Numeric vectors of length n with indicators of 1 if the event was observed and 0 otherwise
Xmat1, Xmat2, Xmat3	Numeric matrices with n rows and q_1,q_2,q_3 columns containing covariates.
hazard	String specifying the form of the baseline hazard.
frailty	Boolean indicating whether a gamma distributed subject-specific frailty should be included. Currently this must be set to TRUE.
model	String specifying the transition assumption
basis1, basis2, basis3, basis3_y1	Numeric matrices with n rows and k_1,k_2,k_3 columns with piecewise/spline basis function values at the corresponding y1 and y2 values. Under semi-Markov model, basis3 represents basis derived from y_2-y_1 and basis3_y1 is unused, while under Markov model, basis3 represents basis derived from y_2 and basis3_y1 is from y_1 Not used under Weibull model.
dbasis1, dbasis2, dbasis3	Numeric matrices with n rows and k_1,k_2,k_3 columns with piecewise/spline basis function derivative values at the corresponding y1 and y2 values. Used only under Royston-Parmar model.
penalty	A string value indicating the form of parameterwise penalty to apply. "lasso", "scad", and "mcp" are the options.
lambda	The strength of the parameterwise penalty. Either a single non-negative numeric value for all three transitions, or a length 3 vector with elements corresponding to the three transitions.
a	For two-parameter penalty functions (e.g., scad and mcp), the second parameter.
penalty_fusedcoef	A string value indicating the form of the fusion penalty to apply to the regression parameters. "none" and "fusedlasso" are the options.
lambda_fusedcoef	The strength of the fusion penalty on the regression parameters. Either a single non-negative numeric value for all three transitions, or a length 3 vector with elements corresponding to the three transitions.
penalty_fusedbaseline	A string value indicating the form of the fusion penalty to apply to the baseline hazard parameters. "none" and "fusedlasso" are the options.
lambda_fusedbaseline	The strength of the fusion penalty on the regression parameters. Either a single non-negative numeric value for all three transitions, or a length 3 vector with elements corresponding to the three transitions.
penweights_list	A list of numeric vectors representing weights for each penalty term (e.g., for adaptive lasso.) Elements of the list should be indexed by the names "coef1", "coef2", "coef3", "fusedcoef12", "fusedcoef13", "fusedcoef23", "fusedbaseline12", "fusedbaseline13", and "fusedbaseline23"
mu_smooth_fused	A non-negative numeric value for the Nesterov smoothing parameter applied to the fusion penalty.
step_size_init	Positive numeric value for the initial step size.
step_size_min	Positive numeric value for the minimum allowable step size to allow during backtracking.
step_size_max	Positive numeric value for the maximum allowable step size to allow by size increase at each iteration.
step_size_scale	Positive numeric value for the multiplicative change in step size at each step of backtracking.
ball_L2	Positive numeric value for l_2 ball constraint around the origin for the regression parameters. Typically set to Inf indicating no constraint, otherwise equivalent to an extra l_2 penalty.
maxit	Positive integer maximum number of iterations.
select_tol	Positive numeric value for thresholding estimates to be equal to zero.
conv_crit	String (possibly vector) giving the convergence criterion.
conv_tol	Positive numeric value giving the convergence tolerance for the chosen criterion.
verbose	Numeric indicating the amount of iteration information should be printed to the user. Higher numbers provide more detailed information to user, but will slow down the algorithm.

Value

A list.

hreed7/SemiCompRisksPen documentation built on Dec. 15, 2024, 5:41 p.m.