# Interpretable Causal Inference for Analyzing Wearable, Sensor, and Distributional Data

arXiv: https://arxiv.org/abs/2312.10569 · HTML: https://mlsanity.com/paper/2312.10569/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 52 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Wasserstein Regression](https://mlsanity.com/paper/2006.09660/) (2020)
- [Functional Regression](https://mlsanity.com/paper/1406.4068/) (2014)
- [Distribution-on-Distribution Regression via Optimal Transport Maps](https://mlsanity.com/paper/2104.09418/) (2021)
- [Characterization of Overlap in Observational Studies](https://mlsanity.com/paper/1907.04138/) (2019)
- [MALTS: Matching After Learning to Stretch](https://mlsanity.com/paper/1811.07415/) (2018)
- [Causal Inference on Distribution Functions](https://mlsanity.com/paper/2101.01599/) (2021)
- [Distributional synthetic controls](https://mlsanity.com/paper/2001.06118/) (2020)
- [High-Dimensional Spatial Quantile Function-on-Scalar Regression](https://mlsanity.com/paper/2012.10579/) (2020)
- [Effects of Epileptiform Activity on Discharge Outcome in Critically Ill Patients](https://mlsanity.com/paper/2203.04920/) (2022)
- [Shape-constrained Estimation in Functional Regression with Bernstein Polynomials](https://mlsanity.com/paper/2209.04476/) (2022)
- [Matched Machine Learning: A Generalized Framework for Treatment Effect Inference With Learned Metrics](https://mlsanity.com/paper/2304.01316/) (2023)

## Built on by (most cited first, 2 of 2)

- [Doctor Rashomon and the UNIVERSE of Madness: Variable Importance with Unobserved Confounding and the Rashomon Effect](https://mlsanity.com/paper/2510.12734/) (2025)
- [Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data](https://mlsanity.com/paper/2505.08698/) (2025)

## Abstract (arXiv)

Many modern causal questions ask how treatments affect complex outcomes that are measured using wearable devices and sensors. Current analysis approaches require summarizing these data into scalar statistics (e.g., the mean), but these summaries can be misleading. For example, disparate distributions can have the same means, variances, and other statistics. Researchers can overcome the loss of information by instead representing the data as distributions. We develop an interpretable method for distributional data analysis that ensures trustworthy and robust decision-making: Analyzing Distributional Data via Matching After Learning to Stretch (ADD MALTS). We (i) provide analytical guarantees of the correctness of our estimation strategy, (ii) demonstrate via simulation that ADD MALTS outperforms other distributional data analysis methods at estimating treatment effects, and (iii) illustrate ADD MALTS' ability to verify whether there is enough cohesion between treatment and control units within subpopulations to trustworthily estimate treatment effects. We demonstrate ADD MALTS' utility by studying the effectiveness of continuous glucose monitors in mitigating diabetes risks.