Factorizing multivariate time series operators

Factorizing Multivariate Function Classes

The mathematical framework for factorizing equivalence classes of multivariate functions is formulated in this paper. Independent component analysis is shown to be a special case of this decomposition. Using only the local geometric structure of a class representative, we derive an analytic solution for the factorization. We demonstrate the factorization solution with numerical experiments and ...

Factorizing Markov Models for Categorical Time Series Prediction

During the last decade, recommender systems became a popular class of models for many commercial websites. One of the best state-of-the-art methods for recommender systems are Matrix and Tensor Factorization models. Besides, Markov Chain models are common for representing sequential data problems (e.g. categorical time series data). The item recommendation problem of recommender systems in fact...

Modelling Multivariate Time Series

Multivariate time series (MTS) data are widely available in di erent elds including medicine, nance, science and engineering. Modelling MTS data e ectively is important for many decision-making activities. In this paper, we will describe some of our e orts in modelling these data for numerous tasks such as outlier analysis, forecasting and explanation. Through the analysis of various kinds of M...

Factorizing Multivariate Polynomials Over Finite Fields

Modelling of Multivariate Time Series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs ...