Structure learning for CTBN's via penalized maximum likelihood methods

TL;DR

This paper introduces a penalized likelihood approach for learning the structure of continuous-time Bayesian networks, demonstrating its high-probability accuracy and effectiveness through theoretical and numerical analysis.

Contribution

It proposes a novel penalized maximum likelihood method for structure learning in CTBNs, addressing a less-explored area with proven high-probability recognition of the graph structure.

Findings

Algorithm recognizes dependence structure with high probability

Method is effective in numerical simulations

Provides theoretical guarantees under mild conditions

Abstract

The continuous-time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, in social science models or in medicine. The literature on this topic is usually focused on the case when the dependence structure of a system is known and we are to determine conditional transition intensities (parameters of the network). In the paper, we study the structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes the dependence structure of the graph with high probability. We also investigate the properties of the procedure in numerical studies to demonstrate its effectiveness.