TY - CONF A1 - Gregorová, Magda A1 - Kalousis, Alexandros A1 - Marchand-Maillet, Stéphane A2 - Ceci, Michelangelo A2 - Hollmén, Jaakko A2 - Todorovski, Ljupco A2 - Vens, Celine A2 - Dzeroski, Saso T1 - Forecasting and Granger Modelling with Non-linear Dynamical Dependencies T2 - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2017, Skopje, Macedonia, September 18-22, 2017, Proceedings, Part II N2 - Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques. Y1 - 2017 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/4968 VL - 10535 SP - 544 EP - 558 ER -