arXiv subjects

Penghui Fu

Publications and source records attributed to Penghui Fu.

3 recordsLinked to original sources

arXiv2026

Nearest-Neighbor Non-Gaussian Processes for Geostatistical Modeling

We develop a general class of nearest-neighbor non-Gaussian processes (NNnGP) for modeling geostatistical data. By introducing non-linear conditional mean functions into the Vecchia approximation, NNnGP extends the popular nearest-neighbor Gaussian process (NNGP) to effectively capture complex, non-Gaussian spatial characteristics. To ensure coherent spatial predictions from a single realization, we propose a regularized homogeneity condition across the univariate conditionals. We then formulate a Bayesian non-parametric construction of the conditional mean using Gaussian processes and embed the resulting NNnGP as a non-Gaussian spatial prior within a hierarchical regression model. For posterior computation and prediction, we adopt a normalizing flow-based variational inference approach. Numerical experiments on synthetic data and real-world PRISM precipitation anomalies demonstrate that NNnGP captures local non-linear dependencies and significantly mitigates the underestimation of extreme spatial events, all the while maintaining global predictive accuracy.

stat.ME↗

arXiv2023

Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretations

We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov analyses, for achieving accelerated convergence rates which match Nesterov's methods in the strongly and general convex settings. Next, we study the convergence of limiting ordinary differential equations (ODEs) and point out currently notable gaps between the convergence properties of the corresponding algorithms and ODEs. Finally, we propose a novel class of discrete algorithms, called the Hamiltonian assisted gradient method, directly based on a Hamiltonian function and several interpretable operations, and then demonstrate meaningful and unified interpretations of our acceleration conditions.

math.OC↗

arXiv2022

Block-wise Primal-dual Algorithms for Large-scale Doubly Penalized ANOVA Modeling

For multivariate nonparametric regression, doubly penalized ANOVA modeling (DPAM) has recently been proposed, using hierarchical total variations (HTVs) and empirical norms as penalties on the component functions such as main effects and multi-way interactions in a functional ANOVA decomposition of the underlying regression function. The two penalties play complementary roles: the HTV penalty promotes sparsity in the selection of basis functions within each component function, whereas the empirical-norm penalty promotes sparsity in the selection of component functions. We adopt backfitting or block minimization for training DPAM, and develop two suitable primal-dual algorithms, including both batch and stochastic versions, for updating each component function in single-block optimization. Existing applications of primal-dual algorithms are intractable in our setting with both HTV and empirical-norm penalties. Through extensive numerical experiments, we demonstrate the validity and advantage of our stochastic primal-dual algorithms, compared with their batch versions and a previous active-set algorithm, in large-scale scenarios.

stat.CO↗