Tensor-Train networks for learning predictive modeling of multidimensional data

In this work, we firstly apply Tensor-Train (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor model and standard multilayer neural networks is also carried out in the context of prediction of the Mackey-Glass noisy chaotic time series and NASDAQ index. We show that the weights of a multidimensional regression model can be learned by means of TT network and the optimization of TT weights is more robust to the impact of coefficient initialization and hyper-parameter setting. Furthermore, an efficient algorithm based on alternating least squares has been proposed for approximating the weights in TT format with a reduction of computational calculus, providing a much faster convergence than the well-known adaptive learning-method algorithms, widely applied for optimizing neural networks.