Hamiltonian Monte Carlo based on evidence framework for Bayesian learning to neural network

  • Hassan Ramchoun
  • Mohamed Ettaouil
Methodologies and Application


The multilayer perceptron is the most useful artificial neural network widely used to approximate the nonlinear function in various fields, but the determination of its suitable weights and regularization parameters is a fundamental problem due to their direct impact on the network convergence and generalization performance. The Bayesian approach for neural networks is to consider all parameters of networks are random variables; then, computation of the posterior distribution is based on prior overall parameters and likelihood function through the use of Bayes’ theorem. In this paper, we train the network weights by means of Hamiltonian Monte Carlo (HMC); for hyperparameters, we propose to sample from posterior distribution using HMC in order to approximate the derivative of evidence which allow to re-estimate hyperparameters. The case problem studied in this paper includes a regression and classification problem. The obtained results illustrate the advantages of our approach in terms of accuracy compared to old Bayesian approach for neural network.


Multilayer perceptron Bayesian learning Hamiltonian Monte Carlo Evidence framework Hyperparameter 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of modelling and scientific Computing, Department of Mathematics and Informatics, Faculty of Sciences and Techniques, University of Sidi Mohamed Ben AbdellahFezMorocco

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