Riccardo Boscolo

Network component analysis: Reconstruction of regulatory signals in biological systems

High-dimensional data sets generated by high-throughput technologies, such as DNA microarray, are often the outputs of complex networked systems driven by hidden regulatory signals. Traditional statistical methods for computing low-dimensional or hidden representations of these data sets, such as principal component analysis and independent component analysis, ignore the underlying network structures and provide decompositions based purely on a priori statistical constraints on the computed component signals. The resulting decomposition thus provides a phenomenological model for the observed data and does not necessarily contain physically or biologically meaningful signals. Here, we develop a method, called network component analysis, for uncovering hidden regulatory signals from outputs of networked systems, when only a partial knowledge of the underlying network topology is available. The a priori network structure information is first tested for compliance with a set of identifiability criteria. For networks that satisfy the criteria, the signals from the regulatory nodes and their strengths of influence on each output node can be faithfully reconstructed. This method is first validated experimentally by using the absorbance spectra of a network of various hemoglobin species. The method is then applied to microarray data generated from yeast Saccharamyces cerevisiae and the activities of various transcription factors during cell cycle are reconstructed by using recently discovered connectivity information for the underlying transcriptional regulatory networks.

Independent component analysis based on nonparametric density estimation

In this paper, we introduce a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following the proposed approach, the blind signal separation framework can be posed as a nonlinear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. We conducted a series of Monte Carlo simulations, involving linear mixtures of various source signals with different statistical characteristics and sample sizes. The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics, can consistently achieve an accurate separation of all the mixed signals. 2) Adopting a suitably designed optimization framework, it is possible to derive a flexible ICA algorithm that matches the stability and convergence properties of conventional algorithms. 3) A nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions.

An Information Theoretic Exploratory Method for Learning Patterns of Conditional Gene Coexpression from Microarray Data

In this paper, we introduce an exploratory framework for learning patterns of conditional coexpression in gene expression data. The main idea behind the proposed approach consists of estimating how the information content shared by a set of M nodes in a network (where each node is associated to an expression profile) varies upon conditioning on a set of L conditioning variables (in the simplest case represented by a separate set of expression profiles). The method is nonparametric, and it is based on the concept of statistical coinformation, which, unlike conventional correlation-based techniques, is not restricted in scope to linear conditional dependency patterns. Moreover, such conditional coexpression relationships can potentially indicate regulatory interactions that do not manifest themselves when only pairwise relationships are considered. A moment-based approximation of the coinformation measure is derived that efficiently gets around the problem of estimating high-dimensional multivariate probability density functions from the data, a task usually not viable due to the intrinsic sample size limitations that characterize expression-level measurements. By applying the proposed exploratory method, we analyzed a whole genome microarray assay of the eukaryote Saccharomices cerevisiae and were able to learn statistically significant patterns of conditional coexpression. A selection of such interactions that carry a meaningful biological interpretation are discussed.

Inferring Regulatory Interactions between Transcriptional Factors and Genes by Propagating Known Regulatory Links

Determining transcriptional regulatory networks has been one of the most important goals in the field of functional genomics. Despite the recent advances in experimental techniques, complementary computational techniques have lagged behind. We introduce a novel computational methodology that uses DNA microarray data and known regulatory interactions to predict unknown regulatory interactions. Our method involves three steps: in the training stage, we utilize network component analysis (NCA) (Liao et al., 2003; Kao et al., 2004; Boscolo et al., 2005) to reconstruct the hidden activity profiles of transcriptional factors (TF); then we cluster TFs into functional modules according to the similarities of their reconstructed activity profiles; in the prediction stage, we infer additional TF-gene regulatory links by selecting TF profiles that best interpret genes expression profiles via a linear model. We applied the methodology to a gene expression dataset of bacterium Escherichia coli, whose partial TF-gene regulatory structure is obtained from RegulonDB (Salgado et al., 2004). Cross-validation results show that when the profiles of all TFs regulating a gene are reconstructed from NCA, we could identify 36% of the TF-gene interactions, and the prediction accuracy is 89%. And when the profiles of partial (50% or more) TFs regulating a gene can be reconstructed, we can identify 14% of the TF-gene interactions, and the accuracy rate is 69%. These represent some of the best known accuracy and coverage statistics reported in the literature so far