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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.2 Bogotá July/Dec. 2018

http://dx.doi.org/10.15446/rce.v41n2.55250 

Artículos originales de investigación

Artificial Neuronal Networks: A Bayesian Approach Using Parallel Computing

Redes neuronales regularizadas: un enfoque bayesiano usando cómputo paralelo

Eduardo Guzmán1  a  , Mario Vázquez2  b  , David del Valle1  c  , Paulino Pérez-Rodríguez1  d 

1 Estadística, Socio Economía Estadística e Informática, Colegio de Postgraduados, Texcoco, México.

2 Matemáticas y Cómputo, Departamento de Irrigación, Universidad Autónoma Chapingo, Texcoco, México.

Abstract

An Artificial Neural Network (ANN) is a learning paradigm and automatic processing inspired in the biological behavior of neurons and the brain structure. The brain is a complex system; its basic processing unit are the neurons, which are distributed massively in the brain sharing multiple connections between them. The ANNs try to emulate some characteristics of humans, and can be thought as intelligent systems that perform some tasks in a dierent way that actual computer does. The ANNs can be used to perform complex activities, for example: pattern recognition and classification, weather prediction, genetic values prediction, etc. The algorithms used to train the ANN, are in general complex, so therefore there is a need to have alternatives which lead to a significant reduction of times employed to train an ANN. In this work, we present an algorithm based in the strategy “divide and conquer” which allows to train an ANN with a single hidden layer. Part of the sub problems of the general algorithm used for training are solved by using parallel computing techniques, which allows to improve the performance of the resulting application. The proposed algorithm was implemented using the C++ programming language, and the libraries Open MPI and ScaLAPACK. We present some application examples and we asses the application performance. The results shown that it is possible to reduce significantly the time necessary to execute the program that implements the algorithm to train the ANN.

Key words: Empirical Bayes; Nonlinear models; Parallel processing

Resumen

Una Red Neuronal Artificial (RNA) es un paradigma de aprendizaje y procesamiento automático inspirado en el comportamiento biológico de las neuronas y en la estructura del cerebro. El cerebro es un sistema altamente complejo; su unidad básica de procesamiento son las neuronas, las cuales se encuentra distribuidas de forma masiva compartiendo múltiples conexiones entre ellas. Las RNAs intentan emular ciertas características propias de los humanos, pueden ser vistas como un sistema inteligente que lleva a cabo tareas de manera distinta a como lo hacen las computadoras actuales. Las RNAs pueden emplearse para realizar actividades complejas, por ejemplo: reconocimiento y clasificación de patrones, predicción del clima, predicción de valores genéticos, etc. Los algoritmos utilizados para entrenar las redes, son en general complejos, por lo cual surge la necesidad de contar con alternativas que permitan reducir de manera significativa el tiempo necesario para entrenar una red. En este trabajo se presenta una propuesta de algoritmos basados en la estrategia “divide y conquista” que permiten entrenar las RNAs de una sola capa oculta. Parte de los sub problemas del algoritmo general de entrenamiento se resuelven utilizando técnicas de cómputo paralelo, lo que permite mejorar el desempeño de la aplicación resultante. El algoritmo propuesto fue implementado utilizando el lenguaje de programación C++, así como las librerías Open MPI y ScaLAPACK. Se presentan algunos ejemplos de aplicación y se evalúa el desempeño del programa resultante. Los resultados obtenidos muestran que es posible reducir de manera significativa los tiempos necesarios para ejecutar el programa que implementa el algoritmo para el ajuste de la RNA.

Palabras-clave: Bayes empírico; Modelos no lineales; Procesamiento en paralelo

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References

Blackford, L. S., Choi, J., Cleary, A., D'Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. & Whaley, R. C. (2012), `ScaLAPACK users' guide', Netlib's official site. 2015-03-14. * *http://netlib.org/scalapack/slug/index.htmlLinks ]

Crossa, J., de los Campos, G., Pérez-Rodríguez, P., Gianola, D., no, J. B., Araus, J. L., Makumbi, D., Singh, R. P., Dreisigacker, S., Yan, J., Arief, V., Banziger, M. & Braun, H.-J. (2010), `Prediction of genetic values of quantitative traints in plant breeding using pedigree and molecular markers', Genetics 186(2), 714-724. [ Links ]

