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Deep neural network models (DGPs) can be represented hierarchically by a sequential composition of layers. When the prior distribution over the weights and biases are independently identically distributed, there is an equivalence with Gaussian processes (GP) in the limit of an infinite net[1]work width. DGPs are non-parametric statistical models used to character[1]ize patterns of complex non-linear systems due to their flexibility, greater generalization capacity, and a natural way of making inferences about the parameters and states of the system. This article proposes a hierarchi[1]cal Bayesian structure to model the weights and biases of a deep neural network. We deduce a general formula to calculate the integrals of Gaussian processes with non-linear transfer densities and obtain a kernel to estimate the covariance functions. In the methodology, we conduct an empirical study analyzing an electroencephalogram (EEG) database for diagnosing Alzheimer’s disease. Additionally, the DGPs models are esti[1]mated and compared with the NN models for 5, 10, 50, 100, 500, and 1000 neurons in the hidden layer, considering two transfer functions: Recti[1]fied Linear Unit (ReLU) and hyperbolic Tangent (Tanh). The results show good performance in the classification of the signals. Finally, we use the mean square error as a goodness of fit measure to validate the proposed models, obtaining low estimation errors. Los modelos de redes neuronales profundos (DGPs) se pueden repre[1]sentar jerárquicamente mediante una composición secuencial de capas. Cuando la distribución prior sobre los pesos y sesgos son independien[1]tes idénticamente distribuidos, existe una equivalencia con los procesos Gaussiano (GP), en el límite de una anchura de red infinita. Los DGPs son modelos estadísticos no paramétricos y se utilizan para caracterizar los patrones de sistema no lineales complejos, por su flexibilidad, mayor capacidad de generalización, y porque proporcionan una forma natural para hacer inferencia sobre los parámetros y estados del sistema. En este artículo se propone una estructura Bayesiana jerárquica para modelar los pesos y sesgos de la red neuronal profunda, se deduce una formula general para calcular las integrales de procesos Gaussianos con funciones de trans[1]ferencias no lineles, y se obtiene un núcleo para estimar las funciones de covarianzas. Para ilustrar la metodología se realiza un estudio empírico analizando una base de datos de electroencefalogramas (EEG) para el diagnóstico de la enfermedad de Alzheimer. Adicionalmente, se estiman los modelos DGPs, y se comparan con los modelos de NN para 5, 10, 50, 100, 500 y 1000 neuronas en la capa oculta, considerando dos funciones de transferencia: Unidad Lineal Rectificada (ReLU) y tangenge hiperbólica (Tanh). Los resultados demuestran buen desempeño en la clasificación de las señales. Finalmente, utilizó como medida de bondad de ajuste el error cuadrático medio para validar los modelos propuestos, obteniéndose errores de estimación bajos.

Multimodal biometric schemes arise as an interesting solution to the multidimensional reinforcement problem for biometric security systems. Along with the performance dimension, these systems should also comply with required levels for other conditions such as permanence, collectability, and circumvention, among others. In response to the demand for a multimodal and synchronous dataset, we introduce in this paper an open-access database of synchronously recorded electroencephalogram signals (EEG), voice signals, and video feed from 51 volunteers, 25 female, 26 male, captured for, but not limited to, biometric purposes. A total of 140 samples were collected from each user when pronouncing single digits in Spanish, giving a total of 7140 instances. EEG signals were captured using a 14-channel Emotiv™ Epoc headset. The resulting set becomes a valuable resource when working on unimodal biometric systems, but significantly more for the evaluation of multimodal variants. Furthermore, the usefulness of the collected signals extends to being exploited by projects in brain-computer interfaces and face recognition to name just a few. As an initial report on data separability of the related samples, five user recognition experiments are presented: a face recognition identifier with an accuracy of 99%, a speaker identification system with accuracy of 94.2%, a bimodal face-speech verification case with Equal Error Rate around 2.64, an EEG identification example, and a bimodal user identification exercise based on EEG and voice modalities with a registered accuracy of 97.6%.

We propose a new Domain Specific Language (DSL) to represent and solve resource allocation problems of indivisible goods. Resource allocation problems can be represented using matrices; this representation is flexible and has interesting mathematical properties that the solution can exploit. However, the programming of such a problem using a general-purpose programming language might include an unnecessary level of complexity. This new DSL allows the user to declare the agents and their preferences of resources. Also, the language can manipulate those elements with the proper operations involved in the resource allocation problem. The proposed DSL can measure efficiency criteria such as Pareto optimality, measure fairness criteria such as Envy-free, and represent results using matrices. This work shows the structure of the interpreter of this language and provides details about the scanner, parser, and interpreter for this language. This DSL will be called Resource Allocation Programming Language (RAPL). We hope that the easiness of use of this DSL can motivate further research on this topic.