arXiv subjects

Athénaïs Gautier

Publications and source records attributed to Athénaïs Gautier.

5 recordsLinked to original sources

arXiv2026

SLGP: An R Package for Spatial Conditional Density Estimation

The SLGP package provides nonparametric estimation of fields of probability densities indexed by covariates, from unevenly sized samples with few or no replicates. A Spatial Logistic Gaussian Process applies a logistic density transformation to a finite-rank Gaussian process over a joint index-response domain, yielding a prior over conditional densities that adapts in location, shape, and modality. The contribution of this paper is the implementation: a finite-rank Random-Fourier-Feature representation that keeps the transformed process numerically tame, a log-concave likelihood that makes the fit a convex problem, and a family of quadrature shortcuts for the normalising integrals that turn a per-observation cost into a per-grid cost. Three estimation modes are available: MAP, Laplace, and full MCMC. We demonstrate the package throughout on the classical Fiji-Tonga earthquake catalogue, estimating how the distribution of hypocentre depths deforms across the region, and on a discrete-response variant.

stat.ME↗

arXiv2025

CRPS-Based Targeted Sequential Design with Application in Chemical Space

Sequential design of real and computer experiments via Gaussian Process (GP) models has proven useful for parsimonious, goal-oriented data acquisition purposes. In this work, we focus on acquisition strategies for a GP model that needs to be accurate within a predefined range of the response of interest. Such an approach is useful in various fields including synthetic chemistry, where finding molecules with particular properties is essential for developing useful materials and effective medications. GP modeling and sequential design of experiments have been successfully applied to a plethora of domains, including molecule research. Our main contribution here is to use the threshold-weighted Continuous Ranked Probability Score (CRPS) as a basic building block for acquisition functions employed within sequential design. We study pointwise and integral criteria relying on two different weighting measures and benchmark them against competitors, demonstrating improved performance with respect to considered goals. The resulting acquisition strategies are applicable to a wide range of fields and pave the way to further developing sequential design relying on scoring rules.

stat.ML↗

arXiv2025

On the Usage of Gaussian Process for Efficient Data Valuation

In machine learning, knowing the impact of a given datum on model training is a fundamental task referred to as Data Valuation. Building on previous works from the literature, we have designed a novel canonical decomposition allowing practitioners to analyze any data valuation method as the combination of two parts: a utility function that captures characteristics from a given model and an aggregation procedure that merges such information. We also propose to use Gaussian Processes as a means to easily access the utility function on ``sub-models'', which are models trained on a subset of the training set. The strength of our approach stems from both its theoretical grounding in Bayesian theory, and its practical reach, by enabling fast estimation of valuations thanks to efficient update formulae.

cs.LG↗

arXiv2025

Continuous logistic Gaussian random measure fields for spatial distributional modelling

We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their densities, investigating the relationships between SLGPs and underlying processes. Our inquiries are motivated by SLGP's abilities in delivering probabilistic predictions of conditional distributions at candidate points, allowing conditional simulations of probability densities, and jointly predicting multiple functionals of target distributions. We demonstrate that SLGP models exhibit joint Gaussianity of their log-increments, enabling us to establish theoretical results regarding spatial regularity. Additionally, we extend the notion of mean-square continuity to random measure fields and establish sufficient conditions on covariance kernels underlying SLGPs to ensure these models enjoy such regularity properties. Finally, we propose an implementation using Random Fourier Features and showcase its applicability on synthetic examples and on temperature distributions at meteorological stations.

math.ST↗

arXiv2021

Goal-oriented adaptive sampling under random field modelling of response probability distributions

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation.

stat.ME↗