A non-homogeneous dynamic Bayesian network with a hidden Markov model dependency structure among the temporal data points

Abstract

In the topical field of systems biology there is considerable interest in learning regulatory networks, and various probabilistic machine learning methods have been proposed to this end. Popular approaches include non-homogeneous dynamic Bayesian networks (DBNs), which can be employed to model time-varying regulatory processes. Almost all non-homogeneous DBNs that have been proposed in the literature follow the same paradigm and relax the homogeneity assumption by complementing the standard homogeneous DBN with a multiple changepoint process. Each time series segment defined by two demarcating changepoints is associated with separate interactions, and in this way the regulatory relationships are allowed to vary over time. However, the configuration space of the data segmentations (allocations) that can be obtained by changepoints is restricted. A complementary paradigm is to combine DBNs with mixture models, which allow for free allocations of the data points to mixture components. But this extension of the configuration space comes with the disadvantage that the temporal order of the data points can no longer be taken into account. In this paper I present a novel non-homogeneous DBN model, which can be seen as a consensus between the free allocation mixture DBN model and the changepoint-segmented DBN model. The key idea is to assume that the underlying allocation of the temporal data points follows a Hidden Markov model (HMM). The novel HMM---DBN model takes the temporal structure of the time series into account without putting a restriction onto the configuration space of the data point allocations. I define the novel HMM---DBN model and the competing models such that the regulatory network structure is kept fixed among components, while the network interaction parameters are allowed to vary, and I show how the novel HMM---DBN model can be inferred with Markov Chain Monte Carlo (MCMC) simulations. For the new HMM---DBN model I also present two new pairs of MCMC moves, which can be incorporated into the recently proposed allocation sampler for mixture models to improve convergence of the MCMC simulations. In an extensive comparative evaluation study I systematically compare the performance of the proposed HMM---DBN model with the performances of the competing DBN models in a reverse engineering context, where the objective is to learn the structure of a network from temporal network data.