Cluster Variational Approximations for Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data
This work addresses the challenge of structure learning for continuous-time stochastic processes in domains like biology or finance, though it is incremental as it builds on variational approximations.
The paper tackles the problem of learning directed structures in continuous-time Bayesian networks from incomplete data by introducing a cluster-variational approximation method, which improves scalability compared to existing techniques.
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics. Existing approximation techniques, such as sampling and low-order variational methods, either scale unfavorably in system size, or are unsatisfactory in terms of accuracy. Inspired by recent advances in statistical physics, we present a new approximation scheme based on cluster-variational methods significantly improving upon existing variational approximations. We can analytically marginalize the parameters of the approximate CTBN, as these are of secondary importance for structure learning. This recovers a scalable scheme for direct structure learning from incomplete and noisy time-series data. Our approach outperforms existing methods in terms of scalability.