# Learning latent causal relationships in multiple time series

arXiv: https://arxiv.org/abs/2203.10679 · HTML: https://mlsanity.com/paper/2203.10679/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 54 references that are in the map.
- First posted on arXiv 21 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [In reply to Faes et al. and Barnett et al. regarding "A study of problems encountered in Granger causality analysis from a neuroscience perspective"](https://mlsanity.com/paper/1709.10248/) (2017)
- [Validity of time reversal for testing Granger causality](https://mlsanity.com/paper/1509.07636/) (2015)
- [Improving the condition number of estimated covariance matrices](https://mlsanity.com/paper/1810.10984/) (2018)

## Abstract (arXiv)

Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between observed signals that are selected a priori. Here it is posited that, in many systems, the causal relations are embedded in a latent space that is expressed in the observed data as a linear mixture. A technique for blindly identifying the latent sources is presented: the observations are projected into pairs of components -- driving and driven -- to maximize the strength of causality between the pairs. This leads to an optimization problem with closed form expressions for the objective function and gradient that can be solved with off-the-shelf techniques. After demonstrating proof-of-concept on synthetic data with known latent structure, the technique is applied to recordings from the human brain and historical cryptocurrency prices. In both cases, the approach recovers multiple strong causal relationships that are not evident in the observed data. The proposed technique is unsupervised and can be readily applied to any multiple time series to shed light on the causal relationships underlying the data.