Graduated Optimisation to solve the SLISE problem

Usage

graduated_optimisation(
  alpha,
  X,
  Y,
  epsilon,
  beta = 0,
  lambda1 = 0,
  lambda2 = 0,
  weight = NULL,
  beta_max = 20/epsilon^2,
  max_approx = 1.15,
  max_iterations = 300,
  beta_min_increase = beta_max * 5e-04,
  debug = FALSE,
  ...
)

Arguments

alpha: Initial linear model (if NULL then OLS)
X: Data matrix
Y: Response vector
epsilon: Error tolerance
beta: Starting sigmoid steepness (default: 0 == convex problem)
lambda1: L1 coefficient (default: 0)
lambda2: L1 coefficient (default: 0)
weight: Weight vector (default: NULL == no weights)
beta_max: Stopping sigmoid steepness (default: 20 / epsilon^2)
max_approx: Approximation ratio when selecting the next beta (default: 1.15)
max_iterations: Maximum number of OWL-QN iterations (default: 300)
beta_min_increase: Minimum amount to increase beta (default: beta_max * 0.0005)
debug: Should debug statement be printed each iteration (default: FALSE)
...: Additional parameters to OWL-QN

Value

lbfgs object with beta (max) and the number of iteration steps