arXiv subjects

Hao-Yun Huang

Publications and source records attributed to Hao-Yun Huang.

4 recordsLinked to original sources

arXiv2026

Structured Covariate-Informed Empirical Orthogonal Functions for Spatio-Temporal Environmental Fields

Low-rank representations such as empirical orthogonal function (EOF) decompositions are widely used for analyzing large spatio-temporal environmental fields. However, conventional EOF identifies latent modes solely from covariance structure and does not utilize observed environmental covariates, limiting its ability to incorporate external information into low-rank representations. This study introduces Structured Covariate-Informed EOF (SCIEOF), a covariate-informed extension of EOF that bridges low-rank dimension reduction and prediction-oriented spatio-temporal modeling. SCIEOF embeds spatial and temporal covariates into the latent bases while incorporating spatio-temporal covariates through an additive component, yielding low-rank representations with latent modes informed by observed covariates. Estimation procedures are developed and evaluated through simulation studies and an application to global near-surface air temperature from the MERRA-2 reanalysis. Simulation studies demonstrate that incorporating informative covariates improves latent structure recovery and predictive accuracy, particularly when the spatial basis is appropriately specified. The advantage is more pronounced at moderate-to-large sample sizes, while methods with stronger structural assumptions remain competitive when data are limited. In the MERRA-2 application, SCIEOF achieves competitive or improved predictive performance relative to commonly used methods while providing a compact and physically interpretable low-rank representation. Overall, SCIEOF provides a flexible and computationally scalable framework for integrating structural covariate information into low-rank spatio-temporal representations, extending EOF toward predictive environmental modeling.

stat.ME↗

arXiv2026

Cluster-Aware Conformal Calibration for Spatio-Temporal Distributional Prediction

DeepKriging-style models, such as Spatio-Temporal DeepKriging, improve scalability through basis-function embeddings and stochastic gradient learning; however, fixed regular-grid spatial bases remain inefficient under highly non-uniform sampling patterns, often over-allocating capacity to sparse regions while under-resolving dense clusters. To address this limitation, we propose a practical extension of DeepKriging for reliable spatio-temporal distributional forecasting, incorporating cluster-adaptive spatial bases - whose centers and scales are initialized from {the spatial sampling density} - to better capture heterogeneous spatial sampling, together with cluster-aware conformal calibration that determines prediction-interval widths within spatial clusters (with a global fallback when calibration samples are insufficient). The resulting calibration pipeline explicitly targets spatial heterogeneity and local miscalibration, and experiments, including simulation studies and PM$_{2.5}$ data analysis, demonstrate substantially improved coverage accuracy and tail reliability under clustered observation patterns compared with a global conformal baseline.

stat.ME↗

arXiv2026

Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictors

We present the Spatial Adapter, a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured spatial representation of its residual field and an induced closed-form spatial covariance. The adapter operates as a cascade second stage on residuals, jointly learning a spatially regularized orthonormal basis and per-sample scores via a tractable mini-batch ADMM procedure, without modifying any first-stage parameter. Because the first-stage parameters are frozen, the adapter does not retrain the backbone; its role is to supply a compressed distributional summary of the residual field. Smoothness, sparsity, and orthogonality together turn a generic low-rank factorization into an identifiable spatial representation whose induced residual covariance admits a closed-form low-rank-plus-noise estimator; the effective rank is determined data-adaptively by spectral thresholding, while the nominal rank K is an optimization-side upper bound only. This covariance enables kriging-style spatial prediction at unobserved locations, with plug-in uncertainty quantification as a secondary downstream use. Across synthetic data, Weather2K for spatial-holdout prediction, and GWHD patch grids as a basis-transferability diagnostic, the adapter recovers residual spatial structure when paired with frozen first stages from linear models to deep spatiotemporal and vision backbones; the added representation uses fewer than K(N+T) parameters alongside a compact residual-trend network.

stat.ML↗

arXiv2026

DeepKriging on the global Data

The increasing availability of large-scale global datasets has generated a demand for scalable spatial prediction methods defined on spherical domains. Classical spatial models that rely on Euclidean distance representations are inappropriate for spherical data because planar projections distort geodesic distances and spatial neighborhood structures, while traditional kriging-based prediction methods are often computationally prohibitive for massive datasets. To address these challenges, we propose a Spherical DeepKriging framework for spatial prediction on $\mathbb{S}^2$. The proposed approach constructs a flexible prediction model by integrating thin-plate spline (TPS) basis functions defined intrinsically on the sphere. Simulation studies and real data analyses are presented to demonstrate the superior predictive performance of the proposed method.

stat.ME↗