# Causal Inference with High-dimensional Discrete Covariates

arXiv: https://arxiv.org/abs/2405.00118 · HTML: https://mlsanity.com/paper/2405.00118/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [Probably approximately correct high-dimensional causal effect estimation given a valid adjustment set](https://mlsanity.com/paper/2411.08141/) (2024)
- [CausalSmith: A Formally Grounded, Self-Improving Agentic Framework for Automated Research in Causal Inference](https://mlsanity.com/paper/2607.22511/) (2026)
- [Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes](https://mlsanity.com/paper/2410.04996/) (2024)

## Abstract (arXiv)

When estimating causal effects from observational studies, researchers often need to adjust for many covariates to deconfound the non-causal relationship between exposure and outcome, among which many covariates are discrete. The behavior of commonly used estimators in the presence of many discrete covariates is not well understood since their properties are often analyzed under structural assumptions including sparsity and smoothness, which do not apply in discrete settings. In this work, we study the estimation of causal effects in a model where the covariates required for confounding adjustment are discrete but high-dimensional, meaning the number of categories d is comparable with or even larger than sample size n. Specifically, we show the mean squared error of commonly used regression, weighting and doubly robust estimators is bounded by fracd2n2+frac1n. We then prove the minimax lower bound for the average treatment effect is of order fracd2n2 log2 n+frac1n, which characterizes the fundamental difficulty of causal effect estimation in the high-dimensional discrete setting, and shows the estimators mentioned above are rate-optimal up to log-factors. We further consider additional structures that can be exploited, namely effect homogeneity and prior knowledge of the covariate distribution, and propose new estimators that enjoy faster convergence rates of order fracdn2 + frac1n, which achieve consistency in a broader regime. The results are illustrated empirically via simulation studies.