Exploiting local and repeated structure in Dynamic Bayesian Networks

BackgroundMocapy++ is a toolkit for parameter learning and inference in dynamic Bayesian networks (DBNs). It supports a wide range of DBN architectures and probability distributions, including distributions from directional statistics (the statistics of angles, directions and orientations).ResultsThe program package is freely available under the GNU General Public Licence (GPL) from SourceForge http://sourceforge.net/projects/mocapy. The package contains the source for building the Mocapy++ library, several usage examples and the user manual.ConclusionsMocapy++ is especially suitable for constructing probabilistic models of biomolecular structure, due to its support for directional statistics. In particular, it supports the Kent distribution on the sphere and the bivariate von Mises distribution on the torus. These distributions have proven useful to formulate probabilistic models of protein and RNA structure in atomic detail.

Network inference algorithms are powerful computational tools for identifying putative causal interactions among variables from observational data. Bayesian network inference algorithms hold particular promise in that they can capture linear, non-linear, combinatorial, stochastic and other types of relationships among variables across multiple levels of biological organization. However, challenges remain when applying these algorithms to limited quantities of experimental data collected from biological systems. Here, we use a simulation approach to make advances in our dynamic Bayesian network (DBN) inference algorithm, especially in the context of limited quantities of biological data. We test a range of scoring metrics and search heuristics to find an effective algorithm configuration for evaluating our methodological advances. We also identify sampling intervals and levels of data discretization that allow the best recovery of the simulated networks. We develop a novel influence score for DBNs that attempts to estimate both the sign (activation or repression) and relative magnitude of interactions among variables. When faced with limited quantities of observational data, combining our influence score with moderate data interpolation reduces a significant portion of false positive interactions in the recovered networks. Together, our advances allow DBN inference algorithms to be more effective in recovering biological networks from experimentally collected data. Source code and simulated data are available upon request. http://www.jarvislab.net/Bioinformatics/BNAdvances/

This paper compares the performance of inference in static and dynamic Bayesian Networks. For the comparison both kinds of Bayesian networks are created for the exemplary application activity recognition. Probability and structure of the Bayesian Networks have been learnt automatically from a recorded data set consisting of acceleration data observed from an inertial measurement unit. Whereas dynamic networks incorporate temporal dependencies which affect the quality of the activity recognition, inference is less complex for dynamic networks. As performance indicators recall, precision and processing time of the activity recognition are studied in detail. The results show that dynamic Bayesian Networks provide considerably higher quality in the recognition but entail longer processing times.

Dynamic Bayesian networks (DBNs) are probabilistic graphical models that have become a ubiquitous tool for compactly describing statistical relationships among a group of stochastic processes. A suite of elaborately designed inference algorithms makes it possible for intelligent systems to use a DBN to make inferences in uncertain conditions. Unfortunately, exact inference or even approximation in a DBN has been proved to be NP-hard and is generally computationally prohibitive. In this paper, we investigate a sliding window framework for approximate inference in DBNs to reduce the computational burden. By introducing a sliding window that moves forward as time progresses, inference at any time is restricted to a quite narrow region of the network. The main contributions to the sliding window framework include an exploration of its foundations, explication of how it operates, and the proposal of two strategies for adaptive window size selection. To make this framework available as an inference engine, the interface algorithm widely used in exact inference is then integrated with the framework for approximate inference in DBNs. After analyzing its computational complexity, further empirical work is presented to demonstrate the validity of the proposed algorithms.

Background:Ex vivo machine perfusion (MP) can better preserve organs for transplantation. We have recently reported on the first application of an MP protocol in which liver allografts were fully oxygenated, under dual pressures and subnormothermic conditions, with a new hemoglobin-based oxygen carrier (HBOC) solution specifically developed for ex vivo utilization. In those studies, MP improved organ function post-operatively and reduced inflammation in porcine livers. Herein, we sought to refine our knowledge regarding the impact of MP by defining dynamic networks of inflammation in both tissue and perfusate.Methods: Porcine liver allografts were preserved either with MP (n = 6) or with cold static preservation (CSP; n = 6), then transplanted orthotopically after 9 h of preservation. Fourteen inflammatory mediators were measured in both tissue and perfusate during liver preservation at multiple time points, and analyzed using Dynamic Bayesian Network (DyBN) inference to define feedback interactions, as well as Dynamic Network Analysis (DyNA) to define the time-dependent development of inflammation networks.Results: Network analyses of tissue and perfusate suggested an NLRP3 inflammasome-regulated response in both treatment groups, driven by the pro-inflammatory cytokine interleukin (IL)-18 and the anti-inflammatory mediator IL-1 receptor antagonist (IL-1RA). Both DyBN and DyNA suggested a reduced role of IL-18 and increased role of IL-1RA with MP, along with increased liver damage with CSP. DyNA also suggested divergent progression of responses over the 9 h preservation time, with CSP leading to a stable pattern of IL-18-induced liver damage and MP leading to a resolution of the pro-inflammatory response. These results were consistent with prior clinical, biochemical, and histological findings after liver transplantation.Conclusion: Our results suggest that analysis of dynamic inflammation networks in the setting of liver preservation may identify novel diagnostic and therapeutic modalities.

