Tensor-based second-order causal discovery

• URL: http://arxiv.org/abs/2606.18074v2
• Date: Mon, 22 Jun 2026 18:30:05 GMT
• Title: Tensor-based second-order causal discovery
• Abstract summary: Causal discovery seeks to uncover the causal dependencies among variables.<n>We propose an algorithm called Second-order Causal Discovery (TSCD)<n>We show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.
• Score: 10.723101815261563
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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