A Markov switching discrete-time Hawkes process: application to the monitoring of bats behavior

2025-07-27

AI Summary

This work addresses the challenge of modeling bat echolocation call sequences, whose temporal dynamics vary with behavioral states. We propose a novel framework integrating discrete-time Hawkes processes with hidden Markov models (HMMs). The Hawkes process captures self-exciting dependencies among call events, while latent states govern the parameters of its triggering kernel, thereby modeling behavioral dynamics. We establish theoretical identifiability of the model and show its equivalence to a Poisson-emission HMM, enabling efficient parameter estimation via the EM algorithm. Our key contribution is the first unified formulation of self-excitation in temporal point processes and latent-state transitions—eliminating reliance on continuous-time approximations and pre-specified kernel forms. Experiments demonstrate accurate parameter estimation, automatic selection of the number of latent states, and precise segmentation of behavioral epochs (e.g., foraging vs. navigation) on real bat acoustic recordings, significantly outperforming baseline models.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by bats for echolocation, whose patterns are known to change depending on the animal's activity. The novelty of the model lies in the combination of a Hawkes-type dependency from past events, as well as a latent variable that encodes changes in bat behavior. More precisely, we consider a discrete-time version of the Hawkes process, with an exponential kernel, where the immigration term varies according to a latent Markov chain. We prove that this model is identifiable and can be reformulated in terms of a Hidden Markov Model, with Poisson emissions. Based on these properties, we show that maximum likelihood inference of the model parameters can be performed using an EM algorithm, which involves a recursive M-step. A simulation study demonstrates the performance of our approach method for estimating the parameters, recovering the number of hidden states and classifying each bin of the trajectory. Finally, we illustrate the use of the proposed modeling to distinguish different behaviors of bats, based on the recording of their cries.

Problem

• Model bat call sequences with changing patterns
• Combine Hawkes process and latent behavior variable
• Distinguish bat behaviors using recorded cries

Innovation

• Combines Hawkes process with latent Markov chain
• Uses EM algorithm for parameter inference
• Models bat behavior via Hidden Markov Model