[2B6-GS-2] Machine learning: Basics / Theory

[2B6-GS-2-01] Joint Estimation of Latent Event Types and Differential Equations from Temporal Point Processes

〇Shuichi Miyazawa^1,2, Daichi Mochihashi^1,3 (1. The Graduate University for Advanced Studies, 2. AGC Inc., 3. The Institue of Statistical Mathematics)

Keywords:Ordinary Differential Equations, Temporal Point Processes, Gaussian processes, Gradient Matching

Ordinary differential equations (ODEs) help the interpretation of phenomena in various scientific fields. ODEs are often applied to numerical data, but we proposed a modeling method using ODEs for sequences of events occurring in continuous time (temporal point processes) [Miyazawa 23]. Here, event series with labels indicating the type of components of the nonlinear dynamical system described by the ODEs are required, but in real settings, there are many event series that do not have such labels explicitly. Real event data is often accompanied by covariates, e.g., abstracts of inventions in patent applications. Such additional information, called marks, is useful for identifying latent event types. Therefore, we propose a method for modeling the generating process of event series by ODEs, using marks to estimate latent event types for event series without explicit labels indicating the components of the ODEs. The proposed method can be considered as an extension of latent Poisson process allocation [Lloyd 16], where each event is assigned to one of a set of latent Poisson processes, using ODEs. We demonstrated that the proposed method can estimate and recover latent event types and parameters of ODE using simulated data, and showed the applicability of the proposed method to a real problem using the USPTO patent dataset.