We present two online causal structure learning algorithms which can track changes in a causal structure and process data in a dynamic real-time manner. Standard causal structure learning algorithms assume that causal structure does not change during the data collection process, but in real-world scenarios, it does often change. Therefore, it is inappropriate to handle such changes with existing batch-learning approaches, and instead, a structure should be learned in an online manner. The online causal structure learning algorithms we present here can revise correlation values without reprocessing the entire dataset and use an existing model to avoid relearning the causal links in the prior model, which still fit data. Proposed algorithms are tested on synthetic and real-world datasets, the latter being a seasonally adjusted commodity price index dataset for the U.S. The online causal structure learning algorithms outperformed standard FCI by a large margin in learning the changed causal structure correctly and efficiently when latent variables were present.
@cite_20: We consider the problem of Bayesian inference of graphical structure describing the interactions among multiple vector time-series. A directed temporal interaction model is presented which assumes a fixed dependence structure among time-series. Using a conjugate prior over this model’s structure and parameters, we focus our attention on characterizing the exact posterior uncertainty in the structure given data. The model is extended via the introduction of a dynamically evolving latent variable which indexes dependence structures over time. Performing inference using this model yields promising results when analyzing the interaction of multiple tracked moving objects.
@cite_23: When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof. Copyright 2005 Royal Statistical Society.
Talih and Hengartner @cite_23 do other related work. In their work, the data sets are taken sequentially as input and divided into a fixed number of data intervals, each with an associated undirected graph that differentiates one edge from its neighbours. In contrast to our work, in their work, they focus on a particular type of graphical structure change (a single edge added or removed), only work in batch mode and use undirected graphics instead of directed acyclic graphical models. Next, Siracusa @cite_20 uses a Bayesian approach to find posterior uncertainty on possible directed edges at different points in a time series. Our work differs from their work because we use frequentist methods instead of Bayesian methods, and we can work in real time in an incoming data stream.