We consider the problem of learning a high-dimensional multi-task regression model, under sparsity constraints induced by presence of grouping structures on the input covariates and on the output predictors. This problem is primarily motivated by expression quantitative trait locus (eQTL) mapping, of which the goal is to discover genetic variations in the genome (inputs) that influence the expression levels of multiple co-expressed genes (outputs), either epistatically, or pleiotropically, or both. A structured input-output lasso (SIOL) model based on an intricate l1/l2-norm penalty over the regression coefficient matrix is employed to enable discovery of complex sparse input/output relationships; and a highly efficient new optimization algorithm called hierarchical group thresholding (HiGT) is developed to solve the resultant non-differentiable, non-separable, and ultra high-dimensional optimization problem. We show on both simulation and on a yeast eQTL dataset that our model leads to significantly better recovery of the structured sparse relationships between the inputs and the outputs, and our algorithm significantly outperforms other optimization techniques under the same model. Additionally, we propose a novel approach for efficiently and effectively detecting input interactions by exploiting the prior knowledge available from biological experiments.

In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in Lp-norm. We show that the natural combinatorial optimization problems obtained may be relaxed into convex optimization problems and introduce a notion, the lower combinatorial envelope of a set-function, that characterizes the tightness of our relaxations. We moreover establish links with norms based on latent representations including the latent group Lasso and block-coding, and with norms obtained from submodular functions.

Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm that, based on the current state, dynamically switches between a sequential policy and a batch policy with variable batch sizes. We provide theoretical justification for our algorithm and present experimental results on eight benchmark BO problems. The results show that our method achieves substantial speedup (up to %78) compared to a pure sequential policy, without suffering any significant performance loss.

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with traffic anomaly detection in backbone networks, and subsumes compressed sensing as well as the timely low-rank plus sparse matrix recovery tasks encountered in matrix decomposition problems. Leveraging the ability of $\ell_1$- and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property when restricted to operate on sparse vectors. When the low-rank, sparse, and compression matrices are drawn from certain random ensembles, it is established that exact recovery is possible with high probability. First-order algorithms are developed to solve the nonsmooth convex optimization problem with provable iteration complexity guarantees. Insightful tests with synthetic and real network data corroborate the effectiveness of the novel approach in unveiling traffic anomalies across flows and time, and its ability to outperform existing alternatives.

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the regularization by the $\ell_1$-norm. In this paper, we consider situations where we are not only interested in sparsity, but where some structural prior knowledge is available as well. We show that the $\ell_1$-norm can then be extended to structured norms built on either disjoint or overlapping groups of variables, leading to a flexible framework that can deal with various structures. We present applications to unsupervised learning, for structured sparse principal component analysis and hierarchical dictionary learning, and to supervised learning in the context of non-linear variable selection.

We suggest using the max-norm as a convex surrogate constraint for clustering. We show how this yields a better exact cluster recovery guarantee than previously suggested nuclear-norm relaxation, and study the effectiveness of our method, and other related convex relaxations, compared to other clustering approaches.

In this paper, we address the general case of a coordinated secondary network willing to exploit communication opportunities left vacant by a licensed primary network. Since secondary users (SU) usually have no prior knowledge on the environment, they need to learn the availability of each channel through sensing techniques, which however can be prone to detection errors. We argue that cooperation among secondary users can enable efficient learning and coordination mechanisms in order to maximize the spectrum exploitation by SUs, while minimizing the impact on the primary network. To this goal, we provide three novel contributions in this paper. First, we formulate the spectrum selection in secondary networks as an instance of the Multi-Armed Bandit (MAB) problem, and we extend the analysis to the collaboration learning case, in which each SU learns the spectrum occupation, and shares this information with other SUs. We show that collaboration among SUs can mitigate the impact of sensing errors on system performance, and improve the convergence of the learning process to the optimal solution. Second, we integrate the learning algorithms with two collaboration techniques based on modified versions of the Hungarian algorithm and of the Round Robin algorithm that allows reducing the interference among SUs. Third, we derive fundamental limits to the performance of cooperative learning algorithms based on Upper Confidence Bound (UCB) policies in a symmetric scenario where all SU have the same perception of the quality of the resources. Extensive simulation results confirm the effectiveness of our joint learning-collaboration algorithm in protecting the operations of Primary Users (PUs), while maximizing the performance of SUs.

In general Evolutionary Computation (EC) includes a number of optimization methods inspired by biological mechanisms of evolution. The methods catalogued in this area use the Darwinian principles of life evolution to produce algorithms that returns high quality solutions to hard-to-solve optimization problems. The main strength of EC is precisely that they provide good solutions even if the computational resources (e.g., running time) are limited. Astronomy and Astrophysics are two fields that often require optimizing problems of high complexity or analyzing a huge amount of data and the so-called complete optimization methods are inherently limited by the size of the problem/data. For instance, reliable analysis of large amounts of data is central to modern astrophysics and astronomical sciences in general. EC techniques perform well where other optimization methods are inherently limited (as complete methods applied to NP-hard problems), and in the last ten years, numerous proposals have come up that apply with greater or lesser success methodologies of evolutional computation to common engineering problems. Some of these problems, such as the estimation of non-lineal parameters, the development of automatic learning techniques, the implementation of control systems, or the resolution of multi-objective optimization problems, have had (and have) a special repercussion in the fields. For these reasons EC emerges as a feasible alternative for traditional methods. In this paper, we discuss some promising applications in this direction and a number of recent works in this area; the paper also includes a general description of EC to provide a global perspective to the reader and gives some guidelines of application of EC techniques for future research

Many real-world phenomena can be represented by a spatio-temporal signal: where, when, and how much. Social media is a tantalizing data source for those who wish to monitor such signals. Unlike most prior work, we assume that the target phenomenon is known and we are given a method to count its occurrences in social media. However, counting is plagued by sample bias, incomplete data, and, paradoxically, data scarcity -- issues inadequately addressed by prior work. We formulate signal recovery as a Poisson point process estimation problem. We explicitly incorporate human population bias, time delays and spatial distortions, and spatio-temporal regularization into the model to address the noisy count issues. We present an efficient optimization algorithm and discuss its theoretical properties. We show that our model is more accurate than commonly-used baselines. Finally, we present a case study on wildlife roadkill monitoring, where our model produces qualitatively convincing results.