# Active Learning of Continuous-time Bayesian Networks through Interventions

arXiv: https://arxiv.org/abs/2105.14742 · HTML: https://mlsanity.com/paper/2105.14742/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 9 of 9)

- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Experimental Design for Cost-Aware Learning of Causal Graphs](https://mlsanity.com/paper/1810.11867/) (2018)
- [Kullback-Leibler Divergence for the Normal-Gamma Distribution](https://mlsanity.com/paper/1611.01437/) (2016)
- [Probabilistic Active Learning of Functions in Structural Causal Models](https://mlsanity.com/paper/1706.10234/) (2017)
- [Maximizing Information Gain for the Characterization of Biomolecular Circuits](https://mlsanity.com/paper/2101.02924/) (2021)
- [Cluster Variational Approximations for Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data](https://mlsanity.com/paper/1809.04294/) (2018)
- [Scalable Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data](https://mlsanity.com/paper/1909.04570/) (2019)

## Built on by (most cited first, 2 of 2)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)

## Abstract (arXiv)

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.