Selected work

Representative Papers

Rainfall is rough

Jul 29, 2026

This study addresses the challenge of modeling the clustering and long-range dependence of rainfall processes across multiple timescales by proposing a novel framework based on a critical Hawkes point process. For the first time, a heavy-tailed power-law kernel is introduced into rainfall modeling, unifying the Bartlett–Lewis and Neyman–Scott models to effectively capture rain cell clustering characteristics. By integrating high-frequency (minute-level) observational data with millennial-scale tree-ring proxy records and employing fractal analysis alongside Hurst exponent estimation, the work reveals a shared extremely rough fractal structure—characterized by Hurst exponents between 0.01 and 0.1—spanning from meteorological to paleoclimatic timescales. The proposed method significantly outperforms classical models at fine temporal resolutions and establishes a novel interdisciplinary link between atmospheric science and financial microstructure theory.

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Fast Gaussian process inference by exact Matérn kernel decomposition

Aug 03, 2025

To address the high computational complexity and poor scalability of kernel matrix–vector multiplication (MVM) in Gaussian process inference—particularly for large-scale, low-dimensional datasets—this paper introduces the first exact, fast MVM algorithm for multivariate Matérn kernels with half-integer smoothness parameters. Methodologically, the approach leverages an analytic decomposition of the Matérn kernel, combined with a divide-and-conquer strategy, weighted empirical cumulative distribution functions, and a persistent sorted data structure, while integrating linear fixed-effect prediction. This yields an overall time complexity of *O*(*N* log *N*). Experiments demonstrate substantial speedups over standard implementations on datasets comprising hundreds of thousands of low-dimensional points. The implementation is publicly available. The core contribution is the first exact, scalable MVM decomposition for Matérn kernels—achieving simultaneous gains in numerical accuracy, computational efficiency, and modeling expressivity.

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Recent publications

Latest Papers

Rainfall is rough

Jul 29, 2026

This study addresses the challenge of modeling the clustering and long-range dependence of rainfall processes across multiple timescales by proposing a novel framework based on a critical Hawkes point process. For the first time, a heavy-tailed power-law kernel is introduced into rainfall modeling, unifying the Bartlett–Lewis and Neyman–Scott models to effectively capture rain cell clustering characteristics. By integrating high-frequency (minute-level) observational data with millennial-scale tree-ring proxy records and employing fractal analysis alongside Hurst exponent estimation, the work reveals a shared extremely rough fractal structure—characterized by Hurst exponents between 0.01 and 0.1—spanning from meteorological to paleoclimatic timescales. The proposed method significantly outperforms classical models at fine temporal resolutions and establishes a novel interdisciplinary link between atmospheric science and financial microstructure theory.

0 citationsRead paper

Fast Gaussian process inference by exact Matérn kernel decomposition

Aug 03, 2025

To address the high computational complexity and poor scalability of kernel matrix–vector multiplication (MVM) in Gaussian process inference—particularly for large-scale, low-dimensional datasets—this paper introduces the first exact, fast MVM algorithm for multivariate Matérn kernels with half-integer smoothness parameters. Methodologically, the approach leverages an analytic decomposition of the Matérn kernel, combined with a divide-and-conquer strategy, weighted empirical cumulative distribution functions, and a persistent sorted data structure, while integrating linear fixed-effect prediction. This yields an overall time complexity of *O*(*N* log *N*). Experiments demonstrate substantial speedups over standard implementations on datasets comprising hundreds of thousands of low-dimensional points. The implementation is publicly available. The core contribution is the first exact, scalable MVM decomposition for Matérn kernels—achieving simultaneous gains in numerical accuracy, computational efficiency, and modeling expressivity.

0 citationsRead paper