A randomised approach for NARX model identification based on a multivariate Bernoulli distribution

F. Bianchi, A. Falsone, M. Prandini, L. Piroddi
2016 International Journal of Systems Science  
The identification of polynomial NARX models is typically performed by incremental model building techniques that progressively select from a candidate set the terms (regressors) to include in the model. The main limitation of these methods stems from the difficulty to correctly assess the importance of each regressor based on the evaluation of partial individual models, which may ultimately lead to erroneous model selections. A more robust assessment of the significance of a specific model
more » ... can be obtained by considering ensembles of models, as demonstrated by the recently developed RaMSS algorithm. In that context, the identification task is formulated in a probabilistic fashion and a Bernoulli distribution is employed to represent the probability that a regressor is actually part of the target model. Then, a randomized method is used to sample from the model distribution and gather reliable information to update the distribution, until convergence to a specific model is achieved. The basic version of the RaMSS algorithm employs multiple independent univariate Bernoulli distributions associated to the different candidate model terms, thus overlooking the correlations between different terms, which are typically important in the selection process. In this research endeavor a more complex multivariate Bernoulli distribution is employed, in which the sampling of a given term is conditioned by the sampling of the others. The added complexity inherent in considering the regressor correlation properties is more than compensated by the achievable improvements in terms of accuracy of the model selection process.
doi:10.1080/00207721.2016.1244309 fatcat:lxwsfnbwwvhkjfmzegmnv3vony