# Targeted Highly Adaptive Lasso Minimum Loss Estimation of Target Functions

arXiv: https://arxiv.org/abs/2607.03824 · HTML: https://mlsanity.com/paper/2607.03824/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 4 Jul 2026.

## Builds on (most cited first, 8 of 8)

- [Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts](https://mlsanity.com/paper/2402.01972/) (2024)
- [Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation](https://mlsanity.com/paper/2106.11009/) (2021)
- [Orthogonal prediction of counterfactual outcomes](https://mlsanity.com/paper/2311.09423/) (2023)
- [Adaptive-TMLE for the Average Treatment Effect based on Randomized Controlled Trial Augmented with Real-World Data](https://mlsanity.com/paper/2405.07186/) (2024)
- [Constructing Confidence Intervals for Infinite-Dimensional Functional Parameters by Highly Adaptive Lasso](https://mlsanity.com/paper/2507.10511/) (2025)
- [HAL-Based Plug-in Estimation with Pointwise Asymptotic Normality of the Causal Dose-Response Curve](https://mlsanity.com/paper/2406.05607/) (2024)
- [Regularized Targeted Maximum Likelihood Estimation in Highly Adaptive Lasso Implied Working Models](https://mlsanity.com/paper/2506.17214/) (2025)
- [Kernel Smoothing of the Treatment Effect CDF](https://mlsanity.com/paper/1811.06514/) (2018)

## Abstract (arXiv)

We propose a Targeted Highly Adaptive Lasso for estimation of non-pathwise differentiable functional parameters such as the dose-response curve (DRC) for continuous exposure. We assume the target function lies in the k-th order smoothness class used to define the k-th order Highly Adaptive Lasso (HAL), which can be well approximated by linear spans of k-th order spline basis functions. We construct a projection of the true target function onto a large finite dimensional working model spanned by an initial set of k-th order spline basis functions, which defines a pathwise differentiable approximation of the target functional parameter. A standard TMLE is then applied with a data-adaptive initial fit, replacing the MLE targeting step with a LASSO step over HAL spline basis functions that span the target function. We prove that the resulting Targeted HAL-MLE is pointwise asymptotically normally distributed and achieves a convergence rate determined solely by the dimension and smoothness of the target function, giving dimension free rates up till log n-factors. Through a simulation study for the DRC, we show that the Targeted HAL outperforms a HAL plug-in estimator in terms of bias and mean squared error. Targeted HAL offers a fully data-adaptive approach to inference on functional parameters without requiring sieve specification or parametric assumptions.