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Pierre Neuvial

Publications and source records attributed to Pierre Neuvial.

At least 19 recordsLinked to original sources
arXiv2026

Semi-knockoffs: a model-agnostic conditional independence testing method with finite-sample guarantees

Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the underlying distribution. However, model-agnostic approaches require a train-test split, which reduces statistical power. We introduce Semi-knockoffs, a CIT method that can accommodate any pre-trained model, avoids this split, and provides valid p-values and false discovery rate (FDR) control for high-dimensional settings. Unlike methods that rely on the model-$X$ assumption (known input distribution), Semi-knockoffs only require conditional expectations for continuous variables. This makes the procedure less restrictive and more practical for machine learning integration. To ensure validity when estimating these expectations, we present two new theoretical results of independent interest: (i) stability for regularized models trained with a null feature and (ii) the double-robustness property.

math.ST↗
arXiv2026

Overcoming Barriers to Computational Reproducibility

Computational reproducibility, the possibility for independent researchers to exactly reproduce published empirical results, is fundamental to science. Despite its importance, the proportion of research articles aiming for reproducibility remains low and uneven across disciplines. Barriers include a perceived lack of incentives for researchers and journals, practical challenges in preparing reproducible materials, and the absence of harmonised standards of reproducibility processes and requirements by journals. Existing guidance is often highly technical, reaching mainly those already engaged with reproducible research. In this paper, we first synthesize evidence on the benefits of reproducibility for both authors and journals. Drawing on our extensive experience in reproducibility checking at various journals, we then put forward concise, pragmatic guidelines for creating reproducible analyses across disciplines. We further review current reproducibility policies of selected journals, illustrating the substantial heterogeneity in requirements and procedures. Motivated by the latter, we propose conceptual foundations for a harmonised multi-tier system of reproducibility standards that could support transparent, consistent assessment across journals and research communities. Our goal as journal (reproducibility) editors and contributors to the MaRDI initiative is to encourage broader adoption of reproducibility practices, in particular by lowering practical barriers for authors and journals.

cs.DL↗
arXiv2025

Cluster Size Matters: A Comparative Study of Notip and pARI for Post Hoc Inference in fMRI

All Resolutions Inference (ARI) is a post hoc inference method for functional Magnetic Resonance Imaging (fMRI) data analysis that provides valid lower bounds on the proportion of truly active voxels within any, possibly data-driven, cluster. As such, it addresses the paradox of spatial specificity encountered with more classical cluster-extent thresholding methods. It allows the cluster-forming threshold to be increased in order to locate the signal with greater spatial precision without overfitting, also known as the drill-down approach. Notip and pARI are two recent permutation-based extensions of ARI designed to increase statistical power by accounting for the strong dependence structure typical of fMRI data. A recent comparison between these papers based on large voxel clusters concluded that pARI outperforms Notip. We revisit this conclusion by conducting a systematic comparison of the two. Our reanalysis of the same fMRI data sets from the Neurovault database demonstrates the existence of complementary performance regimes: while pARI indeed achieves higher sensitivity for large clusters, Notip provides more informative and robust results for smaller clusters. In particular, while Notip supports informative ``drill-down'' exploration into subregions of activation, pARI often yields non-informative bounds in such cases, and can even underperform the baseline ARI method.

math.ST↗
arXiv2025

A Principled Approach for Defining and Comparing Variable Importance Measures

Variable importance measures (VIMs) aim to quantify the contribution of each input covariate to the predictability of a given output. With the growing interest in explainable AI, numerous VIMs have been proposed, many of which are heuristic in nature. This is often justified by the inherent subjectivity of the notion of importance. This raises important questions regarding usage: What makes a good VIM? How can we compare different VIMs? In this paper, we address these questions by: (1) proposing an axiomatic framework that bridges the gap between variable importance and variable selection. This allows VIM methods to leverage the extensive literature on statistical guarantees developed for conditional independence testing. Our framework formalizes the intuitive principle that features providing no additional information should not be assigned importance, helping avoid false positives due to spurious correlations, which can arise with popular methods such as Shapley values; and (2) advocating for a general pipeline for constructing VIMs based on the definition of a theoretical index, its estimation, and the derivation of associated statistical guarantees. This pipeline clarifies the objective of various VIMs and thus facilitates meaningful comparisons. While this approach is natural from a statistical perspective, much of the literature has diverged from it, as we illustrate using the popular Total Sobol' Index. Finally, we apply this framework to an extensive set of VIMs, showing how practitioners can select and estimate indices aligned with their specific goals. Our results are supported by numerical experiments on simulated and real data.

stat.ME↗
arXiv2025

Inference post region selection

Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem, where the model selection step consists in selecting a rectangular region in a spatial domain. The inference step then consists in constructing confidence intervals on the average signal of this region. This is motivated by applications such as genetics or brain imaging. Our confidence intervals are constructed in dimension one, and then extended to higher dimension. They are based on the process mapping all possible selected regions to their corresponding estimation errors on the average signal. We prove the functional convergence of this process to a limiting Gaussian process with explicit covariance. This enables us to provide confidence intervals with asymptotic guarantees. In numerical experiments with simulated data, we show that our coverage proportions are fairly close to the nominal level already for small to moderate data-set size. We also highlight the impact of various possible noise distributions and the robustness of our intervals. Finally, we illustrate the relevance of our method to a segmentation problem inspired by the analysis of DNA copy number data in cancerology.

