THE ADJACENCY MATRIX RECONSTRUCTION ALGORITHM FOR CAUSAL GRAPH MODELS IN THE ABSENCE OF OBSERVABLE VARIABLES

Abstract

The paper deals with the problem of modeling complex systems in the absence of observable
variables. To solve this problem, it is proposed to use causal graph models. The class of causal
models considered here is defined as non-stochastic causal models with unobservable variables.
These models are presented in the form of a directed graph, created on the basis of human mental
representations. In this case, on the arcs, causality is expressed in the form of some marks with a
sign that determines the direction of change in the state of the system. The considered causal models
include heterogeneous, complex and qualitative types of variables that illustrate the nonnumerical
nature of nodes and links and, as a consequence, the absence and impossibility of obtaining
time series data. In the absence of observable variables and the impossibility of conducting
experiments, the problem of reconstructing the adjacency matrix of the causal graph model becomes
much more complicated. It is required to obtain a model with a certain spectral decomposition
that implements the main function of the modeled system. Based on this concept, a new method
for reconstructing the adjacency matrix is proposed, implemented on the basis of the corresponding
causal propagation matrix or transmission matrix. The idea is to use combinatorial optimization
based on spectral graph theory to generate data from a qualitative non-stochastic causal
model and reconstruct an adjacency matrix using that data. In this case, the eigenvectors are
identified as key objectives of the matrix reconstruction process, which postulates a fundamental
approach based on the spectral properties of the graph. The results of computational experiments
on solving the problem of reconstructing the adjacency matrix for causal graph models in the absence
of observable variables using the developed algorithm have shown that the algorithm effectively
reconstructs matrices from the given parameters with admissible similarity indices. The
convergence of the approximation to the solution of the matrix reconstruction algorithm is proved
no slower than with the speed of a geometric progression. From a technical point of view, the
advantage of the algorithm is the implementation of a tool for automatic adjustment of the regularization
parameter, suitable for users without prior mathematical knowledge.