The paper introduces the determinant-ratio point process (DRPP), a new model that captures both attraction and repulsion in subset selection by using a ratio of determinants from two symmetric positive-definite kernels. DRPP retains the feature-based interpretability of standard determinantal point processes while allowing separate specification of attraction and repulsion effects. The authors provide an auxiliary-variable representation that enables efficient MCMC sampling and tractable expectation formulas, facilitating maximum-likelihood learning, and theoretically show that DRPP can realize clustered attraction with fewer parameters than nonsymmetric DPPs.
By Hideaki Ishibashi, Takahiro Kawashima, Hideitsu Hino
The paper introduces the Sparse Landmark Embedding (SLE) kernel, a new framework that removes the need for conditionally negative definite (CND) distance measures in kernel methods and Gaussian Processes. By embedding each input into a sparse feature vector using compactly supported bump functions centered at all training points, any standard positive semi-definite (PSD) kernel can be applied in this embedding space, guaranteeing PSD for arbitrary distance measures. The authors provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show through experiments with geodesic and Wasserstein distances that the SLE kernel matches or surpasses domain-specific baselines in predictive accuracy and uncertainty quantification.
By Marcus M. Noack, Maher B. Alghalayini, Mark D. Risser
arXiv:2603. 23746v2 Announce Type: replace Abstract: Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges.
By Zhitong Xu, Qiwei Yuan, Yinghao Chen, Yan Sun, Bin Shen, Shandian Zhe
arXiv:2605. 10285v2 Announce Type: replace-cross Abstract: We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels.
By Anthony Stephenson
The paper introduces Total Sensitivity Kernels (TSKs), a weighted ANOVA kernel framework that learns the importance of individual inputs and their interactions for approximating a multivariable black-box function from limited data. By selecting an RKHS where the target function has minimum norm, the authors derive a unique solution and prove consistency for finite-data interpolation. Numerical experiments show that adapting the kernel to the learned multivariable structure can significantly improve approximation accuracy compared to a standard product kernel.
By John E. Darges, Laura Weidensager
Kernel Singular Value Decomposition (KSVD) learns singular vectors for an asymmetric kernel matrix derived from two data sources. The paper extends KSVD to multiple data sources, introducing eKSVD, which jointly learns nonlinear feature mappings and captures maximal information across all sources while incorporating pair‑wise couplings. The authors derive a dual optimization framework, a covariance‑based approach, and demonstrate the effectiveness of eKSVD and neural‑network‑based feature mappings through numerical experiments.
By Xinjie Zeng, Qinghua Tao, Johan Suykens