# Sample Complexity of Causal Identification with Temporal Heterogeneity

arXiv: https://arxiv.org/abs/2602.06899 · HTML: https://mlsanity.com/paper/2602.06899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Causal discovery for time series from multiple datasets with latent contexts](https://mlsanity.com/paper/2306.12896/) (2023)
- [Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments](https://mlsanity.com/paper/2506.11756/) (2025)

## Abstract (arXiv)

Recovering a unique causal graph from observational data is an ill-posed problem because multiple generating mechanisms can lead to the same observational distribution. This problem becomes solvable only by exploiting specific structural or distributional assumptions. While recent work has separately utilized time-series dynamics or multi-environment heterogeneity to constrain this problem, we integrate both as complementary sources of heterogeneity. This integration yields unified necessary identifiability conditions and enables a rigorous analysis of the statistical limits of recovery under thin versus heavy-tailed noise. In particular, temporal structure is shown to effectively substitute for missing environmental diversity, possibly achieving identifiability even under insufficient heterogeneity. Extending this analysis to heavy-tailed (Student's t) distributions, we demonstrate that while geometric identifiability conditions remain invariant, the sample complexity diverges significantly from the Gaussian baseline. Explicit information-theoretic bounds quantify this cost of robustness, establishing the fundamental limits of covariance-based causal graph recovery methods in realistic non-stationary systems. This work shifts the focus from whether causal structure is identifiable to whether it is statistically recoverable in practice.