The estimation of the qualitative behaviour of fractional Brownian motion is an important topic for modelling real-world applications. Permutation entropy is a well-known approach to quantify the complexity of univariate time series in a scalar-valued representation. As an extension often used for outlier detection, weighted permutation entropy takes amplitudes within time series into account. As many real-world problems deal with multivariate time series, these measures need to be extended though. First, we introduce multivariate weighted permutation entropy, which is consistent with standard multivariate extensions of permutation entropy. Second, we investigate the behaviour of weighted permutation entropy on both univariate and multivariate fractional Brownian motion and show revealing results.
Machine learning models are omnipresent for predictions on big data. One challenge of deployed models is the change of the data over time-a phenomenon called concept drift. If not handled correctly, a concept drift can lead to significant mispredictions. We explore a novel approach for concept drift handling, which depicts a strategy to switch between the application of simple and complex machine learning models for regression tasks. We assume that the approach plays out the individual strengths of each model, switching to the simpler model if a drift occurs and switching back to the complex model for typical situations. We instantiate the approach on a real-world data set of taxi demand in New York City, which is prone to multiple drifts, e.g. the weather phenomena of blizzards, resulting in a sudden decrease of taxi demand. We are able to show that our suggested approach outperforms all regarded baselines significantly.
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