A. F. López-Lopera | Searcharxiv

arXiv2025

Block-Additive Gaussian Processes under Monotonicity Constraints

We generalize the additive constrained Gaussian process framework to handle interactions between input variables while enforcing monotonicity constraints everywhere on the input space. The block-additive structure of the model is particularly suitable in the presence of interactions, while maintaining tractable computations. In addition, we develop a sequential algorithm, MaxMod, for model selection (i.e., the choice of the active input variables and of the blocks). We speed up our implementations through efficient matrix computations and thanks to explicit expressions of criteria involved in MaxMod. The performance and scalability of our methodology are showcased with several numerical examples in dimensions up to 120, as well as in a 5D real-world coastal flooding application, where interpretability is enhanced by the selection of the blocks.

stat.ME↗

arXiv2021

Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment

Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are conveniently parameterized by scalar representations, neglecting that the inputs are actually time series and that floods propagate spatially inland. Both facts are crucial in flood prediction for complex coastal systems. Our aim is to establish a surrogate model that accounts for time-varying inputs and provides information on spatially varying inland flooding. We introduce a multioutput Gaussian process model based on a separable kernel that correlates both functional inputs and spatial locations. Efficient implementations consider tensor-structured computations or sparse-variational approximations. In several experiments, we demonstrate the versatility of the model for both learning maps and inferring unobserved maps, numerically showing the convergence of predictions as the number of learning maps increases. We assess our framework in a coastal flood prediction application. Predictions are obtained with small error values within computation time highly compatible with short-term forecast requirements (on the order of minutes compared to the days required by hydrodynamic simulators). We conclude that our framework is a promising approach for forecast and early-warning systems.

stat.ML↗