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The Scalable Highly Adaptive Lasso

Authors: Jeremy Coyle, Nima Hejazi, and Mark van der Laan

What’s hal9001?

hal9001 is an R package providing an implementation of the scalable highly adaptive lasso (HAL), a nonparametric regression estimator that applies L1-regularized regression (i.e., the lasso) to a design matrix composed of indicator functions corresponding to a set of covariates and interactions thereof. Recent theoretical results show that HAL is endowed with several important optimality properties, making it well-suited for the estimation of highly complex functional forms while attaining fast convergence rates ((n^(1/4)) and better) when used in the estimation of nuisance functions. HAL has been quite successfully used in the construction of estimators at the intersection of semiparametric theory and nonparametric causal inference (e.g., the construction of efficient one-step or targeted minimum loss estimators).

For detailed discussions of the highly adaptive lasso estimator, consider consulting Benkeser and van der Laan (2016), van der Laan (2017a), and van der Laan (2017b), among other recent works.


To contribute, install the development version of hal9001 from GitHub via remotes:

remotes::install_github("tlverse/hal9001", build_vignettes = FALSE)


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


This minimal example shows how to use hal9001 to obtain predictions based on the Highly Adaptive Lasso. For details on the properties of the estimator, the interested reader is referred to Benkeser and van der Laan (2016) and van der Laan (2017a).

# load the hal9001 package
#> Loading required package: Rcpp
#> hal9001 v0.2.5: The Scalable Highly Adaptive Lasso

# simulate data
n <- 100
p <- 3
x <- xmat <- matrix(rnorm(n * p), n, p)
y <- x[, 1] * sin(x[, 2]) + rnorm(n, mean = 0, sd = 0.2)

# fit the HAL regression
hal_fit <- fit_hal(X = x, Y = y)
#> [1] "I'm sorry, Dave. I'm afraid I can't do that."
#>                   user.self sys.self elapsed user.child sys.child
#> enumerate_basis       0.002     0.00   0.001          0         0
#> design_matrix         0.001     0.00   0.002          0         0
#> remove_duplicates     0.005     0.00   0.004          0         0
#> reduce_basis          0.000     0.00   0.000          0         0
#> lasso                 0.226     0.02   0.247          0         0
#> total                 0.234     0.02   0.254          0         0

# training sample prediction
preds <- predict(hal_fit, new_data = x)
mean(hal_mse <- (preds - y)^2)
#> [1] 0.006991539


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


After using the hal9001 R package, please cite the following:

      author = {Coyle, Jeremy R and Hejazi, Nima S and {van der Laan}, Mark
      title = {{hal9001}: The scalable highly adaptive lasso},
      year  = {2019},
      howpublished = {\url{https://github.com/tlverse/hal9001}},
      note = {{R} package version 0.2.5},
      url = {https://doi.org/10.5281/zenodo.3558314},
      doi = {10.5281/zenodo.3558314}


© 2017-2020 Jeremy R. Coyle & Nima S. Hejazi

The contents of this repository are distributed under the GPL-3 license. See file LICENSE for details.


Benkeser, David, and Mark J van der Laan. 2016. “The Highly Adaptive Lasso Estimator.” In 2016 IEEE International Conference on Data Science and Advanced Analytics (DSAA). IEEE. https://doi.org/10.1109/dsaa.2016.93.

van der Laan, Mark J. 2017a. “A Generally Efficient Targeted Minimum Loss Based Estimator Based on the Highly Adaptive Lasso.” The International Journal of Biostatistics. De Gruyter. https://doi.org/10.1515/ijb-2015-0097.

———. 2017b. “Finite Sample Inference for Targeted Learning.” ArXiv E-Prints.