Method and system for differentially private learning of Hawkes processes

A computing apparatus for preserving privacy with respect to modeling a sequence of events, the computing apparatus comprising:

• a processor;
• a memory;
• and
• a communication interface coupled to each of the processor and the memory,
• wherein the processor is configured to:
• receive, via the communication interface, first information that relates to a sequence of events;
• model, based on the received first information, the sequence of events by a Hawkes process that has an intensity that is characterized by an exogenous base intensity rate and an indigenous component that relates to an impact of previous events, the indigenous component being characterized by an excitation rate and a decay rate;
• analyze the received first information;
• and
• determine, based on a result of the analysis, an estimated value of the exogenous base intensity rate and an estimated value of the excitation rate,
• wherein the processor is further configured to calculate, for a predetermined distance between true values of the exogenous base intensity rate and the excitation rate and the estimated values of the exogenous base intensity rate and the excitation rate, a first minimum amount of time over which the sequence of events is observable.

A non-transitory computer readable storage medium storing instructions for preserving privacy with respect to modeling a sequence of events, the storage medium comprising executable code which, when executed by a processor, causes the processor to:

• receive first information that relates to a sequence of events;
• model, based on the received first information, the sequence of events by a Hawkes process that has an intensity that is characterized by an exogenous base intensity rate and an indigenous component that relates to an impact of previous events, the indigenous component being characterized by an excitation rate and a decay rate;
• analyze the received first information;
• and
• determine, based on a result of the analysis, an estimated value of the exogenous base intensity rate and an estimated value of the excitation rate,
• wherein when executed by the processor, the executable code further causes the processor to calculate, for a predetermined distance between true values of the exogenous base intensity rate and the excitation rate and the estimated values of the exogenous base intensity rate and the excitation rate, a first minimum amount of time over which the sequence of events is observable.