2019/09/10 by Dominik Linzner, Michael Schmidt, Linzner, Dominik +3
Computer Science · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.1909.04570
openalex publication_date 2019/09/10 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful\nframework for understanding multivariate time-series data. Given complete data,\nparameters and structure can be estimated efficiently in closed-form. However,\nif data is incomplete, the latent states of the CTBN have to be estimated by\nlaboriously simulating the intractable dynamics of the assumed CTBN. This is a\nproblem, especially for structure learning tasks, where this has to be done for\neach element of a super-exponentially growing set of possible structures. In\norder to circumvent this notorious bottleneck, we develop a novel\ngradient-based approach to structure learning. Instead of sampling and scoring\nall possible structures individually, we assume the generator of the CTBN to be\ncomposed as a mixture of generators stemming from different structures. In this\nframework, structure learning can be performed via a gradient-based\noptimization of mixture weights. We combine this approach with a new\nvariational method that allows for a closed-form calculation of this mixture\nmarginal likelihood. We show the scalability of our method by learning\nstructures of previously inaccessible sizes from synthetic and real-world data.\n