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Table 2 TPC causal learning

From: Deep bidirectional intelligence: AlphaZero, deep IA-search, deep IA-infer, and TPC causal learning

Solving joint equations for CI \(\rho\)-tree by Theorem 2 and for CI \(\rho\)-DAG by Theorems 3 and 4
Joint equations Topology identification (T-phase) Parameter reestimation (P-phase) Causal \(\rho\)-tree search (C-phase)
No solution Inconsistent with data NA NA
Unique solution As the necessary and sufficient condition for identifying this CI topology of \(\rho\)-tree or \(\rho\)-DAG, which is an equivalence class of a number of causal \(\rho\)-trees or \(\rho\)-DAGs. At least, one of them models data well Each in this equivalence class is modeled in SEM equations with coefficients as parameters that are re-estimated via iterating one SEM-based constrained sparse optimisation with coefficients get in T-phase as initialisation Search the best one among the equivalence class with each one enumerated by a search strategy, estimated in P-phase, and evaluated by a measure that considers both best-fit and causality to get a directional generalisation error.
Many or infinite many solutions As a necessary condition that this CI topology satisfies