Foresee, F. D. & Hagan, M. T. (1997), `Gauss Newton approximation to Bayesian learning', Proc. IEEE International Conference Neural Networks 3, 1931- 1933. [ Links ]

Fox, J. (2008), Applied Regression Analysis and Generalized Linear Models, SAGE Publications. *http://books.google.ch/books?id=GKkn3LSSHFsCLinks ]

Gabriel, E., Fagg, G. E., Bosilca, G., Angskun, T., Dongarra, J. J., Squyres, J. M., Sahay, V., Kambadur, P., Barrett, B., Lumsdaine, A., Castain, R. H., Daniel, D. J., Graham, R. L. & Woodall, T. S. (2004), Open MPI: Goals, concept, and design of a next generation MPI implementation, in `Proceedings, 11th European PVM/MPI Users' Group Meeting', Budapest, Hungary, pp. 97- 104. [ Links ]

Gianola, D., Okut, H., Weigel, K. A. & Rosa, G. J. (2011), `Predicting complex quantitative traits with bayesian neural networks: a case study with jersey cows and wheat', BMC Genetics 87, 7-8. [ Links ]

Girosi, F. & Poggio, T. (1989), `Representation properties of networks: Kolmogorov's theorem is irrelevant', Neural Computation 1(4), 465-469. *http://dx.doi.org/10.1162/neco.1989.1.4.465Links ]

Kolmogorov, A. K. (1957), `On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition', Doklady Akademii Nauk SSSR 114, 369-373. [ Links ]

Lampinen, J. & Vehtari, A. (2001), `Bayesian approach for neural networks review and case studies', Neural networks 14(3), 259-262. [ Links ]

Lampinen, J., Vehtari, A. & Leinonen, K. (1999), `Application of bayesian neural network in electrical impedance tomography', 6, 3942-3947. [ Links ]

Lebrón-Aldea, D., Dhurandhar, E. J., Pérez-Rodríguez, P., Klimentidis, Y. C., Tiwari, H. K. & Vazquez, A. I. (2015), `Integrated genomic and bmi analysis for type 2 diabetes risk assessment', Frontiers in Genetics 6, 1-8. [ Links ]

Levenberg, K. (1944), `A method for the solution of certain problems in least squares', Quart. Applied Math. 2, 164-168. [ Links ]

MacKay, D. J. (1994), `Bayesian non-linear modelling for the prediction competition', ASHRAE transactions 100, 5-12. [ Links ]

Marquardt, D. W. (1963), `An algorithm for least-squares estimation of nonlinear parameters', SIAM Journal on Applied Mathematics 11(2), 431-441. [ Links ]

Neal, R. M. (1996), Bayesian Learning for Neural Networks, Springer-Verlag New York, Inc., Secaucus, NJ, USA. [ Links ]

Nguyen, D. & Widrow, B. (1990), Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights, in `International Symposium on Neural Networks'. [ Links ]

Okut, H., Gianola, D., Rosa, G. J. & Weigel, K. (2011), `Prediction of body mass index in mice using dense molecular markers and a regularized neural network', Genetics research 93, 189-201. [ Links ]

Pérez-Rodríguez, P., Gianola, D., González-Camacho, J. M., Crossa, J., Manes, Y. & Dreisigacker, S. (2012), `Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat', G3 2(12), 1595- 1605. [ Links ]

Pérez-Rodríguez, P., Gianola, D., Weigel, K. A., Rosa, G. J. M. & Crossa, J. (2013), `Technical note: An R package for fitting Bayesian regularized neural networks with applications in animal breeding', Journal of Animal Science 91, 3522-3525. [ Links ]

Prechelt, L. (2012), Early stopping but when?, in G. Montavon, G. B. Orr & K.-R. Müller, eds, `Neural Networks: Tricks of the Trade: Second Edition', Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 53-67. *https://doi.org/10.1007/978-3-642-35289-8_5Links ]

Yoginath, S., Bauer, D., Kora, G., Samatova, N., Kora, G., Fann, G. & Geist, A. (2009), `RScaLAPACK: High-performance parallel statistical computing with R and ScaLAPACK'. 2016-01-12. *http://web.ornl.gov/webworks/cppr/y2001/pres/124121.pdfLinks ]

a E-mail: eduguz.h@gmail.com

b E-mail: mavp52@hotmail.com

c E-mail: dhvallep@gmail.com

d E-mail: perpdgo@gmail.com

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