A Nonparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Prior

Hawkes process models are used in settings where past events increase the likelihood of future events occurring. Many applications record events as counts on a regular grid, yet discrete-time Hawkes models remain comparatively underused and are often constrained by fixed-form baselines and excitation kernels. In particular, there is a lack of flexible, nonparametric treatments of both the baseline and the excitation in discrete time. To this end, we propose the Gaussian Process Discrete Hawkes Process (GP-DHP), a nonparametric framework that places Gaussian process priors on both the baseline and the excitation and performs inference through a collapsed latent representation. This yields smooth, data-adaptive structure without prespecifying trends, periodicities, or decay shapes, and enables maximum a posteriori (MAP) estimation with near-linear-time \(O(T\log T)\) complexity. A closed-form projection recovers interpretable baseline and excitation functions from the optimized latent trajectory. In simulations, GP-DHP recovers diverse excitation shapes and evolving baselines. In case studies on U.S. terrorism incidents and weekly Cryptosporidiosis counts, it improves test predictive log-likelihood over standard parametric discrete Hawkes baselines while capturing bursts, delays, and seasonal background variation. The results indicate that flexible discrete-time self-excitation can be achieved without sacrificing scalability or interpretability.

Context-Aware Palmprint Recognition via a Relative Similarity Metric

We propose a new approach to matching mechanism for palmprint recognition by introducing a Relative Similarity Metric (RSM) that enhances the robustness and discriminability of existing matching frameworks. While conventional systems rely on direct pairwise similarity measures, such as cosine or Euclidean distances, these metrics fail to capture how a pairwise similarity compares within the context of the entire dataset. Our method addresses this by evaluating the relative consistency of similarity scores across up to all identities, allowing for better suppression of false positives and negatives. Applied atop the CCNet architecture, our method achieves a new state-of-the-art 0.000036% Equal Error Rate (EER) on the Tongji dataset, outperforming previous methods and demonstrating the efficacy of incorporating relational structure into the palmprint matching process.