Linear constraints on variables in influence diagrams for causal models

Abstract

The paper considers some ways of representing probabilistic causal models using Bayesian network theory (hereafter referred to as BN). These models describe well problems with different types of uncertainty. The theory of BN extended with some additional types of nodes called influence diagrams or IDs. Influence diagrams make it possible to consider a number of solution options, to evaluate them quantitatively, and to select the best of the considered options. However, it is practically impossible to find an optimal solution in an ID. It is not even possible to create a system of linear constraints on some variables in an ID, although there is a large class of practical problems with such constraints.

The paper describes the idea of extending ID to describe linear constraints on some variables of the BN. In the future, it will help to use the ideas of linear programming in ID to find an optimal solution in the sense of LP for problems with different types of uncertainties and causal relationships between some variables. This work has been done under grant AP19679142 "Search for optimal solutions in Bayesian networks in models with linear constraints and linear functionals. Development of algorithms and programs " (2023-2025) of MES RK. This project will develop the theory for finding optimal solutions in Bayesian networks. Optimality will be understood in the sense of linear programming - a system of linear constraints, extremum of a linear functional. The theory will be implemented in a software product.