Heterogeneous continuous dynamic Bayesian networks with flexible structure and inter-time segment information sharing

Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with heterogeneity and non-stationarity in temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper aims to improve the shortcomings of three recent versions of heterogeneous DBNs along the following lines: (i) avoiding the need for data discretization, (ii) increasing the flexibility over a time-invariant network structure, (iii) avoiding over-flexibility and overfitting by introducing a regularization scheme based in inter-time segment information sharing. The improved method is evaluated on synthetic data and compared with alternative published methods on gene expression time series from Drosophila melanogaster. 1

Post-Regularization Inference for Time-Varying Nonparanormal Graphical Models

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range of values. The tests are developed for a high-dimensional regime, are robust to model selection mistakes and do not require commonly assumed minimum signal strength. The testing procedures are based on a high dimensional, debiasing-free moment estimator, which uses a novel kernel smoothed Kendall's tau correlation matrix as an input statistic. The estimator consistently estimates the latent inverse Pearson correlation matrix uniformly in both the index variable and kernel bandwidth. Its rate of convergence is shown to be minimax optimal. Our method is supported by thorough numerical simulations and an application to a neural imaging data set

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

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 dynamicBayesian 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-DBNmodel 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

Bayesian inference for protein signalling networks

Cellular response to a changing chemical environment is mediated by a complex system of interactions involving molecules such as genes, proteins and metabolites. In particular, genetic and epigenetic variation ensure that cellular response is often highly specific to individual cell types, or to different patients in the clinical setting. Conceptually, cellular systems may be characterised as networks of interacting components together with biochemical parameters specifying rates of reaction. Taken together, the network and parameters form a predictive model of cellular dynamics which may be used to simulate the effect of hypothetical drug regimens. In practice, however, both network topology and reaction rates remain partially or entirely unknown, depending on individual genetic variation and environmental conditions. Prediction under parameter uncertainty is a classical statistical problem. Yet, doubly uncertain prediction, where both parameters and the underlying network topology are unknown, leads to highly non-trivial probability distributions which currently require gross simplifying assumptions to analyse. Recent advances in molecular assay technology now permit high-throughput data-driven studies of cellular dynamics. This thesis sought to develop novel statistical methods in this context, focussing primarily on the problems of (i) elucidating biochemical network topology from assay data and (ii) prediction of dynamical response to therapy when both network and parameters are uncertain