A randomised primal-dual algorithm for distributed radio-interferometric imaging

Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets is of prime importance. Motivated by this, we investigate herein a convex optimisation algorithmic structure, based on primal-dual forward-backward iterations, for solving the radio interferometric imaging problem. It can encompass any convex prior of interest. It allows for the distributed processing of the measured data and introduces further flexibility by employing a probabilistic approach for the selection of the data blocks used at a given iteration. We study the reconstruction performance with respect to the data distribution and we propose the use of nonuniform probabilities for the randomised updates. Our simulations show the feasibility of the randomisation given a limited computing infrastructure as well as important computational advantages when compared to state-of-the-art algorithmic structures.Comment: 5 pages, 3 figures, Proceedings of the European Signal Processing Conference (EUSIPCO) 2016, Related journal publication available at https://arxiv.org/abs/1601.0402

Computing Minimal Polynomials of Matrices

We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We compare features of the algorithm with several other algorithms in the literature. In addition we present a deterministic verification procedure which is similarly efficient in most cases but has a worst-case complexity of $O(n^4)$. Finally, we report the results of practical experiments with an implementation of our algorithms in comparison with the current algorithms in the {\sf GAP} library

Sparse reduced-rank regression for imaging genetics studies: models and applications

We present a novel statistical technique; the sparse reduced rank regression (sRRR) model which is a strategy for multivariate modelling of high-dimensional imaging responses and genetic predictors. By adopting penalisation techniques, the model is able to enforce sparsity in the regression coefficients, identifying subsets of genetic markers that best explain the variability observed in subsets of the phenotypes. To properly exploit the rich structure present in each of the imaging and genetics domains, we additionally propose the use of several structured penalties within the sRRR model. Using simulation procedures that accurately reflect realistic imaging genetics data, we present detailed evaluations of the sRRR method in comparison with the more traditional univariate linear modelling approach. In all settings considered, we show that sRRR possesses better power to detect the deleterious genetic variants. Moreover, using a simple genetic model, we demonstrate the potential benefits, in terms of statistical power, of carrying out voxel-wise searches as opposed to extracting averages over regions of interest in the brain. Since this entails the use of phenotypic vectors of enormous dimensionality, we suggest the use of a sparse classification model as a de-noising step, prior to the imaging genetics study. Finally, we present the application of a data re-sampling technique within the sRRR model for model selection. Using this approach we are able to rank the genetic markers in order of importance of association to the phenotypes, and similarly rank the phenotypes in order of importance to the genetic markers. In the very end, we illustrate the application perspective of the proposed statistical models in three real imaging genetics datasets and highlight some potential associations

Bridging topological and functional information in protein interaction networks by short loops profiling

Protein-protein interaction networks (PPINs) have been employed to identify potential novel interconnections between proteins as well as crucial cellular functions. In this study we identify fundamental principles of PPIN topologies by analysing network motifs of short loops, which are small cyclic interactions of between 3 and 6 proteins. We compared 30 PPINs with corresponding randomised null models and examined the occurrence of common biological functions in loops extracted from a cross-validated high-confidence dataset of 622 human protein complexes. We demonstrate that loops are an intrinsic feature of PPINs and that specific cell functions are predominantly performed by loops of different lengths. Topologically, we find that loops are strongly related to the accuracy of PPINs and define a core of interactions with high resilience. The identification of this core and the analysis of loop composition are promising tools to assess PPIN quality and to uncover possible biases from experimental detection methods. More than 96% of loops share at least one biological function, with enrichment of cellular functions related to mRNA metabolic processing and the cell cycle. Our analyses suggest that these motifs can be used in the design of targeted experiments for functional phenotype detection.This research was supported by the Biotechnology and Biological Sciences Research Council (BB/H018409/1 to AP, ACCC and FF, and BB/J016284/1 to NSBT) and by the Leukaemia & Lymphoma Research (to NSBT and FF). SSC is funded by a Leukaemia & Lymphoma Research Gordon Piller PhD Studentship

Splitting strategies for post-selection inference

We consider the problem of providing valid inference for a selected parameter in a sparse regression setting. It is well known that classical regression tools can be unreliable in this context due to the bias generated in the selection step. Many approaches have been proposed in recent years to ensure inferential validity. Here, we consider a simple alternative to data splitting based on randomising the response vector, which allows for higher selection and inferential power than the former and is applicable with an arbitrary selection rule. We provide a theoretical and empirical comparison of both methods and extend the randomisation approach to non-normal settings. Our investigations show that the gain in power can be substantial.Comment: 24 pages, 2 figure

Hierarchical modularity in human brain functional networks

The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging (fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I=0.63. The largest 5 modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions

Espace intrinsèque d'un graphe et recherche de communautés

12 pNational audienceDetermining the number of relevant dimensions in the eigen-space of a graph Laplacian matrix is a central issue in many spectral graph-mining applications. We tackle here the problem of finding the "right" dimensionality of Laplacian matrices, especially those often encountered in the domains of social or biological graphs: the ones underlying large, sparse, unoriented and unweighted graphs, often endowed with a power-law degree distribution. We present here the application of a randomization test to this problem. We validate our approach first on an artificial sparse and power-law type graph, with two intermingled clusters, then on a real-world social graph ("Football-league"), where the actual, intrinsic dimension appears to be 11 ; we illustrate the optimality of this transformed dataspace both visually and numerically, by means of a density-based clustering technique and a decision tree