Online Learning Mixture Hawkes Processes Event Sequence Modeling
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Solution Overview
Problem
Existing methods for modeling sequences of events, such as those in medical and financial applications, fail to effectively capture the latent structure of networks and rich interactions across events due to their inability to handle asynchronous and irregular data, leading to limitations in predicting next events and inferring causal relations.
Innovation Solution
An online learning framework for mixture of multivariate Hawkes processes is employed, which generates a model by receiving event sequences, updating responsibility parameters, and adjusting Hawkes processes parameters using an E-step and M-step, allowing for the prediction of next events, cluster determination, and causal relationship identification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional time-series approaches are used to model sequential events, then the modeling process is simple, but the rich information in occurrence times cannot be captured
Solution Approach 1:
The patent transitions from conventional time-series parameterization to point process parameterization, where the occurrence times are explicitly modeled using intensity functions. This parameter change allows the model to capture the rich temporal information in event occurrence times while maintaining tractability through the mathematical framework of point processes.
2Measurement precision
If non-parametric or neural network-based approaches are used to model complex dependencies, then the dependency modeling capability is improved, but a single dependency pattern is learned for all sequences
Solution Approach 1:
The patent segments the homogeneous dependency model into multiple heterogeneous Hawkes processes, each capturing a distinct impact pattern. By dividing the single model into K separate processes with different parameters, the system can simultaneously model multiple dependency patterns across different event sequences, improving both precision and adaptability.
Solution Approach 2:
The patent creates a universal framework that can handle multiple impact patterns through a single mixture model formulation. The model universally applies to diverse event sequences by allowing each sequence to be represented as a mixture of K Hawkes processes, making the system adaptable to various applications including financial transactions, social media events, and healthcare data.
3Adaptability or versatility
If mixture of multivariate Hawkes processes is used to model multiple impact patterns, then the adaptability to different event sequences is improved, but the model complexity increases
Solution Approach 1:
The patent implements an online learning algorithm that performs self-service by automatically updating model parameters as new events are observed. The algorithm incrementally learns the mixture weights and Hawkes process parameters without requiring full retraining, allowing the complex model to adapt to new data patterns while maintaining computational efficiency through stochastic gradient descent.
Solution Approach 2:
The patent employs preliminary action by pre-specifying the mixture model structure and impact function forms before observing the data. This preliminary setup includes defining the K-component mixture framework and choosing appropriate impact function families, which simplifies the subsequent online learning process by reducing the search space and enabling efficient parameter estimation.
4Reliability
If batch learning methods are used for mixture models, then the model convergence is improved, but the inability to handle streaming data in real-time occurs
Solution Approach 1:
The patent transforms the static batch learning approach into a dynamic online learning system. The model parameters are updated dynamically as new events arrive in the stream, allowing the system to adapt to changing patterns in real-time. This dynamic approach maintains reliability through proper convergence guarantees while achieving productivity through incremental updates that process data in constant time per event.
Data Source
AI summary
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.