090-hal9001.Rmd

# Highly Adaptive Lasso with `hal9001`

_Jeremy Coyle_

## Intro
## Architecture
## Other

## Previous Documentation


## Introduction

The _highly adaptive Lasso_ (HAL) is a flexible machine learning algorithm that
nonparametrically estimates a function based on available data by embedding a
set of input observations and covariates in an extremely high-dimensional space
(i.e., generating basis functions from the available data). For an input data
matrix of $n$ observations and $d$ covariates, the number of basis functions
generated is approximately $n \cdot 2^{d - 1}$. To select a set of basis
functions from among the full set generated, the Lasso is employed. The
`hal9001` R package provides an efficient implementation of this routine,
relying on the `glmnet` R package for compatibility with the canonical Lasso
implementation while still providing a (faster) custom C++ routine for using the
Lasso with an input matrix composed of indicator functions. Consider consulting
@benkeser2016hal, @vdl2015generally, @vdl2017finite for detailed theoretical
descriptions of the highly adaptive Lasso and its various optimality properties.

TODO: port documentation from https://github.com/tlverse/hal9001/blob/master/vignettes/intro_hal9001.Rmd