Open directions for scalable and causal tensor-network recovery

Investigate approximate contraction methods for larger numbers of variables, develop alternating-least-squares optimization for faster training, combine tensor-network structure recovery with interventional data to recover full causal DAGs, and derive sample-complexity bounds for the empirical-distribution regime.

Background

The proposed fully connected tensor-network method has exponential exact-contraction cost in the number of variables, and the paper identifies approximate contraction as a route toward larger systems. It also points to alternating least squares as a possible faster optimization strategy.

The method currently recovers an undirected moral graph rather than orientations of the causal DAG. Interventional information could potentially extend the method to full DAG recovery. Finally, the theoretical analysis assumes access to the distribution itself, leaving statistical guarantees for finite observational samples unresolved.