An Empirical-Bayes Score for Discrete Bayesian Networks

Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions; and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate.Comment: 12 pages, PGM 201

Learning Bayesian Networks with the bnlearn R Package

bnlearn is an R package (R Development Core Team 2010) which includes several algorithms for learning the structure of Bayesian networks with either discrete or continuous variables. Both constraint-based and score-based algorithms are implemented, and can use the functionality provided by the snow package (Tierney et al. 2008) to improve their performance via parallel computing. Several network scores and conditional independence algorithms are available for both the learning algorithms and independent use. Advanced plotting options are provided by the Rgraphviz package (Gentry et al. 2010).

Who Learns Better Bayesian Network Structures: Accuracy and Speed of Structure Learning Algorithms

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known (Cowell, 2001). In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and real-world complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.Comment: 27 pages, 8 figure

OXIDATIVE CHANGES OF LIPIDS, PROTEINS AND ANTIOXIDANTS IN YOGURT DURING THE SHELF LIFE

Background: Oxidation processes in milk and yogurt during the shelf life can result in an alteration of protein and lipid constituents. Therefore, the antioxidant properties of yogurt in standard conditions of preservation were evaluated. Results: Total phenols, free radical scavenger activity, degree of lipid peroxidation and protein oxidation were determined in plain and skim yogurts with or without fruit puree. After production, plain, skim, plain berries and skim berries yogurts were compared during the shelf life up to 9 weeks. All types of yogurts revealed a basal antioxidant activity that was higher when a fruit puree was present but gradually decreased during the shelf life. However, after five-eight weeks, antioxidant activity increased again. Both in plain and berries yogurts lipid peroxidation increased until the seventh week of shelf life and after decreased, while protein oxidation of all yogurts was similar either in the absence or presence of berries and increased during shelf life. Conclusion: During the shelf life, a different behavior between lipid and protein oxidation takes place and the presence of berries determines a protection only against lipid peroxidation

NATbox: a network analysis toolbox in R

Background: There has been recent interest in capturing the functional relationships (FRs) from high-throughput assays using suitable computational techniques. FRs elucidate the working of genes in concert as a system as opposed to independent entities hence may provide preliminary insights into biological pathways and signalling mechanisms. Bayesian structure learning (BSL) techniques and its extensions have been used successfully for modelling FRs from expression profiles. Such techniques are especially useful in discovering undocumented FRs, investigating non-canonical signalling mechanisms and cross-talk between pathways. The objective of the present study is to develop a graphical user interface (GUI), NATbox: Network Analysis Toolbox in the language R that houses a battery of BSL algorithms in conjunction with suitable statistical tools for modelling FRs in the form of acyclic networks from gene expression profiles and their subsequent analysis. Results: NATbox is a menu-driven open-source GUI implemented in the R statistical language for modelling and analysis of FRs from gene expression profiles. It provides options to (i) impute missing observations in the given data (ii) model FRs and network structure from gene expression profiles using a battery of BSL algorithms and identify robust dependencies using a bootstrap procedure, (iii) present the FRs in the form of acyclic graphs for visualization and investigate its topological properties using network analysis metrics, (iv) retrieve FRs of interest from published literature. Subsequently, use these FRs as structural priors in BSL (v) enhance scalability of BSL across high-dimensional data by parallelizing the bootstrap routines. Conclusion: NATbox provides a menu-driven GUI for modelling and analysis of FRs from gene expression profiles. By incorporating readily available functions from existing R-packages, it minimizes redundancy and improves reproducibility, transparency and sustainability, characteristic of open-source environments. NATbox is especially suited for interdisciplinary researchers and biologists with minimal programming experience and would like to use systems biology approaches without delving into the algorithmic aspects. The GUI provides appropriate parameter recommendations for the various menu options including default parameter choices for the user. NATbox can also prove to be a useful demonstration and teaching tool in graduate and undergraduate course in systems biology. It has been tested successfully under Windows and Linux operating systems. The source code along with installation instructions and accompanying tutorial can be found at: http://bioinformatics.ualr.edu/natboxWiki/index.php/Main_Page. </p

Learning Bayesian Networks with the bnlearn R Package

bnlearn is an R package (R Development Core Team 2010) which includes several algorithms for learning the structure of Bayesian networks with either discrete or continuous variables. Both constraint-based and score-based algorithms are implemented, and can use the functionality provided by the snow package (Tierney et al. 2008) to improve their performance via parallel computing. Several network scores and conditional independence algorithms are available for both the learning algorithms and independent use. Advanced plotting options are provided by the Rgraphviz package (Gentry et al. 2010)