text: We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.
  @cite_4: Motivation: We have used state-space models (SSMs) to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T cell activation. SSMs are a class of dynamic Bayesian networks in which the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be directly measured in a gene expression profiling experiment, for example: genes that have not been included in the microarray, levels of regulatory proteins, the effects of mRNA and protein degradation, etc. Results: We have approached the problem of inferring the model structure of these state-space models using both classical and Bayesian methods. In our previous work, a bootstrap procedure was used to derive classical confidence intervals for parameters representing 'gene--gene' interactions over time. In this article, variational approximations are used to perform the analogous model selection task in the Bayesian context. Certain interactions are present in both the classical and the Bayesian analyses of these regulatory networks. The resulting models place JunB and JunD at the centre of the mechanisms that control apoptosis and proliferation. These mechanisms are key for clonal expansion and for controlling the long term behavior (e.g. programmed cell death) of these cells. Availability: Supplementary data is available at http: public.kgi.edu wild index.htm and Matlab source code for variational Bayesian learning of SSMs is available at http: www.cse.ebuffalo.edu faculty mbeal software.html Contact: David_Wild@kgi.edu
  @cite_8: 
  @cite_10: Motivation: In systems like Escherichia Coli, the abundance of sequence information, gene expression array studies and small scale experiments allows one to reconstruct the regulatory network and to quantify the effects of transcription factors on gene expression. However, this goal can only be achieved if all information sources are used in concert. Results: Our method integrates literature information, DNA sequences and expression arrays. A set of relevant transcription factors is defined on the basis of literature. Sequence data are used to identify potential target genes and the results are used to define a prior distribution on the topology of the regulatory network. A Bayesian hidden component model for the expression array data allows us to identify which of the potential binding sites are actually used by the regulatory proteins in the studied cell conditions, the strength of their control, and their activation profile in a series of experiments. We apply our methodology to 35 expression studies in E.Coli with convincing results. Availability: www.genetics.ucla.edu labs sabatti software.html Supplementary information: The supplementary material are available at Bioinformatics online. Contact: csabatti@mednet.ucla.edu
  @cite_3: 
  @cite_0: Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not fixed. This paper proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of differing dimensionality, which is flexible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple change-point analysis in one and two dimensions, and to a Bayesian comparison of binomial experiments.
  @cite_13: Motivation: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. Recent experimental high-throughput techniques, such as Chromatin Immunoprecipitation (ChIP) provide important information about the architecture of the regulatory networks in the cell. However, it is very difficult to measure the concentration levels of transcription factor proteins and determine their regulatory effect on gene transcription. It is therefore an important computational challenge to infer these quantities using gene expression data and network architecture data. Results: We develop a probabilistic state space model that allows genome-wide inference of both transcription factor protein concentrations and their effect on the transcription rates of each target gene from microarray data. We use variational inference techniques to learn the model parameters and perform posterior inference of protein concentrations and regulatory strengths. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates, as well as providing a tool to detect which binding events lead to significant regulation. We demonstrate our model on artificial data and on two yeast datasets in which the network structure has previously been obtained using ChIP data. Predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell. Availability: MATLAB code is available from http: umber.sbs.man.ac.uk resources puma Contact: guido@dcs.shef.ac.uk Supplementary information: Supplementary Data are available at Bioinformatics online
  @cite_12: We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical biomarkers. Based on the metaphor of statistically derived “factors” as representing biological “subpathway” structure, we explore the decomposition of fitted sparse factor models into pathway subcomponents and investigate how these components overlay multiple aspects of known biological activity. Our methodology is based on sparsity modeling of multivariate regression, ANOVA, and latent factor models, as well as a class of models that combines all components. Hierarchical sparsity priors address questions of dimension reduction and multiple co...
  @cite_11: We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. This tree-dependent component analysis (TCA) provides a tractable and flexible approach to weakening the assumption of independence in ICA. In particular, TCA allows the underlying graph to have multiple connected components, and thus the method is able to find "clusters" of components such that components are dependent within a cluster and independent between clusters. Finally, we make use of a notion of graphical models for time series due to Brillinger (1996) to extend these ideas to the temporal setting. In particular, we are able to fit models that incorporate tree-structured dependencies among multiple time series.
summary: A number of probabilistic approaches have been proposed in the past for the problem of gene-regulatory network reconstruction @cite_10 @cite_13 @cite_4 @cite_3 . Some take into account the information on the prior network topology @cite_10 , which is not always available. Most assume the number of factors is known. To get around this, one can perform model selection via Reversible Jump MCMC @cite_0 or evolutionary stochastic model search @cite_12 . Unfortunately, these methods are often difficult to design and may take quite long to converge. Moreover, they are difficult to integrate with other forms of prior knowledge (eg., factor hierarchies). A somewhat similar approach to ours is the infinite independent component analysis (iICA) model of @cite_8 which treats factor analysis as a special case of ICA. However, their model is limited to factor analysis and does not take into account feature selection, factor hierarchy and factor regression. As a generalization to the standard ICA model, @cite_11 proposed a model in which the components can be related via a tree-structured graphical model. It, however, assumes a fixed number of components.