# Theta-regularized Kriging: Modelling and Algorithms

arXiv: https://arxiv.org/abs/2604.14975 · HTML: https://mlsanity.com/paper/2604.14975/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 53 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [Accelerated iterative regularization via dual diagonal descent](https://mlsanity.com/paper/1912.12153/) (2019)
- [Nystr"om Regularization for Time Series Forecasting](https://mlsanity.com/paper/2111.07109/) (2021)
- [Enhanced Universal Kriging for Transformed Input Parameter Spaces](https://mlsanity.com/paper/2307.06906/) (2023)

## Abstract (arXiv)

To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.