# Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

## TL;DR

This paper introduces an information-theoretic method to identify 1-step causal influences in stochastic dynamical systems with latent variables, including a linear regression-based approach for linear dynamics, validated through simulations.

## Contribution

It presents a novel approach for causal discovery in systems with latent variables, extending existing methods to nonlinear and linear cases with validation.

## Key findings

- Successfully recovers causal relations among observed variables.
- Effective in systems where latent variables lack exogenous noise.
- Validated through numerical simulations demonstrating practical applicability.

## Abstract

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations.