Bertrand Thirion

Bruno Aristimunha, Ce Ju, Antoine Collas et al.

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.

Joseph Paillard, Angel Reyero Lobo, Denis A. Engemann et al.

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.

Nicolas Salvy, Hugues Talbot, Bertrand Thirion

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 judgment.

Joseph Paillard, Antoine Collas, Denis A. Engemann et al.

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.

Ce Ju, Reinmar J. Kobler, Antoine Collas et al.

Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities. While modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets, decoding task-specific signatures must contend with inherent neuroimaging constraints, for example, low signal-to-noise ratios in raw electrophysiological recordings, cross-session non-stationarity, and limited sample sizes. This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships. By equipping the space of SPD matrices with Riemannian metrics (e.g., affine-invariant or log-Euclidean), their space forms a Riemannian manifold enabling geometric analysis. We unify methodologies operating on this manifold under the SPD learning framework, which systematically leverages the SPD manifold's geometry to process covariance features, thereby advancing brain imaging analytics.