Controlled Causal Hallucinations Can Estimate Phantom Nodes in Multiexpert Mixtures of Fuzzy Cognitive Maps

Abstract

An adaptive multiexpert mixture of feedback causal models can approximate missing or phantom nodes in large-scale causal models. The result gives a scalable form of \emph{big knowledge}. The mixed model approximates a sampled dynamical system by approximating its main limit-cycle equilibria. Each expert first draws a fuzzy cognitive map (FCM) with at least one missing causal node or variable. FCMs are directed signed partial-causality cyclic graphs. They mix naturally through convex combination to produce a new causal feedback FCM. Supervised learning helps each expert FCM estimate its phantom node by comparing the FCM's partial equilibrium with the complete multi-node equilibrium. Such phantom-node estimation allows partial control over these causal hallucinations and helps approximate the future trajectory of the dynamical system. But the approximation can be computationally heavy. Mixing the tuned expert FCMs gives a practical way to find several phantom nodes and thereby better approximate the feedback system's true equilibrium behavior.