haldensify: Cross-validated HAL Conditional Density Estimation
In haldensify: Highly Adaptive Lasso Conditional Density Estimation

Description Usage Arguments Details Value Note Examples

Cross-validated HAL Conditional Density Estimation

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,
  hal_basis_list = NULL,
  ...
)

`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 constant `numeric` vector or `NULL`.
`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. 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 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` via its argument `lambda`.
`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.
`hal_basis_list`	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.

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.

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.

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))
)