arXiv subjects

Javier González-Delgado

Publications and source records attributed to Javier González-Delgado.

2 recordsLinked to original sources

arXiv2025

Post-clustering Inference under Dependence

Recent work by Gao et al. (JASA 2022) has laid the foundations for post-clustering inference, establishing a theoretical framework allowing to test for differences between means of estimated clusters. Additionally, they studied the estimation of unknown parameters while controlling the selective type I error. However, their theory was developed for independent observations identically distributed as $p$-dimensional Gaussian variables, where the parameter estimation could only be performed for spherical covariance matrices. Here, we aim at extending this framework to a more convenient scenario for practical applications, where arbitrary dependence structures between observations and features are allowed. We establish sufficient conditions for extending the setting presented by Gao et al. to the general dependence framework. Moreover, we assess theoretical conditions allowing the compatible estimation of a covariance matrix. The theory is developed for hierarchical agglomerative clustering algorithms with several types of linkages, and for the $k$-means algorithm. We illustrate our method with synthetic data and real data of protein structures.

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arXiv2023

Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology

This work is motivated by the study of local protein structure, which is defined by two variable dihedral angles that take values from probability distributions on the flat torus. Our goal is to provide the space $\mathcal{P}(\mathbb{R}^2/\mathbb{Z}^2)$ with a metric that quantifies local structural modifications due to changes in the protein sequence, and to define associated two-sample goodness-of-fit testing approaches. Due to its adaptability to the space geometry, we focus on the Wasserstein distance as a metric between distributions. We extend existing results of the theory of Optimal Transport to the $d$-dimensional flat torus $\mathbb{T}^d=\mathbb{R}^d/\mathbb{Z}^d$, in particular a Central Limit Theorem. Moreover, we propose different approaches for two-sample goodness-of-fit testing for the one and two-dimensional case, based on the Wasserstein distance. We prove their validity and consistency. We provide an implementation of these tests in \textsf{R}. Their performance is assessed by numerical experiments on synthetic data and illustrated by an application to protein structure data.

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