Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin

Quadratic approximate dynamic programming for scheduling water resources: a case study

We address the problem of scheduling water resources in a power system via approximate dynamic programming.To this goal, we model a finite horizon economic dispatch problemwith convex stage cost and affine dynamics, and consider aquadratic approximation of the value functions. Evaluating theachieved policy entails solving a quadratic program at each timestep, while value function fitting can be cast as a semidefiniteprogram. We test our proposed algorithm on a simplified versionof the Uruguayan power system, achieving a four percent costreduction with respect to the myopic polic

Inference of Gene Regulatory Networks with Sparse Structural Equation Models Exploiting Genetic Perturbations

<div><p>Integrating genetic perturbations with gene expression data not only improves accuracy of regulatory network topology inference, but also enables learning of causal regulatory relations between genes. Although a number of methods have been developed to integrate both types of data, the desiderata of efficient and powerful algorithms still remains. In this paper, sparse structural equation models (SEMs) are employed to integrate both gene expression data and <i>cis</i>-expression quantitative trait loci (<i>cis</i>-eQTL), for modeling gene regulatory networks in accordance with biological evidence about genes regulating or being regulated by a small number of genes. A systematic inference method named sparsity-aware maximum likelihood (SML) is developed for SEM estimation. Using simulated directed acyclic or cyclic networks, the SML performance is compared with that of two state-of-the-art algorithms: the adaptive Lasso (AL) based scheme, and the QTL-directed dependency graph (QDG) method. Computer simulations demonstrate that the novel SML algorithm offers significantly better performance than the AL-based and QDG algorithms across all sample sizes from 100 to 1,000, in terms of detection power and false discovery rate, in all the cases tested that include acyclic or cyclic networks of 10, 30 and 300 genes. The SML method is further applied to infer a network of 39 human genes that are related to the immune function and are chosen to have a reliable eQTL per gene. The resulting network consists of 9 genes and 13 edges. Most of the edges represent interactions reasonably expected from experimental evidence, while the remaining may just indicate the emergence of new interactions. The sparse SEM and efficient SML algorithm provide an effective means of exploiting both gene expression and perturbation data to infer gene regulatory networks. An open-source computer program implementing the SML algorithm is freely available upon request.</p></div

Performance of the SML and AL algorithms for directed <i>acyclic</i> networks of genes [(a) power of detection, and (b) false discover rate].

<p>Expected number of nodes per node is . PD and FDR were obtained from 10 replicates of the network with different sample sizes ( to 1,000).</p

Performance of SML, AL and QDG algorithms for directed <i>acyclic</i> networks of [(a) and (b)] or 30 [(c) and (d)] genes.

<p>Expected number of nodes per node is . PD and FDR were obtained from 100 replicates of the network with different sample sizes ( to 1,000).</p

Performance of SML, AL and QDG algorithms for directed <i>cyclic</i> networks of [(a) and (b)] or 30 [(c) and (d)] genes.

<p>Expected number of nodes per node is . PD and FDR were obtained from 100 replicates of the network with different sample sizes ( to 1,000).</p