math.ST↗
arXiv2025

Conditional Feature Importance revisited: Double Robustness, Efficiency and Inference

Conditional Feature Importance (CFI) is a classical variable importance measure that accounts for the relationship between the studied feature and the others. However, CFI has not yet been studied from a theoretical perspective because the conditional sampling step has generally been considered a purely practical problem. In this article, we demonstrate that the recent Conditional Permutation Importance (CPI) is indeed a valid implementation of this concept. Under the conditional null hypothesis, we then establish a double robustness property that can be used for variable selection. With either a valid model or a valid conditional sampler, the method correctly identifies null coordinates. Under the alternative hypothesis, we study the theoretical target and link it to the popular Total Sobol Index (TSI). We introduce the Sobol-CPI, which generalizes CPI/CFI, prove that it is nonparametrically efficient, and provide a bias correction. Finally, we propose a consistent and valid type-I error test and present numerical experiments that illustrate our findings.

math.ST↗
arXiv2024

When Knockoffs fail: diagnosing and fixing non-exchangeability of Knockoffs

Knockoffs are a popular statistical framework that addresses the challenging problem of conditional variable selection in high-dimensional settings with statistical control. Such statistical control is essential for the reliability of inference. However, knockoff guarantees rely on an exchangeability assumption that is difficult to test in practice, and there is little discussion in the literature on how to deal with unfulfilled hypotheses. This assumption is related to the ability to generate data similar to the observed data. To maintain reliable inference, we introduce a diagnostic tool based on Classifier Two-Sample Tests. Using simulations and real data, we show that violations of this assumption occur in common settings for classical knockoff generators, especially when the data have a strong dependence structure. As a consequence, knockoff-based inference suffers from a massive inflation of false positives. We show that the diagnostic tool correctly detects such behavior. We show that an alternative knockoff construction, based on constructing a predictor of each variable based on all others, solves the issue. We also propose a computationally-efficient variant of this algorithm and show empirically that this approach restores error control on simulated data and semi-simulated experiments based on neuroimaging data.

stat.ME↗
arXiv2023

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.

stat.ME↗
arXiv2023

False Discovery Proportion control for aggregated Knockoffs

Controlled variable selection is an important analytical step in various scientific fields, such as brain imaging or genomics. In these high-dimensional data settings, considering too many variables leads to poor models and high costs, hence the need for statistical guarantees on false positives. Knockoffs are a popular statistical tool for conditional variable selection in high dimension. However, they control for the expected proportion of false discoveries (FDR) and not their actual proportion (FDP). We present a new method, KOPI, that controls the proportion of false discoveries for Knockoff-based inference. The proposed method also relies on a new type of aggregation to address the undesirable randomness associated with classical Knockoff inference. We demonstrate FDP control and substantial power gains over existing Knockoff-based methods in various simulation settings and achieve good sensitivity/specificity tradeoffs on brain imaging and genomic data.

stat.ME↗
arXiv2023

Selective inference after convex clustering with $\ell_1$ penalization

Classical inference methods notoriously fail when applied to data-driven test hypotheses or inference targets. Instead, dedicated methodologies are required to obtain statistical guarantees for these selective inference problems. Selective inference is particularly relevant post-clustering, typically when testing a difference in mean between two clusters. In this paper, we address convex clustering with $\ell_1$ penalization, by leveraging related selective inference tools for regression, based on Gaussian vectors conditioned to polyhedral sets. In the one-dimensional case, we prove a polyhedral characterization of obtaining given clusters, than enables us to suggest a test procedure with statistical guarantees. This characterization also allows us to provide a computationally efficient regularization path algorithm. Then, we extend the above test procedure and guarantees to multi-dimensional clustering with $\ell_1$ penalization, and also to more general multi-dimensional clusterings that aggregate one-dimensional ones. With various numerical experiments, we validate our statistical guarantees and we demonstrate the power of our methods to detect differences in mean between clusters. Our methods are implemented in the R package poclin.

stat.ME↗
arXiv2022

FDP control in multivariate linear models using the bootstrap

In this article we develop a method for performing post hoc inference of the False Discovery Proportion (FDP) over multiple contrasts of interest in the multivariate linear model. To do so we use the bootstrap to simulate from the distribution of the null contrasts. We combine the bootstrap with the post hoc inference bounds of Blanchard (2020) and prove that doing so provides simultaneous asymptotic control of the FDP over all subsets of hypotheses. This requires us to demonstrate consistency of the multivariate bootstrap in the linear model, which we do via the Lindeberg Central Limit Theorem, providing a simpler proof of this result than that of Eck (2018). We demonstrate, via simulations, that our approach provides simultaneous control of the FDP over all subsets and is typically more powerful than existing, state of the art, parametric methods. We illustrate our approach on functional Magnetic Resonance Imaging data from the Human Connectome project and on a transcriptomic dataset of chronic obstructive pulmonary disease.

