Learning an L1-regularized Gaussian Bayesian Network in the Equivalence Class Space

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plant

Hand Image Segmentation by means of Gaussian Multiscale Aggregation for biometric applications

Applying biometrics to daily scenarios involves demanding requirements in terms of software and hardware. On the contrary, current biometric techniques are also being adapted to present-day devices, like mobile phones, laptops and the like, which are far from meeting the previous stated requirements. In fact, achieving a combination of both necessities is one of the most difficult problems at present in biometrics. Therefore, this paper presents a segmentation algorithm able to provide suitable solutions in terms of precision for hand biometric recognition, considering a wide range of backgrounds like carpets, glass, grass, mud, pavement, plastic, tiles or wood. Results highlight that segmentation accuracy is carried out with high rates of precision (F-measure 88%)), presenting competitive time results when compared to state-of-the-art segmentation algorithms time performance

Gaussian Multiscale Aggregation oriented to Hand Biometric Segmentation in Mobile Devices

New trends in biometrics are oriented to mobile devices in order to increase the overall security in daily actions like bank account access, e-commerce or even document protection within the mobile. However, applying biometrics to mobile devices imply challenging aspects in biometric data acquisition, feature extraction or private data storage. Concretely, this paper attempts to deal with the problem of hand segmentation given a picture of the hand in an unknown background, requiring an accurate result in terms of hand isolation. For the sake of user acceptability, no restrictions are done on background, and therefore, hand images can be taken without any constraint, resulting segmentation in an exigent task. Multiscale aggregation strategies are proposed in order to solve this problem due to their accurate results in unconstrained and complicated scenarios, together with their properties in time performance. This method is evaluated with a public synthetic database with 480000 images considering different backgrounds and illumination environments. The results obtained in terms of accuracy and time performance highlight their capability of being a suitable solution for the problem of hand segmentation in contact-less environments, outperforming competitive methods in literature like Lossy Data Compression image segmentation (LDC).

Gaussian Multiscale Aggregation Applied to Segmentation in Hand Biometrics

This paper presents an image segmentation algorithm based on Gaussian multiscale aggregation oriented to hand biometric applications. The method is able to isolate the hand from a wide variety of background textures such as carpets, fabric, glass, grass, soil or stones. The evaluation was carried out by using a publicly available synthetic database with 408,000 hand images in different backgrounds, comparing the performance in terms of accuracy and computational cost to two competitive segmentation methods existing in literature, namely Lossy Data Compression (LDC) and Normalized Cuts (NCuts). The results highlight that the proposed method outperforms current competitive segmentation methods with regard to computational cost, time performance, accuracy and memory usage.

Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation

It is well known that the evaluation of the influence matrices in the boundary-element method requires the computation of singular integrals. Quadrature formulae exist which are especially tailored to the specific nature of the singularity, i.e. log(*- x0)9 Ijx- JC0), etc. Clearly the nodes and weights of these formulae vary with the location Xo of the singular point. A drawback of this approach is that a given problem usually includes different types of singularities, and therefore a general-purpose code would have to include many alternative formulae to cater for all possible cases. Recently, several authors1"3 have suggested a type independent alternative technique based on the combination of standard Gaussian rules with non-linear co-ordinate transformations. The transformation approach is particularly appealing in connection with the p.adaptive version, where the location of the collocation points varies at each step of the refinement process. The purpose of this paper is to analyse the technique in eference 3. We show that this technique is asymptotically correct as the number of Gauss points increases. However, the method possesses a 'hidden' source of error that is analysed and can easily be removed.

Distributed static linear Gaussian models using consensus

Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance tradeoff.

Differential resultant formulas for linear od-polynomials.

Ponencia

Massively parallelizable list-mode reconstruction using a Monte Carlo-based elliptical Gaussian model

Purpose: A fully three-dimensional (3D) massively parallelizable list-mode ordered-subsets expectation-maximization (LM-OSEM) reconstruction algorithm has been developed for high-resolution PET cameras. System response probabilities are calculated online from a set of parameters derived from Monte Carlo simulations. The shape of a system response for a given line of response (LOR) has been shown to be asymmetrical around the LOR. This work has been focused on the development of efficient region-search techniques to sample the system response probabilities, which are suitable for asymmetric kernel models, including elliptical Gaussian models that allow for high accuracy and high parallelization efficiency. The novel region-search scheme using variable kernel models is applied in the proposed PET reconstruction algorithm. Methods: A novel region-search technique has been used to sample the probability density function in correspondence with a small dynamic subset of the field of view that constitutes the region of response (ROR). The ROR is identified around the LOR by searching for any voxel within a dynamically calculated contour. The contour condition is currently defined as a fixed threshold over the posterior probability, and arbitrary kernel models can be applied using a numerical approach. The processing of the LORs is distributed in batches among the available computing devices, then, individual LORs are processed within different processing units. In this way, both multicore and multiple many-core processing units can be efficiently exploited. Tests have been conducted with probability models that take into account the noncolinearity, positron range, and crystal penetration effects, that produced tubes of response with varying elliptical sections whose axes were a function of the crystal's thickness and angle of incidence of the given LOR. The algorithm treats the probability model as a 3D scalar field defined within a reference system aligned with the ideal LOR. Results: This new technique provides superior image quality in terms of signal-to-noise ratio as compared with the histogram-mode method based on precomputed system matrices available for a commercial small animal scanner. Reconstruction times can be kept low with the use of multicore, many-core architectures, including multiple graphic processing units. Conclusions: A highly parallelizable LM reconstruction method has been proposed based on Monte Carlo simulations and new parallelization techniques aimed at improving the reconstruction speed and the image signal-to-noise of a given OSEM algorithm. The method has been validated using simulated and real phantoms. A special advantage of the new method is the possibility of defining dynamically the cut-off threshold over the calculated probabilities thus allowing for a direct control on the trade-off between speed and quality during the reconstruction.

