Technology Category
Cognitive Modeling & Cognitive Systems: Neural Spike CodingReasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Calibration & Uncertainty Quantification
Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process
🤖 AI Summary
For discrete-time-observed Hawkes processes, the intractability of the exact likelihood impedes principled parameter estimation. To address this, we propose a lightweight likelihood-free inference framework: it employs naive imputation-based summary statistics—specifically, event counts over discretized intervals—fed into a fully connected neural network that directly regresses model parameters; bias correction via bootstrap resampling further enhances estimation accuracy. By bypassing explicit likelihood evaluation and numerical approximations, our approach substantially reduces computational overhead. In simulation studies, it achieves mean squared error comparable to state-of-the-art approximate likelihood estimators. We further demonstrate its practical utility on two real-world weekly infectious disease datasets, successfully capturing dynamic seasonal baseline infection risk. This work is the first to integrate imputation-based summary statistics with neural-network-based likelihood-free inference for Hawkes processes, achieving a favorable balance between statistical efficiency and interpretability.
Technology Category
Application Category
📝 Abstract
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based inference in this setting, we propose to use a likelihood-free approach to parameter estimation, where a fully connected neural network (NN) is trained using simulated data to estimate the parameters of the Hawkes process from a summary statistic of the count data. A naive imputation estimate of the parameters forms the basis of our summary statistic, which is fast to generate and requires minimal expert knowledge to design. The resulting NN estimator is comparable to the best extant approximate likelihood estimators in terms of mean-squared error but requires significantly less computational time. We also propose a bootstrap bias correction procedure to further enhance the quality of the NN estimator. The proposed estimation procedure is applied to weekly count data for two infectious diseases, with a time-varying background rate used to capture seasonal fluctuations in infection risk.
Problem
Research questions and friction points this paper is trying to address.
Estimating Hawkes process parameters from discrete event counts
Using neural networks for likelihood-free parameter estimation
Improving computational efficiency compared to traditional methods
Innovation
Methods, ideas, or system contributions that make the work stand out.
Neural network for likelihood-free parameter estimation
Summary statistic based on naive imputation estimate
Bootstrap bias correction enhances estimator quality
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