Um método de aprendizagem sequencial com filtro de Kalman e Extreme Learning Machine para problemas de regressão e previsão de séries temporais

Abstract

In machine learning applications, there are situations where the input dataset is not fully available at the beginning of the training phase. A well known solution for this class of problem is to perform the learning process through the sequential feed of training instances. Among most recent approaches for sequential learning, we can highlight the methods based on Single Layer Feedforward Network (SLFN) and the extensions of the Extreme Learning Machine (ELM) approach for sequential learning. The sequential version of the ELM algorithm, named Online Sequential Extreme Learning Machine (OS-ELM), uses a recursive least squares solution for updating the output weights through a covariance matrix. However, the implementation of OS-ELM and its extensions suffer from the problem of multicollinearity for the hidden layer output matrix. This thesis introduces a new method for sequential learning in which the effects of multi-collinearity is handled. The proposed Kalman Learning Machine (KLM) updates sequentially the output weights of an OS-ELM based network by using the Kalman filter iterative procedure. In this work, in order to reduce the computational complexity of the training process, a new approach for estimating the filter parameters is presented. Moreover, an extension of the method, named Extended Kalman Learning Machine (EKLM), is presented for problems where the dynamics of the model are non linear. The proposed method was evaluated by comparing the related state-of-the-art methods for sequential learning based on the original OS-ELM. The results of the experiments show that the proposed method can achieve the lowest forecast error when compared with most of their counterparts. Moreover, the KLM algorithm achieved the lowest average training time when all experiments were considered, as an evidence that the proposed method can reduce the computational complexity for the sequential learning process. A case study was performed by applying the proposed method for a problem of financial time series forecasting. The results reported confirm that the KLM algorithm can decrease the forecast error and the average training time simultaneously, when compared with other sequential learning algorithms.