Highly Adaptive Lasso Conditional Density Estimation

Authors: Nima Hejazi, David Benkeser, and Mark van der Laan

The haldensify R package is designed to provide facilities for nonparametric conditional density estimation based on a flexible procedure proposed initially by Dı́az and van der Laan (2011). The core of the implemented methodology involves recovering conditional density estimates by performing pooled hazards regressions so as to assess the conditional hazard that an observed value falls in a given bin over the (conditional) support of the variable of interest. Such conditional density estimates are useful, for example, in causal inference problems in which the generalized propensity score (for continuous-valued exposures) must be estimated (Dı́az and van der Laan 2012, 2018; Dı́az and Hejazi 2020). haldensify implements this conditional density estimation strategy for use only with the highly adaptive lasso (HAL) (Benkeser and van der Laan 2016; van der Laan 2017; van der Laan and Benkeser 2018; Coyle et al. 2022; Hejazi, Coyle, and van der Laan 2020). Since the generalized propensity score is a key ingredient in inverse probability weighting (IPW) methods, haldensify builds on the advances of Ertefaie, Hejazi, and van der Laan (2022) and Hejazi et al. (2022) to provide nonparametric IPW estimators of the causal effects for continuous treatments, which achieve the semiparametric efficiency bound by undersmoothing along a family of HAL conditional density estimators.

For standard use, we recommend installing the package from CRAN via

install.packages("haldensify")

To contribute, install the development version of haldensify from GitHub via remotes:

remotes::install_github("nhejazi/haldensify")

A simple example illustrates how haldensify may be used to train a highly adaptive lasso model to obtain conditional density estimates:

library(haldensify)
#> haldensify v0.2.5: Highly Adaptive Lasso Conditional Density Estimation
set.seed(76924)

# simulate data: W ~ U[-4, 4] and A|W ~ N(mu = W, sd = 0.25)
n_train <- 100
w <- runif(n_train, -4, 4)
a <- rnorm(n_train, w, 0.25)

# HAL-based density estimate of A|W
haldensify_fit <- haldensify(
  A = a, W = w,
  n_bins = 10, grid_type = "equal_range",
  lambda_seq = exp(seq(-1, -10, length = 100)),
  # arguments passed to hal9001::fit_hal()
  max_degree = 3,
  reduce_basis = 1 / sqrt(n_train)
)
#> Warning in (function (X, Y, formula = NULL, X_unpenalized = NULL, max_degree = ifelse(ncol(X) >= : Some fit_control arguments are neither default nor glmnet/cv.glmnet arguments: n_folds; 
#> They will be removed from fit_control
haldensify_fit
#> HAL Conditional Density Estimation
#> Number of bins over support of A: 10
#> CV-selected lambda: 0.0016
#> Summary of fitted HAL:
#>          coef                                    term
#>  1:  5.989688                             (Intercept)
#>  2: 10.498800                      [ I(bin_id >= 2) ]
#>  3: -9.673620                      [ I(W >= -3.353) ]
#>  4:  8.686340                      [ I(bin_id >= 6) ]
#>  5: -8.272041 [ I(bin_id >= 2) ] * [ I(W >= -2.371) ]
#>  6: -8.261273                      [ I(W >= -3.109) ]
#>  7:  8.054827                      [ I(bin_id >= 7) ]
#>  8:  8.013383                      [ I(bin_id >= 4) ]
#>  9:  8.001995                      [ I(bin_id >= 5) ]
#> 10: -7.649731                      [ I(W >= -2.157) ]

We can also visualize the empirical risk (with respect to density loss) in terms of the solution path of the lasso regularization parameter:

# just use the built-in plot method
plot(haldensify_fit)

Finally, we can obtain conditional density estimates from the trained model on the training (or on new) data:

# use the built-in predict method to get predictions
pred_haldensify <- predict(haldensify_fit, new_A = a, new_W = w)
head(pred_haldensify)
#> [1] 0.2818730 0.5513780 0.4449961 0.5329549 0.8722028 0.6150810

For more details, check out the package vignette on the corresponding pkgdown site.

If you encounter any bugs or have any specific feature requests, please file an issue.

Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.

After using the haldensify R package, please cite the following:

    @article{hejazi2022efficient,
      author = {Hejazi, Nima S and Benkeser, David and D{\'\i}az, Iv{\'a}n
        and {van der Laan}, Mark J},
      title = {Efficient estimation of modified treatment policy effects
        based on the generalized propensity score},
      year = {2022},
      journal = {},
      publisher = {},
      volume = {},
      number = {},
      pages = {},
      doi = {},
      url = {https://arxiv.org/abs/2205.05777}
    }

    @article{hejazi2022haldensify-joss,
      author = {Hejazi, Nima S and {van der Laan}, Mark J and Benkeser,
        David C},
      title = {{haldensify}: Highly adaptive lasso conditional density
        estimation in {R}},
      year  = {2022},
      doi = {10.21105/joss.04522},
      url = {https://doi.org/10.21105/joss.04522},
      journal = {Journal of Open Source Software},
      publisher = {The Open Journal}
    }

    @software{hejazi2022haldensify-rpkg,
      author = {Hejazi, Nima S and Benkeser, David C and {van der Laan},
        Mark J},
      title = {{haldensify}: Highly adaptive lasso conditional density
        estimation},
      year  = {2022},
      howpublished = {\url{https://github.com/nhejazi/haldensify}},
      doi = {10.5281/zenodo.3698329},
      url = {https://doi.org/10.5281/zenodo.3698329},
      note = {{R} package version 0.2.5}
    }

• R/hal9001 – The highly adaptive lasso estimator used internally to constructed conditional density estimates.

The development of this software was supported in part through grants from the National Library of Medicine (award number T32 LM012417), the National Institute of Allergy and Infectious Diseases (award number R01 AI074345) of the National Institutes of Health, and the National Science Foundation (award number DMS 2102840).

© 2019-2024 Nima S. Hejazi

The contents of this repository are distributed under the MIT license. See below for details:

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Copyright (c) 2019-2024 Nima S. Hejazi

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