Tensor-based second-order causal discovery

2026-06-16

AI Summary

This work addresses the problem of identifying causal dependencies among variables and recovering both the directed acyclic graph (DAG) structure and its functional form from observational and interventional data, assuming only that noise terms are uncorrelated. To this end, the authors propose the TSCD algorithm, which constructs a tensor from covariance matrices to efficiently infer the causal graph under linear structural equation models and extends naturally to nonlinear settings. Relying solely on second-order statistics, the method circumvents restrictive Gaussian assumptions and requires only a logarithmic number of interventions to identify the causal order and model parameters. Empirical results demonstrate that TSCD remains robust and highly noise-tolerant at scales involving hundreds of variables, achieving performance comparable to state-of-the-art methods while substantially reducing the number of required interventions.

Abstract

Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.

Problem

• causal discovery
• tensor
• second-order statistics
• structural equation model
• directed acyclic graph

Innovation

• tensor-based causal discovery
• second-order statistics
• structural equation model
• interventional data
• causal identifiability