The Kernel Pitman-Yor Process

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.

💡 Research Summary

The paper introduces the Kernel Pitman‑Yor Process (KPYP), a novel non‑parametric Bayesian prior designed for clustering data that exhibit spatial or temporal dependencies. Building on the stick‑breaking construction of the Pitman‑Yor process (PYP), the authors replace the uniform discount parameter of the Beta‑distributed stick variables with a location‑dependent kernel function. Specifically, each stick weight vₖ(x) is drawn from a Beta distribution whose first shape parameter equals the kernel similarity k(x, x̂ₖ; ψₖ) between the observation location x and a cluster‑specific location x̂ₖ, while the second shape parameter is α + c