K$^2$IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes
Authors: Hideaki Kim, Tomoharu Iwata, Akinori Fujino
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through experiments on synthetic datasets, we show that K2IE achieves comparable predictive performance while significantly surpassing the state-of-the-art kernel method-based estimator in computational efficiency. In Section 4, we compare K2IE with conventional nonparametric intensity estimators on synthetic datasets, and confirm the effectiveness of the proposed method. |
| Researcher Affiliation | Industry | Hideaki Kim 1 Tomoharu Iwata 1 Akinori Fujino 1 1NTT Corporation, Japan. Correspondence to: Hideaki Kim <EMAIL>. |
| Pseudocode | No | The paper describes mathematical formulations and derivations, but does not contain explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | 2Codes are available at: https://github.com/HidKim/K2IE |
| Open Datasets | Yes | We conducted an additional experiment using an open 2D real-world dataset, bei, in the R package spatsta (GPL3). It consists of locations of 3605 trees of the species Beilschmiedia pendula in a tropical rain forest (Hubbel & Foster, 1983). |
| Dataset Splits | Yes | Following (Cronie et al., 2024), we randomly labeled the data points with independent and identically distributed marks {1, 2, 3} from a multinomial distribution with parameters (p1, p2, p3) = (0.3, 0.3, 0.7), and assigned the points with label 1 and 2 to training data and test data, respectively; we repeated it 100 times for evaluation. |
| Hardware Specification | Yes | All models were implemented using Tensor Flow-2.102 and executed on a Mac Book Pro equipped with a 12-core CPU (Apple M2 Max), with the GPU disabled. |
| Software Dependencies | Yes | All models were implemented using Tensor Flow-2.102 and executed on a Mac Book Pro equipped with a 12-core CPU (Apple M2 Max), with the GPU disabled. |
| Experiment Setup | Yes | KIE optimized the hyper-parameter β through 5-fold cross-validation based on the negative log-likelihood function; FIE optimized the hyper-parameters, (β, γ), using the same cross-validation procedure as KIE; For K2IE, the hyper-parameters, (β, γ), were optimized via 5-fold cross-validation with the least squares loss function (10). For all models, the Monte Carlo cross-validation with p-thinning (Cronie et al., 2024) was adopted, where p was fixed at 0.6. A 10 × 10 logarithmic grid search was conducted for γ ∈ [0.1, 100] and β ∈ [0.1, 100]β, where β = (β1, . . . , βd) for βi = 1/maxj Xmax ij − minj Xmin ij . For FIE, the gradient descent algorithm Adam (Kingma & Ba, 2014) was employed to solve the dual optimization problem (9). |