Fully Neural Network based Model for General Temporal Point Processes

TL;DR

This paper introduces a fully neural network-based model for temporal point processes that flexibly models the intensity function and allows exact likelihood evaluation, outperforming previous methods.

Contribution

It proposes a novel RNN-based approach that models the integral of the intensity function with a neural network, enabling flexible modeling and exact likelihood computation.

Findings

Achieves competitive or superior performance on synthetic datasets.

Enables exact evaluation of the log-likelihood without numerical approximation.

Provides a more flexible model of the intensity function than previous RNN-based models.

Abstract

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets.