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. 1

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 Chromatine Immunoprecipitation 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 data sets in which the network structure has previously been obtained using Chromatine Immunoprecipitation 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

Abstract. Linear Gaussian State-Space Models are widely used and a Bayesian treatment of parameters is therefore of considerable interest. The approximate Variational Bayesian method applied to these models is an attractive approach, used successfully in applications ranging from acoustics to bioinformatics. The most challenging aspect of implementing the method is in performing inference on the hidden state sequence of the model. We show how to convert the inference problem so that standard and stable Kalman Filtering/Smoothing recursions from the literature may be applied. This is in contrast to previously published approaches based on Belief Propagation. Our framework both simplifies and unifies the inference problem, so that future applications may be easily developed. We demonstrate the elegance of the approach on Bayesian temporal ICA, with an application to finding independent components in noisy EEG signals. IDIAP–RR 06-50 1 1 Linear Gaussian State-Space Models Linear Gaussian State-Space Models (LGSSMs) 1 are fundamental in time-series analysis [1, 2, 3]. In these models the observations v1:T 2 are generated from an underlying dynamical system on h1:T according to vt = Bht + η v t, η v t ∼ N(0V,ΣV); ht = Aht−1 + η h t, η h t ∼ N (0H,ΣH), where N(µ,Σ) denotes a Gaussian with mean µ and covariance Σ, and 0X denotes an X-dimensional zero vector. The observation vt has dimension V and the hidden state ht dimension H. Probabilistically, the LGSSM is defined by: T∏ p(v1:T,h1:T |Θ) = p(v1|h1)p(h1) p(vt|ht)p(ht|ht−1), t=2

We propose a model–based approach to unify clustering and network modeling using time–course gene expression data. Specifically, our approach uses a mixture model to cluster genes. Genes within the same cluster share a similar expression profile. The network is built over cluster–specific expression profiles using state–space models. We discuss the application of our model to simulated data as well as to time–course gene expression data arising from animal models on prostate cancer progression. The latter application shows that with a combined statistical/bioinformatics analyses we are able to extract gene-to-gene relationships supported by the literature as well as new plausible relationships. Keywords: Model–based clustering, Bayesian network, dynamic linear model, mixture model, time course gene expression, prostate cancer, bioinformatics. 1

Motivation: Inferring the relationships between transcription factors (TFs) and their targets has utmost importance for understanding the complex regulatory mechanisms in cellular systems. However, the transcription factor activities (TFAs) cannot be measured directly by standard microarray experiment owing to various posttranslational modifications. In particular, cooperative mechanism and combinatorial control are common in gene regulation, e.g. TFs usually recruit other proteins cooperatively to facilitate transcriptional reaction processes. Results: In this paper, we propose a novel method for inferring transcriptional regulatory networks (TRN) from gene expression data based on protein transcription complexes and mass action law. With gene expression data and TFAs estimated from transcription complex information, the inference of TRN is formulated as a linear programming problem which has a globally optimal solution in terms of L1 norm error. The proposed method not only can easily incorporate ChIP-Chip data as prior knowledge but also can integrate multiple gene expression datasets from different experiments simultaneously. A unique feature of our method is to take into account protein cooperation in transcription process. We tested our method by using both synthetic data and several experimental datasets in yeast. The extensive results illustrate the effectiveness of the proposed method for predicting transcription regulatory relationships between TFs with co-regulators and target genes.

Abstract. We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian State-Space models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes. 1

This paper explores how entropy and other information theoretic quantities may be used to reverseengineer genetic regulatory networks from repeated microarray data. The problem of differentiating genes that undergo direct coregulation from genes whose expression is similar because they belong to the same regulatory pathway is studied from a graphical modeling viewpoint. This leads to the criteria of conditional independence which can be evaluated by computing the conditional mutual information. The latter is completely characterized by the sum of the entropies of joint variables, underlining the need for an entropy estimator that is accurate even in low sampling conditions. We introduce a new plug-in entropy estimator obtained from shrinking maximum likelihood multinomial proportions estimates to the maximum entropy target. We derive the closely related ZIPshrink and ZINBshrink entropy estimators which enhance the shrinkage estimator by first adjusting the shrinkage target depending on the fraction of structural zeros in the multinomial model. The fraction of structural zeros is estimated using a Zero-Inflated Poisson or Zero-Inflated Negative Binomial distribution to model the histogram of bin counts. We compare these three new estimators to state of the art estimators. We show that they give acceptable

Abstract. This paper presents a method for regulatory network reconstruction from experimental data. We propose a mathematical model for regulatory interactions, based on the work of Thomas et al. [25] extended with a stochastic element and provide an algorithm for reconstruction of such models from gene expression time series. We examine mathematical properties of the model and the reconstruction algorithm and test it on expression profiles obtained from numerical simulation of known regulatory networks. We compare the reconstructed networks with the ones reconstructed from the same data using Dynamic Bayesian Networks and show that in these cases our method provides the same or better results. The supplemental materials to this article are available from the website

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The understanding of molecular cell biology requires insight into the structure and dynamics of networks that are made up of thousands of interacting molecules of DNA, RNA, proteins, metabolites, and other components. One of the central goals of systems biology is the unraveling of the as yet poorly