國立政治大學統計學系

學  術  演  講

主講人：黃灝勻 助理教授
國立東華大學應用數學系

題  目：Data-Adaptive Kriging for Diffusion-Based Spatiotemporal Prediction at Unobserved Locations

時  間：民國115年11月2日 (星期一) 下午1：30 

地  點：國立政治大學逸仙樓050101教室

摘  要：

Forecasting an environmental process at locations with no monitoring history requires two kinds of structure, namely temporal dynamics at the observed locations and spatial dependence across locations. We combine the two by injecting a fixed, closed-form spatial smoother, adaptive fixed-rank Kriging with a multi-resolution thin-plate-spline basis, into a diffusion-based deep forecaster. This yields three estimators. A two-stage procedure smooths only at the extrapolation stage, a covariate-augmented estimator appends spatial basis functions to the model’s input, and a new penalized criterion shrinks the model’s implicit clean-signal estimate toward the smoother, extending the penalized-estimation tradition of smoothing splines and regularization by denoising to diffusion training. The method is data adaptive in two respects. The smoother’s geometry adapts, because both injection mechanisms accept a planar or a spherical thin-plate-spline kernel, so the same method serves regional and global monitoring networks. The injection structure also adapts. Because the best injection point depends on the sampling regime, a validation-based selection rule chooses between the covariate and penalty routes and selects the kernel and the penalty weight for each fit, with no knowledge of the regime required. In simulations and on nine real datasets the method outperforms established spatio-temporal methods on most datasets, including our implementation of the forecaster that won the space-time track of the 2022 KAUST competition on spatial statistics.Keywords: Density–quantile function; tail exponent; exceedance probability criterion; bootstrap confidence interval; statistical process monitoring.

Keywords: fixed-rank Kriging; diffusion models; spatio-temporal prediction; penalized estimation; thin-plate splines; spherical data.