Vascularized composite allotransplantation (VCA) is aimed at enabling injured individuals to return to their previous lifestyles. Unfortunately, VCA induces an immune/inflammatory response, which mandates lifelong, systemic immunosuppression, with attendant detrimental effects. Mesenchymal stem cells (MSC)-both adipose-derived (AD-MSC) and bone marrow-derived (BM-MSC)-can reprogram inflammation and have been suggested as an alternative to immunosuppression, but their mechanism of action is as yet not fully elucidated. We sought to gain insights into these mechanisms using a systems biology approach. PKH26 (red) dye-labeled AD-MSC or BM-MSC were administered intravenously to Lewis rat recipients of mismatched Brown-Norway hindlimb transplants. Short course tacrolimus (FK-506) monotherapy was withdrawn at postoperative day 21. Sera were collected at 4 weeks, 6 weeks, and 18 weeks; assayed for 29 inflammatory/immune mediators; and the resultant data were analyzed using Dynamic Network Analysis (DyNA), Dynamic Bayesian Network (DyBN) inference, and Principal Component Analysis. DyNA network complexity decreased with time in AD-MSC rats, but increased in BM-MSC rats. DyBN and Principal Component Analysis suggested mostly different central nodes and principal characteristics, respectively, in AD-MSC versus BM-MSC rats. AD-MSC and BM-MSC are associated with both overlapping and distinct dynamic networks and principal characteristics of inflammatory/immune mediators in VCA grafts with short-course tacrolimus induction therapy. The decreasing inflammatory complexity of dynamic networks in the presence of AD-MSC supports the previously suggested role for T regulatory cells induced by AD-MSC. The finding of some overlapping and some distinct central nodes and principal characteristics suggests the role of key mediators in the response to VCA in general, as well as potentially differential roles for other mediators ascribed to the actions of the different MSC populations. Thus, combined in vivo/in silico strategies may yield novel means of optimizing MSC therapy for VCA.

Systems-level insights into inflammatory events after vascularized composite allotransplantation (VCA) are critical to the success of immunomodulatory strategies of these complex procedures. To date, the effects of tacrolimus (TAC) immunosuppression on inflammatory networks in VCA, such as in acute rejection (AR), have not been investigated. We used a systems biology approach to elucidate the effects of tacrolimus on dynamic networks and principal drivers of systemic inflammation in the context of dynamic tissue-specific immune responses following VCA. Lewis (LEW) rat recipients received orthotopic hind limb VCA from fully major histocompatibility complex-mismatched Brown Norway (BN) donors or matched LEW donors. Group 1 (syngeneic controls) received LEW limbs without TAC, and Group 2 (treatment group) received BN limbs with TAC. Time-dependent changes in 27 inflammatory mediators were analyzed in skin, muscle, and peripheral blood using Principal Component Analysis (PCA), Dynamic Bayesian Network (DyBN) inference, and Dynamic Network Analysis (DyNA) to define principal characteristics, central nodes, and putative feedback structures of systemic inflammation. Analyses were repeated on skin + muscle data to construct a “Virtual VCA”, and in skin + muscle + peripheral blood data to construct a “Virtual Animal.” PCA, DyBN, and DyNA results from individual tissues suggested important roles for leptin, VEGF, various chemokines, the NLRP3 inflammasome (IL-1β, IL-18), and IL-6 after TAC treatment. The chemokines MCP-1, MIP-1α; and IP-10 were associated with AR in controls. Statistical analysis suggested that 24/27 inflammatory mediators were altered significantly between control and TAC-treated rats in peripheral blood, skin, and/or muscle over time. “Virtual VCA” and “Virtual Animal” analyses implicated the skin as a key control point of dynamic inflammatory networks, whose connectivity/complexity over time exhibited a U-shaped trajectory and was mirrored in the systemic circulation. Our study defines the effects of TAC on complex spatiotemporal evolution of dynamic inflammation networks in VCA. We also demonstrate the potential utility of computational analyses to elucidate nonlinear, cross-tissue interactions. These approaches may help define precision medicine approaches to better personalize TAC immunosuppression in VCA recipients.

Aiming at the challenging issue of target recognition (TR) in uncertain environment, a soft evidence inference in dynamic Bayesian networks is presented, which not only enriches Bayesian networks theoretically but also offers more flexible and robust target recognition system by exploiting the complementary of other target attributes. The architecture of the target recognition system is designed and an algorithm for TR utilizing soft evidences inferring in dynamic Bayesian network is also advanced. Experimental results illustrate that the proposed TR approach is robust by synthesizing different target characters and amending each other with respect to different time-slices. Moreover, this method can meet the real-time requirement by deriving belief even when some target attributes data are not accessible temporarily.

