# Nonparametric Conditional Local Independence Testing

arXiv: https://arxiv.org/abs/2203.13559 · HTML: https://mlsanity.com/paper/2203.13559/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 68 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [THP: Topological Hawkes Processes for Learning Causal Structure on Event Sequences](https://mlsanity.com/paper/2105.10884/) (2021)
- [The Weighted Generalised Covariance Measure](https://mlsanity.com/paper/2111.04361/) (2021)
- [A General Machine Learning Framework for Survival Analysis](https://mlsanity.com/paper/2006.15442/) (2020)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes](https://mlsanity.com/paper/2105.02088/) (2021)
- [BoXHED: Boosted eXact Hazard Estimator with Dynamic covariates](https://mlsanity.com/paper/2006.14218/) (2020)
- [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)
- [BoXHED2.0: Scalable boosting of dynamic survival analysis](https://mlsanity.com/paper/2103.12591/) (2021)
- [Graphical criteria for the identification of marginal causal effects in continuous-time survival and event-history analyses](https://mlsanity.com/paper/2202.02311/) (2022)

## Built on by (most cited first, 7 of 7)

- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Dynamic Structural Causal Models](https://mlsanity.com/paper/2406.01161/) (2024)
- [Efficient adjustment for complex covariates: Gaining efficiency with DOPE](https://mlsanity.com/paper/2402.12980/) (2024)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)
- [An Asymmetric Independence Model for Causal Discovery on Path Spaces](https://mlsanity.com/paper/2503.09859/) (2025)
- [Binary Expansion Group Intersection Network](https://mlsanity.com/paper/2603.24763/) (2026)

## Abstract (arXiv)

Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional processes, and it is important for the description and learning of causal relations among processes. We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally independent of another process. To this end, we introduce a new functional parameter called the Local Covariance Measure (LCM), which quantifies deviations from the hypothesis. Following the principles of double machine learning, we propose an estimator of the LCM and a test of the hypothesis using nonparametric estimators and sample splitting or cross-fitting. We call this test the (cross-fitted) Local Covariance Test ((X)-LCT), and we show that its level and power can be controlled uniformly, provided that the nonparametric estimators are consistent with modest rates. We illustrate the theory by an example based on a marginalized Cox model with time-dependent covariates, and we show in simulations that when double machine learning is used in combination with cross-fitting, then the test works well without restrictive parametric assumptions.