Probabilistic Structural Controllability in Causal Bayesian Networks

TL;DR

This paper introduces the concept of probabilistic structural controllability in Causal Bayesian Networks, formalizing the problem and identifying driver variables to influence target outcomes under uncertainty.

Contribution

It is the first to define and formalize probabilistic controllability in CBNs and to identify a sufficient set of driver variables for control.

Findings

Formal definition of probabilistic structural controllability in CBNs

Identification of a sufficient set of driver variables

Analysis of minimality conditions for driver sets

Abstract

Humans routinely confront the following key question which could be viewed as a probabilistic variant of the controllability problem: While faced with an uncertain environment governed by causal structures, how should they practice their autonomy by intervening on driver variables, in order to increase (or decrease) the probability of attaining their desired (or undesired) state for some target variable? In this paper, for the first time, the problem of probabilistic controllability in Causal Bayesian Networks (CBNs) is studied. More specifically, the aim of this paper is two-fold: (i) to introduce and formalize the problem of probabilistic structural controllability in CBNs, and (ii) to identify a sufficient set of driver variables for the purpose of probabilistic structural controllability of a generic CBN. We also elaborate on the nature of minimality the identified set of driver variables satisfies. In this context, the term "structural" signifies the condition wherein solely the structure of the CBN is known.