Probabilistic inference for Bayesian networks is in general computationally intensive using either exact algorithms or approximate methods. For general hybrid dynamic Bayesian networks, one has to rely on the approximate methods such as stochastic simulation to provide a solution. Sequential Monte Carlo methods, also known as particle filters, have been introduced to deal with these problems. They allow us to treat any type of probability distribution and nonlinearity although they often suffer major drawbacks of sample degeneracy and inefficiency in high-dimensional cases. This is particularly true when the dynamic networks have extremely unlikely evidence. In this paper, we introduce a very efficient importance sampling inference algorithm for discrete dynamic Bayesian network. This method is designed to iteratively learn the importance function adoptively and asymptotically. We used several partially dynamic Bayesian network models to test our inference method. The preliminary simulation results show that the algorithm is very promising.

To address the current problem of insufficient risk level analysis of gasifier systems, an evaluation method combining the cloud model and dynamic Bayesian network is proposed, taking the gasifier system as the evaluation target, using the cloud model to discretize continuous data, and setting each risk factor in the evaluation system as a node in the dynamic Bayesian network to build a dynamic Bayesian network. The entropy weight method is used to calculate the weight of each risk indicator, the maximum likelihood estimation method is used to process the affiliation degree obtained from the cloud model, and the probability obtained by the affiliation-probability conversion method is input into the dynamic Bayesian network as evidence. Finally, the risk prediction assessment for the gasifier system is completed by using the features of forwarding and backward inference of the dynamic Bayesian network, combined with the comprehensive analysis of importance. The study shows that human maintenance efficiency, equipment integrity, gasifier pressure, and oxygen-coal ratio are the weak points that need to be focused on in the operation of the system.

BackgroundIn computational biology, one often faces the problem of deriving the causal relationship among different elements such as genes, proteins, metabolites, neurons and so on, based upon multi-dimensional temporal data. Currently, there are two common approaches used to explore the network structure among elements. One is the Granger causality approach, and the other is the dynamic Bayesian network inference approach. Both have at least a few thousand publications reported in the literature. A key issue is to choose which approach is used to tackle the data, in particular when they give rise to contradictory results.ResultsIn this paper, we provide an answer by focusing on a systematic and computationally intensive comparison between the two approaches on both synthesized and experimental data. For synthesized data, a critical point of the data length is found: the dynamic Bayesian network outperforms the Granger causality approach when the data length is short, and vice versa. We then test our results in experimental data of short length which is a common scenario in current biological experiments: it is again confirmed that the dynamic Bayesian network works better.ConclusionWhen the data size is short, the dynamic Bayesian network inference performs better than the Granger causality approach; otherwise the Granger causality approach is better.

In the post-genomic era, discovering relationships between genes and further constructing gene regulatory networks (GRNs) is an important problem in system biology. In case the GRNs model for a cell is known, we can simulate the gene expression to predict future states of the cell and discover new drugs based on the relationships in the GRNs. In this paper, our aim is to construct a better gene regulatory network. We present a new informative prior over network structure. In the prior, we combine transcription factor (TF) binding data and gene expression data based on Dempster-Shafer (D-S) evidence theory. In addition, a smooth probabilistic model is used in the TF binding data while the Pearson correlation model is used in the gene expression data. We learn the GRNs through dynamic Bayesian network (DBN) inference algorithms. In order to verify the effectiveness of the proposed method, we use the method on the yeast cell cycle gene expression data and also compare the results with those already reported in the literatures. Results obtained from experimental data demonstrate that combing multiple types of data based on D-S evidence theory in modeling GRNs is more accurate than others.

A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

Dynamic Bayesian networks (DBNs) extend Bayesian networks from static domains to dynamic domains. The only known generic method for exact inference in DBNs is based on dynamic expansion and reduction of active slices. It is effective when the domain evolves relatively slowly, but is reported to be "too expensive" for fast evolving domain where inference is under time pressure. This study explores the stationary feature of problem domains to improve the efficiency of exact inference in DBNs. We propose the construction of a temporally invariant template of a DBN directly supporting exact inference and discuss issues in the construction. This method eliminates the need for the computation associated with dynamic expansion and reduction of the existing method. The method is demonstrated by experimental result.

We propose a dynamic differential Bayesian networks (DDBNs) and nonparametric regression model. This model is an extended model of traditional dynamic Bayesian networks (DBNs), which can incorporate temporal information in a natural way and directly handle real-valued data obtained from microarrays without any transformation. In addition, it can cope with differential information between gene expression levels, without any loss to the traditional advantage, i.e., the capability of estimating non-linear relationships between genes. We apply DDBNs to analyze simulated data and real data, i.e., Saccharomyces cerevisiae cell cycle gene expression data. We have confirmed the effectiveness of our approach in the sense that some edges have been successfully detected only by DDBNs, not by DBNs.