arXiv subjects

Bertrand Thirion

Publications and source records attributed to Bertrand Thirion.

At least 19 recordsLinked to original sources

arXiv2026

Benchmarking External Generalization of SPD Matrix Learning for Resting-State fMRI Connectome Prediction

Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction, but strong performance within one cohort may not generalize to a new cohort. We ask whether within-dataset performance remains when the test data come from an entirely held-out rs-fMRI dataset. Each scan is represented as a regularized symmetric positive definite (SPD) correlation connectome, which allows methods to use the geometry of the SPD manifold. We introduce a reproducible age-prediction benchmark across six rs-fMRI datasets: COBRE, ADNIDOD, Cam-CAN, ABIDE, OASIS-3, and ADNI. The benchmark compares a vectorized correlation baseline, Tangent-Space Ridge, SPDNet, and split-wise Riemannian harmonization under within-dataset GroupKFold, pooled GroupKFold, and leave-one-dataset-out (LODO) evaluation. Within-dataset and pooled GroupKFold results are substantially more favorable than LODO results. When an entire dataset is held out, prediction error increases, differences among methods narrow, and performance is strongly affected by age-range mismatch and cohort heterogeneity. The benchmark provides common inputs, model settings, data splits, and analysis scripts so that future SPD matrix learning methods can be evaluated under the same external-validation protocol.

eess.SP↗

arXiv2026

Fast Whole-Brain, Geometry-Aware Functional Alignment for Cross-Subject Decoding

Decoding brain activity is useful for characterizing brain processes and understanding the functional architecture underlying cognition. However, the inter-individual variability in brain response patterns limits the development of decoders that generalize across individuals. A solution to this challenge is functional alignment: aligning functional data across individuals before training population-level decoders. The core issue is to strike the balance between aligning functional features and preserving the anatomical structure, while maintaining computational efficiency. We introduce a new functional alignment method for fMRI, SpectralOT, that embeds cortical geometry into Laplace-Beltrami eigenmodes along functional data to regularize the alignment.

q-bio.NC↗

arXiv2026

Learning fMRI activations dictionaries across individual geometries via optimal transport

Dictionary learning is a powerful tool for creating interpretable representations. When applied to functional magnetic resonance imaging (fMRI) data, the resulting patterns of brain activity can be used for various downstream tasks, such as brain state classification or population-level analysis. However, a major challenge is the variability in brain geometry across individuals. This is usually addressed by projecting each individual brain geometry onto a common template, which removes subject-specific information. In this work, we introduce a novel approach to dictionary learning on fMRI data that explicitly accounts for this variability. We use the optimal transport-based Fused Gromov-Wasserstein (FGW) distance to compare graphs with different geometries and features. To address the challenge of computing multiple FGW distances for large graphs such as those arising from fMRI data, we rely on amortized optimization to learn a neural network that predicts an approximation of the optimal transport plans, which substantially reduces the computational cost. Additionally, we learn dictionary atoms that depend on the FGW trade-off parameter, which controls the balance between feature alignment and structural consistency. Numerical experiments on the HCP dataset demonstrate that the proposed approach captures different levels of geometric variability in the data and provides representations that preserve essential information.

cs.LG↗

arXiv2026

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

q-bio.NC↗

arXiv2026

GICDM: Mitigating Hubness for Reliable Distance-Based Generative Model Evaluation

Generative model evaluation commonly relies on high-dimensional embedding spaces to compute distances between samples. We show that dataset representations in these spaces are affected by the hubness phenomenon, which distorts nearest-neighbor relationships and biases distance-based metrics. Building on the classical Iterative Contextual Dissimilarity Measure (ICDM), we introduce Generative ICDM (GICDM), a method to correct neighborhood estimation for both real and generated data. We introduce a multi-scale extension to improve empirical behavior. Extensive experiments on synthetic and real benchmarks demonstrate that GICDM resolves hubness-induced failures, restores reliable metric behavior, and improves alignment with human assessment.

cs.LG↗

arXiv2026

Enhanced Generative Model Evaluation with Clipped Density and Coverage

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two complementary concepts: fidelity and coverage. Current quality metrics often lack reliable, interpretable values due to an absence of calibration or insufficient robustness to outliers. To address these shortcomings, we introduce two novel metrics: Clipped Density and Clipped Coverage. By clipping individual sample contributions, as well as the radii of nearest neighbor balls for fidelity, our metrics prevent out-of-distribution samples from biasing the aggregated values. Through analytical and empirical calibration, these metrics demonstrate linear score degradation as the proportion of bad samples increases. Thus, they can be straightforwardly interpreted as equivalent proportions of good samples. Extensive experiments on synthetic and real-world datasets demonstrate that Clipped Density and Clipped Coverage outperform existing methods in terms of robustness, sensitivity, and interpretability when evaluating generative models.

cs.LG↗

arXiv2026

Aggregate Models, Not Explanations: Improving Feature Importance Estimation

Feature-importance methods show promise in transforming machine learning models from predictive engines into tools for scientific discovery. However, due to data sampling and algorithmic stochasticity, expressive models can be unstable, leading to inaccurate variable importance estimates and undermining their utility in critical biomedical applications. Although ensembling offers a solution, deciding whether to explain a single ensemble model or aggregate individual model explanations is difficult due to the nonlinearity of importance measures and remains largely understudied. Our theoretical analysis, developed under assumptions accommodating complex state-of-the-art ML models, reveals that this choice is primarily driven by the model's excess risk. In contrast to prior literature, we show that ensembling at the model level provides more accurate variable-importance estimates, particularly for expressive models, by reducing this leading error term. We validate these findings on classical benchmarks and a large-scale proteomic study from the UK Biobank.

