Differentially Private Hawkes Process Learning
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Solution Overview
Problem
Existing methods for learning Hawkes processes from event sequence data fail to adequately address privacy concerns, as they do not provide mechanisms to preserve the anonymity of individuals whose activities are linked to the time-sequential data.
Innovation Solution
The implementation of differentially private learning methods for Hawkes processes, which involve modeling the sequence of events using a Hawkes process characterized by an exogenous base intensity rate and an indigenous component, and introducing differential privacy by adding noise to the estimated parameters using a Laplace mechanism.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard Hawkes process learning methods are used to model event sequence data, then accurate parameter estimation is achieved, but privacy of individuals whose activity is linked to the data is compromised
Solution Approach 1:
The patent introduces differential privacy as an intermediary mechanism between the Hawkes process learning algorithm and the event sequence data. By adding carefully calibrated noise to the gradient updates during stochastic gradient descent, the system mediates the interaction between model training and personal information, allowing accurate parameter estimation while preventing adversaries from inferring individual identities from the data patterns.
2Object-affected harmful factors
If differential privacy is applied to Hawkes process learning, then privacy of individuals is preserved, but sample complexity and computational requirements increase
Solution Approach 1:
The patent modifies the learning algorithm by changing the parameters of the optimization process to incorporate differential privacy. Specifically, it adjusts the gradient update rules by adding noise with controlled variance, and modifies the convergence criteria to account for the noisy gradients. These parameter changes enable privacy protection while maintaining reasonable computational complexity through efficient noise injection mechanisms.
3Object-affected harmful factors
If differential privacy is applied to Hawkes process learning, then privacy of individuals is preserved, but the amount of data required for accurate learning increases
Solution Approach 1:
The patent applies preliminary actions by pre-calculating the appropriate noise scale and privacy budget allocation before the main learning process begins. By determining the sensitivity of the Hawkes process parameters and pre-setting the differential privacy parameters (epsilon, delta), the system prepares the necessary conditions to achieve both privacy protection and efficient learning with minimal sample complexity during the actual training phase.
Data Source
AI summary
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.