Subtle Techniques for Ubiquitous Interaction on Smart Glasses 

Summary

Hawkes Processes are probabilistic models useful for modelling the occurrences of events over time. They exhibit mutual excitation property, where a past event influences future events. This has been successful in modelling the evolution of memes and user behaviour in social networks. In the Hawkes process, the calculation of the intensity function for every new event requires time proportional to the number of past events. This calculation will become expensive when the number of events is high. We develop a faster approach which takes only constant time complexity to calculate the intensity function for every new event in a mutually exciting Hawkes process. This is achieved by developing a recursive formulation for mutually exciting Hawkes process and maintaining an additional data structure which takes a constant space. We found considerable improvement in runtime performance of the Hawkes process applied to the sequential stance classification task on synthetic and real world datasets.