stat.ML↗

arXiv2026

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↗

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↗

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

Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry

Generating realistic brain connectivity matrices is key to analyzing population heterogeneity in brain organization, understanding disease, and augmenting data in challenging classification problems. Functional connectivity matrices lie in constrained spaces, such as the set of symmetric positive definite or correlation matrices, that can be modeled as Riemannian manifolds. However, using Riemannian tools typically requires redefining core operations (geodesics, norms, integration), making generative modeling computationally inefficient. In this work, we propose DiffeoCFM, an approach that enables conditional flow matching (CFM) on matrix manifolds by exploiting pullback metrics induced by global diffeomorphisms on Euclidean spaces. We show that Riemannian CFM with such metrics is equivalent to applying standard CFM after data transformation. This equivalence allows efficient vector field learning, and fast sampling with standard ODE solvers. We instantiate DiffeoCFM with two different settings: the matrix logarithm for covariance matrices and the normalized Cholesky decomposition for correlation matrices. We evaluate DiffeoCFM on three large-scale fMRI datasets with more than 4600 scans from 2800 subjects (ADNI, ABIDE, OASIS-3) and two EEG motor imagery datasets with over 30000 trials from 26 subjects (BNCI2014-002 and BNCI2015-001). It enables fast training and achieves state-of-the-art performance, all while preserving manifold constraints. Code: https://github.com/antoinecollas/DiffeoCFM

cs.LG↗

arXiv2025

Hierarchical Variable Importance with Statistical Control for Medical Data-Based Prediction

Recent advances in machine learning have greatly expanded the repertoire of predictive methods for medical imaging. However, the interpretability of complex models remains a challenge, which limits their utility in medical applications. Recently, model-agnostic methods have been proposed to measure conditional variable importance and accommodate complex non-linear models. However, they often lack power when dealing with highly correlated data, a common problem in medical imaging. We introduce Hierarchical-CPI, a model-agnostic variable importance measure that frames the inference problem as the discovery of groups of variables that are jointly predictive of the outcome. By exploring subgroups along a hierarchical tree, it remains computationally tractable, yet also enjoys explicit family-wise error rate control. Moreover, we address the issue of vanishing conditional importance under high correlation with a tree-based importance allocation mechanism. We benchmarked Hierarchical-CPI against state-of-the-art variable importance methods. Its effectiveness is demonstrated in two neuroimaging datasets: classifying dementia diagnoses from MRI data (ADNI dataset) and analyzing the Berger effect on EEG data (TDBRAIN dataset), identifying biologically plausible variables.

stat.ML↗

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

Measuring Variable Importance in Heterogeneous Treatment Effects with Confidence

Causal machine learning holds promise for estimating individual treatment effects from complex data. For successful real-world applications of machine learning methods, it is of paramount importance to obtain reliable insights into which variables drive heterogeneity in the response to treatment. We propose PermuCATE, an algorithm based on the Conditional Permutation Importance (CPI) method, for statistically rigorous global variable importance assessment in the estimation of the Conditional Average Treatment Effect (CATE). Theoretical analysis of the finite sample regime and empirical studies show that PermuCATE has lower variance than the Leave-One-Covariate-Out (LOCO) reference method and provides a reliable measure of variable importance. This property increases statistical power, which is crucial for causal inference in the limited-data regime common to biomedical applications. We empirically demonstrate the benefits of PermuCATE in simulated and real-world health datasets, including settings with up to hundreds of correlated variables.

cs.LG↗

arXiv2025

Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.

cs.LG↗

arXiv2025

Optimizing fMRI Data Acquisition for Decoding Natural Speech with Limited Participants

We investigate optimal strategies for decoding perceived natural speech from fMRI data acquired from a limited number of participants. Leveraging Lebel et al. (2023)'s dataset of 8 participants, we first demonstrate the effectiveness of training deep neural networks to predict LLM-derived text representations from fMRI activity. Then, in this data regime, we observe that multi-subject training does not improve decoding accuracy compared to single-subject approach. Furthermore, training on similar or different stimuli across subjects has a negligible effect on decoding accuracy. Finally, we find that our decoders better model syntactic than semantic features, and that stories containing sentences with complex syntax or rich semantic content are more challenging to decode. While our results demonstrate the benefits of having extensive data per participant (deep phenotyping), they suggest that leveraging multi-subject for natural speech decoding likely requires deeper phenotyping or a substantially larger cohort.

q-bio.NC↗

arXiv2025

Causal mediation analysis with one or multiple mediators: a comparative study

Mediation analysis breaks down the causal effect of a treatment on an outcome into an indirect effect, acting through a third group of variables called mediators, and a direct effect, operating through other mechanisms. Mediation analysis is hard because confounders between treatment, mediators, and outcome blur effect estimates in observational studies. Many estimators have been proposed to adjust on those confounders and provide accurate causal estimates. We consider parametric and non-parametric implementations of classical estimators and provide a thorough evaluation for the estimation of the direct and indirect effects in the context of causal mediation analysis for binary, continuous, and multi-dimensional mediators. We assess several approaches in a comprehensive benchmark on simulated data. Our results show that advanced statistical approaches such as the multiply robust and the double machine learning estimators achieve good performances in most of the simulated settings and on real data. As an example of application, we propose a thorough analysis of factors known to influence cognitive functions to assess if the mechanism involves modifications in brain morphology using the UK Biobank brain imaging cohort. This analysis shows that for several physiological factors, such as hypertension and obesity, a substantial part of the effect is mediated by changes in the brain structure. This work provides guidance to the practitioner from the formulation of a valid causal mediation problem, including the verification of the identification assumptions, to the choice of an adequate estimator.

stat.AP↗

arXiv2025

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↗