TSCD: Tensor-based causal discovery needs only log(n) interventions
MIT researchers unveil algorithm using covariance tensors for efficient causal graph learning.
A new paper on arXiv (2606.18074) introduces Tensor-based Second-order Causal Discovery (TSCD), an algorithm that recovers causal graphs from observational and interventional data. By forming a tensor from covariance matrices, TSCD leverages second-order statistics—more efficient than higher-order moments and more identifiable than first-order. The method works under a linear structural equation model on a DAG with uncorrelated noise, and extends to nonlinear models. It requires only O(log n) interventions for n variables, a dramatic reduction from typical O(n) or exponential approaches.
Experiments demonstrate TSCD's robustness to noise, competitive performance against existing causal discovery methods, and scalability to hundreds of variables. The authors provide open-source code on GitHub. This work has significant implications for fields like genomics, neuroscience, and economics, where causal inference often involves many variables and limited intervention budgets. TSCD's efficiency and low intervention requirements could make precise causal discovery practical in large, real-world systems.
- Uses only second-order statistics (covariance matrices), requiring fewer samples than higher-order methods.
- Number of needed interventions scales logarithmically with the number of variables—O(log n) instead of O(n).
- Works for both linear and nonlinear models, and scales to hundreds of variables with robust performance.
Why It Matters
TSCD dramatically reduces the cost of causal discovery, enabling large-scale causal graph learning in real-world settings.