Linear Sparse Differential Resultant Formulas

Let P be a system of n linear nonhomogeneous ordinary differential polynomials in a set U of n-1 differential indeterminates. Differential resultant formulas are presented to eliminate the differential indeterminates in U from P. These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in P, or in a linear perturbation Pe of P. In particular, the formula dfres(P) is the determinant of a matrix M(P) having no zero columns if the system P is ``super essential". As an application, if the system PP is sparse generic, such formulas can be used to compute the differential resultant dres(PP) introduced by Li, Gao and Yuan.

Sparse differential resultant formulas: between the linear and the nonlinear case

A matrix representation of the sparse differential resultant is the basis for efficient computation algorithms, whose study promises a great contribution to the development and applicability of differential elimination techniques. It is shown how sparse linear differential resultant formulas provide bounds for the order of derivation, even in the nonlinear case, and they also provide (in many cases) the bridge with results in the nonlinear algebraic case.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Fully adaptive gaussian mixture metropolis-hastings algorithm

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples from generic multimodal and multidimensional target distributions. The proposal density is a mixture of Gaussian densities with all parameters (weights, mean vectors and covariance matrices) updated using all the previously generated samples applying simple recursive rules. Numerical results for the one and two-dimensional cases are provided.

Determinación de los periodos propios de presas bóveda simétricas mediante formulas empíricas

El artículo presenta una formulación sencilla que permite obtener los seis primeros períodos propios de vibración de una presa bóveda simétrica diseñada según las recomendaciones del U.S. Bureau of Reclamation. Se indican las expresiones polinómicas aproximadas de estos períodos, tanto para embalse vacío como para embalse lleno. El efecto del embalse se modeliza mediante la técnica de Westergaard modificada. Asimismo se indica una expresión que intenta tener en cuenta, de modo tentativo, el efecto de la flexibilidad del terreno

Genetic algorithms and Gaussian Bayesian networks to uncover the predictive core set of bibliometric indices

The diversity of bibliometric indices today poses the challenge of exploiting the relationships among them. Our research uncovers the best core set of relevant indices for predicting other bibliometric indices. An added difficulty is to select the role of each variable, that is, which bibliometric indices are predictive variables and which are response variables. This results in a novel multioutput regression problem where the role of each variable (predictor or response) is unknown beforehand. We use Gaussian Bayesian networks to solve the this problem and discover multivariate relationships among bibliometric indices. These networks are learnt by a genetic algorithm that looks for the optimal models that best predict bibliometric data. Results show that the optimal induced Gaussian Bayesian networks corroborate previous relationships between several indices, but also suggest new, previously unreported interactions. An extended analysis of the best model illustrates that a set of 12 bibliometric indices can be accurately predicted using only a smaller predictive core subset composed of citations, g-index, q2-index, and hr-index. This research is performed using bibliometric data on Spanish full professors associated with the computer science area.

Checking existing formulas for estimating overtopping rates in harbour breakwaters

The purpose of the research work resulting from various studies undertaken in the CEDEX, as summarized in this article, is to make a comparative analysis of methods for calculating overtopping rates developed by different authors. To this effect, in the first place, existing formulas for estimating the overtopping rate on rubble mound and vertical breakwaters were summarised and analysed. Later, the above mentioned formulas were compared using the results obtained in a series of hydraulic model tests at the CEDEX. The results obtained in the Ferrol outer harbour breakwater and Melilla harbour breakwater tests are presented here. A calculation method based on the neural network theory, developed in the European CLASH Project, was applied to a series of sloping breakwater tests in order to complete this research and the results obtained in the Ferrol outer harbour breakwater test are presented in this article. A series of additional tests was also carried out in a physical model on the standard cross section of the Bilbao harbour sloping breakwater’s cross section, the results of which are under study using the empirical formulas applicable to the cross section, as well as the NN-OVERTOPPING neural network