[Paper Review] Discovering the Hidden Structure of Complex Dynamic Systems

Xavier Boyen, Nir Friedman+1 more|arXiv (Cornell University)|Jan 23, 2013

Bayesian Modeling and Causal Inference13 references17 citations

TL;DR

This paper proposes an efficient algorithm for learning the hidden structure of complex dynamic systems using Structural Expectation Maximization (SEM), with a novel approximation for computing sufficient statistics and a method to detect and introduce unobserved variables by identifying violations of the Markov property. The approach enables tractable, data-driven discovery of latent dynamics in systems with partial or unknown observability.

ABSTRACT

Dynamic Bayesian networks provide a compact and natural representation for complex dynamic systems. However, in many cases, there is no expert available from whom a model can be elicited. Learning provides an alternative approach for constructing models of dynamic systems. In this paper, we address some of the crucial computational aspects of learning the structure of dynamic systems, particularly those where some relevant variables are partially observed or even entirely unknown. Our approach is based on the Structural Expectation Maximization (SEM) algorithm. The main computational cost of the SEM algorithm is the gathering of expected sufficient statistics. We propose a novel approximation scheme that allows these sufficient statistics to be computed efficiently. We also investigate the fundamental problem of discovering the existence of hidden variables without exhaustive and expensive search. Our approach is based on the observation that, in dynamic systems, ignoring a hidden variable typically results in a violation of the Markov property. Thus, our algorithm searches for such violations in the data, and introduces hidden variables to explain them. We provide empirical results showing that the algorithm is able to learn the dynamics of complex systems in a computationally tractable way.

Motivation & Objective

• Address the challenge of learning dynamic system structures when no expert model is available.
• Overcome computational bottlenecks in SEM by efficiently estimating sufficient statistics for hidden variables.
• Detect the presence of unobserved variables by identifying violations of the Markov property in observed data.
• Develop a scalable method to infer latent structures in dynamic Bayesian networks without exhaustive search.
• Enable practical learning of complex system dynamics from incomplete or partially observed data.

Proposed method

• Adapt the Structural Expectation Maximization (SEM) algorithm to learn dynamic Bayesian network structures from data.
• Introduce a novel approximation scheme to efficiently compute expected sufficient statistics, reducing computational cost.
• Use temporal dependencies in data to detect violations of the Markov property, signaling the presence of hidden variables.
• Systematically introduce hidden variables to resolve detected Markov property violations and improve model fit.
• Leverage conditional independence tests across time lags to identify structural inconsistencies indicating unobserved confounders.
• Iteratively refine the model structure by adding hidden nodes where necessary, guided by statistical evidence from the data.

Experimental results

Research questions

• RQ1 How can we efficiently learn the structure of dynamic systems when some variables are unobserved or hidden?
• RQ2 What computational techniques can reduce the cost of sufficient statistic estimation in SEM for dynamic systems?
• RQ3 How can we automatically detect the existence of hidden variables without prior knowledge or exhaustive search?
• RQ4 In what ways do violations of the Markov property in time-series data indicate the presence of latent confounders?
• RQ5 Can we develop a scalable, data-driven method to infer hidden structures in complex dynamic systems?

Key findings

• The proposed approximation scheme significantly reduces the computational cost of gathering expected sufficient statistics in SEM.
• The method successfully detects hidden variables by identifying violations of the Markov property in observed temporal data.
• Empirical results demonstrate that the algorithm can learn complex dynamic system structures in a computationally tractable manner.
• The approach enables accurate model discovery even when key variables are partially or entirely unobserved.
• The algorithm avoids exhaustive search for hidden variables by using statistical tests based on temporal dependencies.
• The method achieves effective structure learning on synthetic and real-world dynamic systems, as validated in the UAI 1999 proceedings.