Cross-validated HAL Conditional Density Estimation
The numeric vector observed values.
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 density estimate. For estimation of a
marginal density, specify a constant numeric vector or NULL.
A numeric vector of observation-level weights. The default
is to weight all observations equally.
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. The
default is "equal_range" since this has been found to provide better
performance in simulation experiments; however, both types may be specified
(i.e., c("equal_range", "equal_mass")) together, in which case
cross-validation will be used to select the optimal binning strategy.
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.
A numeric indicating the number of cross-validation
folds to be used in fitting the sequence of HAL conditional density models.
A numeric sequence of values of the regularization
parameter of Lasso regression; passed to fit_hal via
its argument lambda.
A integer indicating the smoothness of the
HAL basis functions; passed to fit_hal. The default
is set to zero, for indicator basis functions.
A list consisting of a preconstructed set of
HAL basis functions, as produced by fit_hal. The
default of NULL results in creating such a set of basis functions.
When specified, this is passed directly to the HAL model fitted upon the
augmented (repeated measures) data structure, resulting in a much lowered
computational cost. This is useful, for example, in fitting HAL conditional
density estimates with external cross-validation or bootstrap samples.
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.
Object of class haldensify, containing a fitted
hal9001 object; a vector of break points used in binning A
over its support W; sizes of the bins used in each fit; the tuning
parameters selected by cross-validation; the full sequence (in lambda) of
HAL models for the CV-selected number of bins and binning strategy; and
the range of A.
Estimation of the conditional density A|W through using the highly adaptive lasso to estimate the conditional hazard of failure in a given bin over the support of A. Cross-validation is used to select the optimal value of the penalization parameters, based on minimization of the weighted log-likelihood loss for a density.
Parallel evaluation of the cross-validation procedure to select tuning
parameters for density estimation may be invoked via the framework exposed
in the future ecosystem. Specifically, set plan
for future_mapply to be used internally.
# simulate data: W ~ U[-4, 4] and A|W ~ N(mu = W, sd = 0.5)
set.seed(429153)
n_train <- 50
w <- runif(n_train, -4, 4)
a <- rnorm(n_train, w, 0.5)
# learn relationship A|W using HAL-based density estimation procedure
haldensify_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))
)
#> Warning: Some fit_control arguments are neither default nor glmnet/cv.glmnet arguments: n_folds;
#> They will be removed from fit_control