Cross-validated HAL Conditional Density Estimation
numeric vector observed values.
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
numeric vector of observation-level weights. The default
is to weight all observations equally.
character indicating the strategy to be used in
creating bins along the observed support of
A. For bins of equal
"equal_range"; consult the documentation of
cut_interval for more information. To ensure each
bin has the same number of observations, use
the documentation of
cut_number for details. The
"equal_range" since this has been found to provide better
performance in simulation experiments; however, both types may be specified
c("equal_range", "equal_mass")) together, in which case
cross-validation will be used to select the optimal binning strategy.
numeric value indicates the number(s) of bins into
which the support of
A is to be divided. As with
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.
numeric indicating the number of cross-validation
folds to be used in fitting the sequence of HAL conditional density models.
numeric sequence of values of the regularization
parameter of Lasso regression; passed to
integer indicating the smoothness of the
HAL basis functions; passed to
fit_hal. The default
is set to zero, for indicator basis functions.
list consisting of a preconstructed set of
HAL basis functions, as produced by
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
that may be used to control fitting of the HAL regression model. Possible
return_x_basis, but this list is not exhaustive. Consult the
fit_hal for complete details.
Object of class
haldensify, containing a fitted
hal9001 object; a vector of break points used in binning
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
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
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)) )