Active Learning of Continuous-time Bayesian Networks through Interventions

TL;DR

This paper introduces a scalable, information-theoretic approach for designing optimal interventions to learn the structure and parameters of Continuous-time Bayesian Networks efficiently, even in high-dimensional settings.

Contribution

It proposes a novel variational criterion for experimental design in CTBNs, enabling efficient structure and parameter learning through master-equation solutions.

Findings

Effective in high-dimensional settings

Reduces computational complexity of experimental design

Demonstrated on synthetic and real data

Abstract

We consider the problem of learning structures and parameters of Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal experimental resources. In practice, the cost of generating experimental data poses a bottleneck, especially in the natural and social sciences. A popular approach to overcome this is Bayesian optimal experimental design (BOED). However, BOED becomes infeasible in high-dimensional settings, as it involves integration over all possible experimental outcomes. We propose a novel criterion for experimental design based on a variational approximation of the expected information gain. We show that for CTBNs, a semi-analytical expression for this criterion can be calculated for structure and parameter learning. By doing so, we can replace sampling over experimental outcomes by solving the CTBNs master-equation, for which scalable approximations exist. This alleviates the computational burden of sampling possible experimental outcomes in high-dimensions. We employ this framework in order to recommend interventional sequences. In this context, we extend the CTBN model to conditional CTBNs in order to incorporate interventions. We demonstrate the performance of our criterion on synthetic and real-world data.