Compute quantile regression via accelerated gradient descent using Huber approximation, warm start based on data subset

Compute quantile regression via accelerated gradient descent using Huber approximation, warm start based on data subset

fit_approx_quantile_model(
  X,
  y,
  X_sub,
  y_sub,
  tau,
  init_beta,
  mu = 1e-15,
  maxiter = 100000L,
  beta_tol = 1e-04,
  check_tol = 1e-06,
  intercept = 1L,
  num_samples = 1000,
  warm_start = 1L,
  scale = 1L,
  lambda = 0,
  min_delta = 1e-10
)

Arguments

X

design matrix

y

outcome vector

X_sub

subset of X matrix to use for "warm start" regression

y_sub

subset of y to use for "warm start" regression

tau

target quantile

init_beta

initial guess at beta

mu

neighborhood over which to smooth

maxiter

maximum number of iterations to run

beta_tol

tolerance for largest element of gradient, used for early stopping

check_tol

loss function change tolerance for early stopping

intercept

location of the intercept column, using R's indexing

num_samples

number of samples used for subset of matrix used for warm start

warm_start

integer indicating whether to "warm up" on a subsample of the data

scale

whether to scale x & y variables

lambda

optional lasso penalty weight

min_delta

smallest allowed step size for gradient descent