Bertrand Thirion

Alexandre Pasquiou, Yair Lakretz, John Hale et al.

Neural Language Models (NLMs) have made tremendous advances during the last years, achieving impressive performance on various linguistic tasks. Capitalizing on this, studies in neuroscience have started to use NLMs to study neural activity in the human brain during language processing. However, many questions remain unanswered regarding which factors determine the ability of a neural language model to capture brain activity (aka its 'brain score'). Here, we make first steps in this direction and examine the impact of test loss, training corpus and model architecture (comparing GloVe, LSTM, GPT-2 and BERT), on the prediction of functional Magnetic Resonance Imaging timecourses of participants listening to an audiobook. We find that (1) untrained versions of each model already explain significant amount of signal in the brain by capturing similarity in brain responses across identical words, with the untrained LSTM outperforming the transformerbased models, being less impacted by the effect of context; (2) that training NLP models improves brain scores in the same brain regions irrespective of the model's architecture; (3) that Perplexity (test loss) is not a good predictor of brain score; (4) that training data have a strong influence on the outcome and, notably, that off-the-shelf models may lack statistical power to detect brain activations. Overall, we outline the impact of modeltraining choices, and suggest good practices for future studies aiming at explaining the human language system using neural language models.

Alexandre Pasquiou, Yair Lakretz, Bertrand Thirion et al.

A fundamental question in neurolinguistics concerns the brain regions involved in syntactic and semantic processing during speech comprehension, both at the lexical (word processing) and supra-lexical levels (sentence and discourse processing). To what extent are these regions separated or intertwined? To address this question, we trained a lexical language model, Glove, and a supra-lexical language model, GPT-2, on a text corpus from which we selectively removed either syntactic or semantic information. We then assessed to what extent these information-restricted models were able to predict the time-courses of fMRI signal of humans listening to naturalistic text. We also manipulated the size of contextual information provided to GPT-2 in order to determine the windows of integration of brain regions involved in supra-lexical processing. Our analyses show that, while most brain regions involved in language are sensitive to both syntactic and semantic variables, the relative magnitudes of these effects vary a lot across these regions. Furthermore, we found an asymmetry between the left and right hemispheres, with semantic and syntactic processing being more dissociated in the left hemisphere than in the right, and the left and right hemispheres showing respectively greater sensitivity to short and long contexts. The use of information-restricted NLP models thus shed new light on the spatial organization of syntactic processing, semantic processing and compositionality.

Binh T. Nguyen, Bertrand Thirion, Sylvain Arlot

Identifying the relevant variables for a classification model with correct confidence levels is a central but difficult task in high-dimension. Despite the core role of sparse logistic regression in statistics and machine learning, it still lacks a good solution for accurate inference in the regime where the number of features $p$ is as large as or larger than the number of samples $n$. Here, we tackle this problem by improving the Conditional Randomization Test (CRT). The original CRT algorithm shows promise as a way to output p-values while making few assumptions on the distribution of the test statistics. As it comes with a prohibitive computational cost even in mildly high-dimensional problems, faster solutions based on distillation have been proposed. Yet, they rely on unrealistic hypotheses and result in low-power solutions. To improve this, we propose \emph{CRT-logit}, an algorithm that combines a variable-distillation step and a decorrelation step that takes into account the geometry of $\ell_1$-penalized logistic regression problem. We provide a theoretical analysis of this procedure, and demonstrate its effectiveness on simulations, along with experiments on large-scale brain-imaging and genomics datasets.

Ahmad Chamma, Denis A. Engemann, Bertrand Thirion

Variable importance assessment has become a crucial step in machine-learning applications when using complex learners, such as deep neural networks, on large-scale data. Removal-based importance assessment is currently the reference approach, particularly when statistical guarantees are sought to justify variable inclusion. It is often implemented with variable permutation schemes. On the flip side, these approaches risk misidentifying unimportant variables as important in the presence of correlations among covariates. Here we develop a systematic approach for studying Conditional Permutation Importance (CPI) that is model agnostic and computationally lean, as well as reusable benchmarks of state-of-the-art variable importance estimators. We show theoretically and empirically that $\textit{CPI}$ overcomes the limitations of standard permutation importance by providing accurate type-I error control. When used with a deep neural network, $\textit{CPI}$ consistently showed top accuracy across benchmarks. An experiment on real-world data analysis in a large-scale medical dataset showed that $\textit{CPI}$ provides a more parsimonious selection of statistically significant variables. Our results suggest that $\textit{CPI}$ can be readily used as drop-in replacement for permutation-based methods.

Joseph Paillard, Angel Reyero Lobo, Vitaliy Kolodyazhniy et al.

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.

Sonia Mazelet, Rémi Flamary, Bertrand Thirion

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.

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.

Antoine Collas, Ce Ju, Nicolas Salvy et al.

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

Himanshu Aggarwal, Liza Al-Shikhley, Bertrand Thirion

Decoding cognitive states from functional magnetic resonance imaging is central to understanding the functional organization of the brain. Within-subject decoding avoids between-subject correspondence problems but requires large sample sizes to make accurate predictions; obtaining such large sample sizes is both challenging and expensive. Here, we investigate an ensemble approach to decoding that combines the classifiers trained on data from other subjects to decode cognitive states in a new subject. We compare it with the conventional decoding approach on five different datasets and cognitive tasks. We find that it outperforms the conventional approach by up to 20% in accuracy, especially for datasets with limited per-subject data. The ensemble approach is particularly advantageous when the classifier is trained in voxel space. Furthermore, a Multi-layer Perceptron turns out to be a good default choice as an ensemble method. These results show that the pre-training strategy reduces the need for large per-subject data.

Hugo Richard, Luigi Gresele, Aapo Hyvärinen et al.

