Abstract: A method for preserving privacy with respect to modeling event sequence data is provided. The method includes: receiving information about a sequence of events; modeling the event sequence by a Hawkes process that has an intensity that includes an exogenous base intensity rate and an indigenous component that has an excitation rate and a decay rate; analyzing the received information; and determining estimated values of the exogenous base intensity rate and the excitation rate, such that an accuracy of the estimates corresponds to a length of time over which the sequence of events is observed. Differential privacy is introduced by adding noise to the sequence of events in order to preserve the privacy of individuals associated with the events, and a cost of the differential privacy is expressible as an additional length of observation time required to ensure the accuracy of the estimates.

Abstract: A method and a system for using an online learning framework for mixture of multivariate Hawkes processes to model sequences of events are provided. The method includes: receiving data that corresponds to a group of event sequences; generating a mixture of multivariate Hawkes processes model based on the group of event sequences; and adjusting the model by applying an online learning algorithm to the generated model. The online learning algorithm includes an E-step that corresponds to updating a set of responsibilities that relates to the group of event sequences and an M-step that corresponds to updating Hawkes processes parameters that relate to the group of event sequences.

Abstract: A method and apparatus are described including receiving sensor data from at least one of a plurality of sensors in a sensor array associated with an environment, detecting a pattern in the received sensor data, determining a profile of at least one user present in the environment from a correlation between the detected pattern and patterns in a first database, determining an action to be performed responsive to the determined age range of the at least one user in the environment to actions associated with the user profile in a second database and performing the determined action on received content.