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.