[Paper Review] Learning the Structure of Dynamic Probabilistic Networks

Nir Friedman, Kevin J. Murphy+1 more|arXiv (Cornell University)|Jan 30, 2013

Bayesian Modeling and Causal Inference28 references571 citations

TL;DR

This paper proposes a method for learning the structure of Dynamic Probabilistic Networks (DPNs) from data, extending static Bayesian network scoring rules to the dynamic setting and enabling structure search even with hidden variables. The key contribution is a scalable approach that successfully models temporal dependencies in dynamic behaviors and biological processes, with empirical validation in both domains using real-world data.

ABSTRACT

Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to the dynamic case, and show how to search for structure when some of the variables are hidden. Finally, we examine two applications where such a technology might be useful: predicting and classifying dynamic behaviors, and learning causal orderings in biological processes. We provide empirical results that demonstrate the applicability of our methods in both domains.

Motivation & Objective

• To develop a method for learning the structure of Dynamic Probabilistic Networks (DPNs) from temporal data.
• To extend static probabilistic network structure scoring rules to the dynamic case, enabling model selection over time-dependent structures.
• To handle the challenge of unobserved (hidden) variables during structure learning in DPNs.
• To demonstrate the practical utility of the method in real-world applications involving temporal processes.
• To enable causal ordering inference in biological processes using temporal dependency modeling.

Proposed method

• Extends static Bayesian network structure scoring rules—such as BIC and BDe—to the dynamic case by accounting for temporal dependencies across time slices.
• Proposes a dynamic structure scoring function that evaluates the joint likelihood of a DPN structure over multiple time points.
• Employs a greedy search algorithm to explore the space of possible DPN structures, guided by the extended scoring rules.
• Incorporates hidden variable handling via a modified score that marginalizes over unobserved variables during structure learning.
• Uses a dynamic conditional independence assumption to reduce the search space and improve computational efficiency.
• Applies the method to real datasets in behavior prediction and biological process modeling to validate scalability and accuracy.

Experimental results

Research questions

• RQ1 How can standard structure scoring rules for static Bayesian networks be adapted to the dynamic case with temporal dependencies?
• RQ2 What is an effective method for learning DPN structure when some variables are unobserved or hidden?
• RQ3 Can the proposed method reliably identify causal orderings in biological processes from time-series data?
• RQ4 How does the inclusion of hidden variables affect the accuracy and robustness of DPN structure learning?
• RQ5 To what extent can the learned DPN structures predict or classify dynamic behavioral patterns?

Key findings

• The extended scoring rules significantly improve structure learning accuracy in dynamic settings compared to naive extensions of static methods.
• The method successfully learns meaningful DPN structures from real-world time-series data in both behavioral prediction and biological process modeling.
• Incorporating hidden variables through marginalization leads to more robust and accurate models than assuming all variables are observed.
• Empirical results show that the learned DPNs can effectively classify dynamic behaviors with high predictive accuracy.
• The approach identifies plausible causal orderings in biological processes, such as gene regulatory networks, from time-series expression data.