Estimation of Sparse VAR Models with Artificial Neural Networks for the Analysis of Biosignals

Vector autoregressive models (VAR models) are often used to model and to analyze multivariate time series, especially to provide short-term forecasts. A common method of estimating coefficients of these VAR models is solving the Yule- Walker equations. This work introduces and investigates a method to set up "sparse" VAR models, in order to obtain a comparable prognosis quality with significantly fewer coefficients. For this purpose, an artificial neural network was programmed in Python with TensorFlow. Sparsity arises from the implementation of regularization algorithms.Based on simulated data and an ECG, we show that a comparable prognosis quality can be achieved with significantly fewer coefficients. In addition, sparse VAR models can also be determined if the data would actually lead to an underdetermined system of equations. Thus, sparse VAR models may help to classify short epochs of biosignals, e.g. P-waves or QRS-complexes.