# Learning sources of variability from high-dimensional observational studies

arXiv: https://arxiv.org/abs/2307.13868 · HTML: https://mlsanity.com/paper/2307.13868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 60 references that are in the map.
- First posted on arXiv 26 Jul 2023.

## Builds on (most cited first, 9 of 9)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Partial Distance Correlation with Methods for Dissimilarities](https://mlsanity.com/paper/1310.2926/) (2013)
- [Entropy Balancing for Continuous Treatments](https://mlsanity.com/paper/2001.06281/) (2020)
- [hyppo: A Multivariate Hypothesis Testing Python Package](https://mlsanity.com/paper/1907.02088/) (2019)
- [The Chi-Square Test of Distance Correlation](https://mlsanity.com/paper/1912.12150/) (2019)
- [Nonparametric Estimation of Population Average Dose-Response Curves using Entropy Balancing Weights for Continuous Exposures](https://mlsanity.com/paper/2003.02938/) (2020)
- [Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges](https://mlsanity.com/paper/1702.01250/) (2017)

## Abstract (arXiv)

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.