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 | ||