Detection of Sources in Non-Negative Blind Source Separation by Minimum Description Length Criterion

While non-negative blind source separation (nBSS) has found many successful applications in science and engineering, model order selection, determining the number of sources, remains a critical yet unresolved problem. Various model order selection methods have been proposed and applied to real-world data sets but with limited success, with both order over- and under-estimation reported. By studying existing schemes, we have found that the unsatisfactory results are mainly due to invalid assumptions, model oversimplification, subjective thresholding, and/or to assumptions made solely for mathematical convenience. Building on our earlier work that reformulated model order selection for nBSS with more realistic assumptions and models, we report a newly and formally revised model order selection criterion rooted in the minimum description length (MDL) principle. Adopting widely invoked assumptions for achieving a unique nBSS solution, we consider the mixing matrix as consisting of deterministic unknowns, with the source signals following a multivariate Dirichlet distribution. We derive a computationally efficient, stochastic algorithm to obtain approximate maximum-likelihood estimates of model parameters and apply Monte Carlo integration to determine the description length. Our modeling and estimation strategy exploits the characteristic geometry of the data simplex in nBSS. We validate our nBSS-MDL criterion through extensive simulation studies and on four real-world data sets, demonstrating its strong performance and general applicability to nBSS. The proposed nBSS-MDL criterion consistently detects the true number of sources, in all of our case studies.

From gene expression to gene regulatory networks in Arabidopsis thaliana

BACKGROUND

The elucidation of networks from a compendium of gene expression data is one of the goals of systems biology and can be a valuable source of new hypotheses for experimental researchers. For Arabidopsis, there exist several thousand microarrays which form a valuable resource from which to learn.

RESULTS

A novel Bayesian network-based algorithm to infer gene regulatory networks from gene expression data is introduced and applied to learn parts of the transcriptomic network in Arabidopsis thaliana from a large number (thousands) of separate microarray experiments. Starting from an initial set of genes of interest, a network is grown by iterative addition to the model of the gene, from another defined set of genes, which gives the 'best' learned network structure. The gene set for iterative growth can be as large as the entire genome. A number of networks are inferred and analysed; these show (i) an agreement with the current literature on the circadian clock network, (ii) the ability to model other networks, and (iii) that the learned network hypotheses can suggest new roles for poorly characterized genes, through addition of relevant genes from an unconstrained list of over 15,000 possible genes. To demonstrate the latter point, the method is used to suggest that particular GATA transcription factors are regulators of photosynthetic genes. Additionally, the performance in recovering a known network from different amounts of synthetically generated data is evaluated.

CONCLUSION

Our results show that plausible regulatory networks can be learned from such gene expression data alone. This work demonstrates that network hypotheses can be generated from existing gene expression data for use by experimental biologists.

Calculation of power and sample size with bounded outcome scores

The two-sample Wilcoxon rank sum test is the most popular non-parametric test for the comparison of two samples when the underlying distributions are not normal. Although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic, parametric assumptions are often made to determine the power of the test or the sample size. We encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients. It is shown that, for power and sample size estimation, it can be dangerous to apply the classical formulae routinely, especially with outcome scores having a U-shaped or a J-shaped distribution. As an example we have taken the Barthel index, a quality-of-life outcome measure in stroke patients. Further, we have investigated alternative methods by means of Monte Carlo simulation. The distributional characteristics of the estimated powers were compared. Our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non-parametric method.