Mathieu Sinn

Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments

Analyzing the probabilities of ordinal patterns is a recent approach to quantifying the complexity of time series and detecting structural changes in the underlying dynamics. The present paper investigates statistical properties of estimators of ordinal pattern probabilities in discrete-time Gaussian processes with stationary increments. It shows that better estimators than the sample frequencies are available and establishes sufficient conditions under which these estimators are consistent and asymptotically normal. The results are applied to derive properties of the Zero Crossing estimator for the Hurst parameter in fractional Brownian motion. In a simulation study, the performance of the Zero Crossing estimator is compared to that of a similar metric estimator; furthermore, the Zero Crossing estimator is applied to the analysis of Nile River data.

Error Bounds for Online Predictions of Linear-Chain Conditional Random Fields: Application to Activity Recognition for Users of Rolling Walkers

Linear-Chain Conditional Random Fields (L-CRFs) are a versatile class of models for the distribution of a sequence of hidden states (labels) conditional on a sequence of observable variables. In general, the exact conditional marginal distributions of the labels can be computed only after the complete sequence of observations has been obtained, which forbids the prediction of labels in an online fashion. This paper considers approximations of the marginal distributions which only take into account past observations and a small number of observations in the future. Based on these approximations, labels can be predicted close to real-time. We establish rigorous bounds for the marginal distributions which can be used to assess the approximation error at runtime. We apply the results to an L-CRF which recognizes the activity of rolling walker users from a stream of sensor data. It turns out that if we allow for a prediction delay of half of a second, the online predictions achieve almost the same accuracy as the offline predictions based on the complete observation sequences.