Nonlinear Causal Discovery via Dynamic Latent Variables

Abstract

Distinguishing causality from mere correlation is a cornerstone in empirical research, as conflating the two can result in significant errors in decision-making, affecting policy formulation and the validity of scientific inferences. Traditional experimental designs, such as randomized trials, often fall short in complex systems where variables interact in a high-dimensional space with limited data. This paper aims to address these challenges by introducing an innovative causal discovery approach, extending beyond conventional methodologies by incorporating algorithmic advances in computational efficiency and design. We present a novel double Gaussian process state space causal model (GPSSCM) that contends with the multifaceted nature of causal inference, accounting for noisy observations and latent variables, which are commonly encountered in dynamic systems. Our methodological contribution includes the application of a Markov chain Monte Carlo technique for unraveling latent state dynamics and an expectation-maximization (EM) algorithm for robust parameter estimation. The acyclic nature of the causal graph is ensured through an integrated acyclic constraint within the EM framework, maintaining the integrity of the causal model. The efficacy of our proposed GPSSCM is evaluated through a series of tests on both synthetic data and empirical case studies from the industrial domain. The results highlight the model’s capacity to accurately infer complex nonlinear causal relationships, demonstrating its superiority over traditional structural equation modeling, especially when dealing with time series data and latent variables. This paper not only contributes a sophisticated tool for researchers and practitioners but also enriches the literature on causal discovery by offering a new perspective on the analysis of intricate systems, thereby facilitating more informed and ethical decision-making across various scientific fields. Note to Practitioners—Understanding the intricate web of causality is crucial for making informed decisions in various scientific and professional fields. Our study presents a Gaussian process state space causal model, which enhances the analysis of dynamic causal relationships in complex systems, particularly when dealing with noisy observations and latent variables. Leveraging a combination of Markov chain Monte Carlo and expectation maximization algorithms, the model ensures accurate estimation of parameters and causal structures. This paper is particularly relevant for those in fields such as economics, transportation, and biology, offering a sophisticated tool to support ethical decision-making and safeguard against errors in high-stakes environments. The practical implications of this research are underscored by its ability to inform targeted interventions and predict outcomes under new conditions, advancing the comprehension and application of causality in real-world scenarios.