Fit Conditional Density Estimation for a Sequence of HAL Models

Fit Conditional Density Estimation for a Sequence of HAL Models

fit_haldensify(
  A,
  W,
  wts = rep(1, length(A)),
  grid_type = "equal_range",
  n_bins = round(c(0.5, 1, 1.5, 2) * sqrt(length(A))),
  cv_folds = 5L,
  lambda_seq = exp(seq(-1, -13, length = 1000L)),
  smoothness_orders = 0L,
  ...
)

Arguments

A

The numeric vector of observed values.

W

A data.frame, matrix, or similar giving the values of baseline covariates (potential confounders) for the observed units. These make up the conditioning set for the conditional density estimate.

wts

A numeric vector of observation-level weights. The default is to weight all observations equally.

grid_type

A character indicating the strategy to be used in creating bins along the observed support of A. For bins of equal range, use "equal_range"; consult the documentation of cut_interval for more information. To ensure each bin has the same number of observations, use "equal_mass"; consult the documentation of cut_number for details.

n_bins

This numeric value indicates the number(s) of bins into which the support of A is to be divided. As with grid_type, multiple values may be specified, in which case cross-validation will be used to choose the optimal number of bins. The default sets the candidate choices of the number of bins based on heuristics tested in simulation.

cv_folds

A numeric indicating the number of cross-validation folds to be used in fitting the sequence of HAL conditional density models.

lambda_seq

A numeric sequence of values of the regularization parameter of Lasso regression; passed to fit_hal.

smoothness_orders

A integer indicating the smoothness of the HAL basis functions; passed to fit_hal. The default is set to zero, for indicator basis functions.

...

Additional (optional) arguments of fit_hal that may be used to control fitting of the HAL regression model. Possible choices include use_min, reduce_basis, return_lasso, and return_x_basis, but this list is not exhaustive. Consult the documentation of fit_hal for complete details.

Value

A list, containing density predictions for the sequence of fitted HAL models; the index and value of the L1 regularization parameter minimizing the density loss; and the sequence of empirical risks for the sequence of fitted HAL models.

Details

Estimation of the conditional density of A|W via a cross-validated highly adaptive lasso, used to estimate the conditional hazard of failure in a given bin over the support of A.

Examples

# simulate data: W ~ U[-4, 4] and A|W ~ N(mu = W, sd = 0.5)
n_train <- 50
w <- runif(n_train, -4, 4)
a <- rnorm(n_train, w, 0.5)
# fit cross-validated HAL-based density estimator of A|W
haldensify_cvfit <- fit_haldensify(
  A = a, W = w, n_bins = 10L, lambda_seq = exp(seq(-1, -10, length = 100)),
  # the following arguments are passed to hal9001::fit_hal()
  max_degree = 3, reduce_basis = 1 / sqrt(length(a))
)