Cross-validated HAL Conditional Density Estimation
Arguments
- A
The
numeric
vector 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 density estimate. For estimation of a marginal density, specify a constantnumeric
vector orNULL
.- 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 ofA
. For bins of equal range, use"equal_range"
; consult the documentation ofcut_interval
for more information. To ensure each bin has the same number of observations, use"equal_mass"
; consult the documentation ofcut_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.- n_bins
This
numeric
value indicates the number(s) of bins into which the support ofA
is to be divided. As withgrid_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 tofit_hal
via its argumentlambda
.- smoothness_orders
A
integer
indicating the smoothness of the HAL basis functions; passed tofit_hal
. The default is set to zero, for indicator basis functions.- hal_basis_list
A
list
consisting of a preconstructed set of HAL basis functions, as produced byfit_hal
. The default ofNULL
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 includeuse_min
,reduce_basis
,return_lasso
, andreturn_x_basis
, but this list is not exhaustive. Consult the documentation offit_hal
for complete details.
Value
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
.
Details
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.
Note
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.
Examples
# simulate data: W ~ U[-4, 4] and A|W ~ N(mu = W, sd = 0.5)
set.seed(11249)
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))
)