Residual TPP: A Unified Lightweight Approach for Event Stream Data Analysis

This work introduces Residual TPP, a novel, unified, and lightweight approach for analyzing event stream data. It leverages the strengths of both simple statistical TPPs and expressive neural TPPs to achieve superior performance. Specifically, we propose the Residual Events Decomposition (RED) technique in temporal point processes, which defines a weight function to quantify how well the intensity function captures the event characteristics. The RED serves as a flexible, plug-and-play module that can be integrated with any TPP model in a wide range of tasks. It enables the identification of events for which the intensity function provides a poor fit, referred to as residual events. By combining RED with a Hawkes process, we capture the self-exciting nature of the data and identify residual events. Then an arbitrary neural TPP is employed to take care of residual events. Extensive experimental results demonstrate that Residual TPP consistently achieves state-of-the-art goodness-of-fit and prediction performance in multiple domains and offers significant computational advantages as well.

Many systems rely on analyzing sequences of events over time, such as online shopping activity, social media interactions, or financial transactions. Traditional models used to fit and predict these events are either simple but limited, or powerful but computationally heavy.We introduce Residual TPP, a new method that combines the strengths of both. It starts with a simple model to capture overall patterns like periodicity and self-excitation, then identifies events where the base model fails to explain, referred to as residual events. These residuals are then handled by a more expressive neural network, which can learn deeper patterns. This approach is both flexible and lightweight, making it suitable for a wide range of data without requiring heavy computation.Experiments show that Residual TPP not only outperforms existing methods in terms of goodness-of-fit and prediction accuracy but also runs faster. This makes it a powerful tool for researchers and industries working with complex event stream data.