stat.ME↗
arXiv2022

Notip: Non-parametric True Discovery Proportion control for brain imaging

Cluster-level inference procedures are widely used for brain mapping. These methods compare the size of clusters obtained by thresholding brain maps to an upper bound under the global null hypothesis, computed using Random Field Theory or permutations. However, the guarantees obtained by this type of inference - i.e. at least one voxel is truly activated in the cluster - are not informative with regards to the strength of the signal therein. There is thus a need for methods to assess the amount of signal within clusters; yet such methods have to take into account that clusters are defined based on the data, which creates circularity in the inference scheme. This has motivated the use of post hoc estimates that allow statistically valid estimation of the proportion of activated voxels in clusters. In the context of fMRI data, the All-Resolutions Inference framework introduced in [25] provides post hoc estimates of the proportion of activated voxels. However, this method relies on parametric threshold families, which results in conservative inference. In this paper, we leverage randomization methods to adapt to data characteristics and obtain tighter false discovery control. We obtain Notip, for Non-parametric True Discovery Proportion control: a powerful, non-parametric method that yields statistically valid guarantees on the proportion of activated voxels in data-derived clusters. Numerical experiments demonstrate substantial gains in number of detections compared with state-of-the-art methods on 36 fMRI datasets. The conditions under which the proposed method brings benefits are also discussed.

stat.ME↗
arXiv2021

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.

stat.ME↗
arXiv2021

Post hoc false discovery proportion inference under a Hidden Markov Model

We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a Hidden Markov Model (HMM), which is recognized as a fundamental setting to model multiple testing under dependence since the seminal work of \citet{sun2009large}. While previous work has concentrated on deriving specific procedures with a controlled False Discovery Rate (FDR) under this model, following a recent trend in selective inference, we consider the problem of establishing confidence bounds on the false discovery proportion (FDP), for a user-selected set of hypotheses that can depend on the observed data in an arbitrary way. We develop a methodology to construct such confidence bounds first when the HMM model is known, then when its parameters are unknown and estimated, including the data distribution under the null and the alternative, using a nonparametric approach. In the latter case, we propose a bootstrap-based methodology to take into account the effect of parameter estimation error. We show that taking advantage of the assumed HMM structure allows for a substantial improvement of confidence bound sharpness over existing agnostic (structure-free) methods, as witnessed both via numerical experiments and real data examples.

stat.ME↗
arXiv2020

Identification of deregulated transcription factors involved in subtypes of cancers

We propose a methodology for the identification of transcription factors involved in the deregulation of genes in tumoral cells. This strategy is based on the inference of a reference gene regulatory network that connects transcription factors to their downstream targets using gene expression data. The behavior of genes in tumor samples is then carefully compared to this network of reference to detect deregulated target genes. A linear model is finally used to measure the ability of each transcription factor to explain those deregulations. We assess the performance of our method by numerical experiments on a breast cancer data set. We show that the information about deregulation is complementary to the expression data as the combination of the two improves the supervised classification performance of samples into cancer subtypes.

q-bio.MN↗
arXiv2019

Applicability and Interpretability of Hierarchical Agglomerative Clustering With or Without Contiguity Constraints

Hierarchical Agglomerative Classification (HAC) with Ward's linkage has been widely used since its introduction in Ward (1963). The present article reviews the different extensions of the method to various input data and the constrained framework, while providing applicability conditions. In addition, various versions of the graphical representation of the results as a dendrogram are also presented and their properties are clarified. While some of these results can sometimes be found in an heteroclite literature, we clarify and complete them all using a uniform background. In particular, this study reveals an important distinction between a consistency property of the dendrogram and the absence of crossover within it. Finally, a simulation study shows that the constrained version of HAC can sometimes provide more relevant results than its unconstrained version despite the fact that the latter optimizes the objective criterion on a reduced set of solutions at each step. Overall, the article provides comprehensive recommandations for the use of HAC and constrained HAC depending on the input data as well as for the representation of the results.

stat.ME↗
arXiv2019

Adjacency-constrained hierarchical clustering of a band similarity matrix with application to Genomics

Motivation: Genomic data analyses such as Genome-Wide Association Studies (GWAS) or Hi-C studies are often faced with the problem of partitioning chromosomes into successive regions based on a similarity matrix of high-resolution, locus-level measurements. An intuitive way of doing this is to perform a modified Hierarchical Agglomerative Clustering (HAC), where only adjacent clusters (according to the ordering of positions within a chromosome) are allowed to be merged. A major practical drawback of this method is its quadratic time and space complexity in the number of loci, which is typically of the order of 10^4 to 10^5 for each chromosome. Results: By assuming that the similarity between physically distant objects is negligible, we propose an implementation of this adjacency-constrained HAC with quasi-linear complexity. Our illustrations on GWAS and Hi-C datasets demonstrate the relevance of this assumption, and show that this method highlights biologically meaningful signals. Thanks to its small time and memory footprint, the method can be run on a standard laptop in minutes or even seconds. Availability and Implementation: Software and sample data are available as an R package, adjclust, that can be downloaded from the Comprehensive R Archive Network (CRAN).

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