Group studies involving large cohorts of subjects are important to draw general conclusions about brain functional organization. However, the aggregation of data coming from multiple subjects is challenging, since it requires accounting for large variability in anatomy, functional topography and stimulus response across individuals. Data modeling is especially hard for ecologically relevant conditions such as movie watching, where the experimental setup does not imply well-defined cognitive operations. We propose a novel MultiView Independent Component Analysis (ICA) model for group studies, where data from each subject are modeled as a linear combination of shared independent sources plus noise. Contrary to most group-ICA procedures, the likelihood of the model is available in closed form. We develop an alternate quasi-Newton method for maximizing the likelihood, which is robust and converges quickly. We demonstrate the usefulness of our approach first on fMRI data, where our model demonstrates improved sensitivity in identifying common sources among subjects. Moreover, the sources recovered by our model exhibit lower between-session variability than other methods.On magnetoencephalography (MEG) data, our method yields more accurate source localization on phantom data. Applied on 200 subjects from the Cam-CAN dataset it reveals a clear sequence of evoked activity in sensor and source space. The code is freely available at https://github.com/hugorichard/multiviewica.

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.

Ahmad Chamma, Bertrand Thirion, Denis A. Engemann

Explaining the decision process of machine learning algorithms is nowadays crucial for both model's performance enhancement and human comprehension. This can be achieved by assessing the variable importance of single variables, even for high-capacity non-linear methods, e.g. Deep Neural Networks (DNNs). While only removal-based approaches, such as Permutation Importance (PI), can bring statistical validity, they return misleading results when variables are correlated. Conditional Permutation Importance (CPI) bypasses PI's limitations in such cases. However, in high-dimensional settings, where high correlations between the variables cancel their conditional importance, the use of CPI as well as other methods leads to unreliable results, besides prohibitive computation costs. Grouping variables statistically via clustering or some prior knowledge gains some power back and leads to better interpretations. In this work, we introduce BCPI (Block-Based Conditional Permutation Importance), a new generic framework for variable importance computation with statistical guarantees handling both single and group cases. Furthermore, as handling groups with high cardinality (such as a set of observations of a given modality) are both time-consuming and resource-intensive, we also introduce a new stacking approach extending the DNN architecture with sub-linear layers adapted to the group structure. We show that the ensuing approach extended with stacking controls the type-I error even with highly-correlated groups and shows top accuracy across benchmarks. Furthermore, we perform a real-world data analysis in a large-scale medical dataset where we aim to show the consistency between our results and the literature for a biomarker prediction.

Houssam Zenati, Judith Abécassis, Julie Josse et al.

Uncovering causal mediation effects is of significant value to practitioners seeking to isolate the direct treatment effect from the potential mediated effect. We propose a double machine learning (DML) algorithm for mediation analysis that supports continuous treatments. To estimate the target mediated response curve, our method uses a kernel-based doubly robust moment function for which we prove asymptotic Neyman orthogonality. This allows us to obtain asymptotic normality with nonparametric convergence rate while allowing for nonparametric or parametric estimation of the nuisance parameters. We then derive an optimal bandwidth strategy along with a procedure for estimating asymptotic confidence intervals. Finally, to illustrate the benefits of our method, we provide a numerical evaluation of our approach on a simulation along with an application to real-world medical data to analyze the effect of glycemic control on cognitive functions.

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.

Nicolas Salvy, Hugues Talbot, Bertrand Thirion

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.

Louis Jalouzot, Alexis Thual, Yair Lakretz et al.

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.

Sonia Mazelet, Rémi Flamary, Bertrand Thirion

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.

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.

Alexandre Pasquiou, Yair Lakretz, Bertrand Thirion et al.

Two fundamental questions in neurolinguistics concerns the brain regions that integrate information beyond the lexical level, and the size of their window of integration. To address these questions we introduce a new approach named masked-attention generation. It uses GPT-2 transformers to generate word embeddings that capture a fixed amount of contextual information. We then tested whether these embeddings could predict fMRI brain activity in humans listening to naturalistic text. The results showed that most of the cortex within the language network is sensitive to contextual information, and that the right hemisphere is more sensitive to longer contexts than the left. Masked-attention generation supports previous analyses of context-sensitivity in the brain, and complements them by quantifying the window size of context integration per voxel.

Hugo Richard, Pierre Ablin, Bertrand Thirion et al.

We consider shared response modeling, a multi-view learning problem where one wants to identify common components from multiple datasets or views. We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear transform of shared independent components contaminated by additive Gaussian noise. We show that this model is identifiable if the components are either non-Gaussian or have enough diversity in noise variances. We then show that in some cases multi-set canonical correlation analysis can recover the correct unmixing matrices, but that even a small amount of sampling noise makes Multiset CCA fail. To solve this problem, we propose to use joint diagonalization after Multiset CCA, leading to a new approach called ShICA-J. We show via simulations that ShICA-J leads to improved results while being very fast to fit. While ShICA-J is based on second-order statistics, we further propose to leverage non-Gaussianity of the components using a maximum-likelihood method, ShICA-ML, that is both more accurate and more costly. Further, ShICA comes with a principled method for shared components estimation. Finally, we provide empirical evidence on fMRI and MEG datasets that ShICA yields more accurate estimation of the components than alternatives.

Marc-Andre Schulz, Bertrand Thirion, Alexandre Gramfort et al.

High-quality data accumulation is now becoming ubiquitous in the health domain. There is increasing opportunity to exploit rich data from normal subjects to improve supervised estimators in specific diseases with notorious data scarcity. We demonstrate that low-dimensional embedding spaces can be derived from the UK Biobank population dataset and used to enhance data-scarce prediction of health indicators, lifestyle and demographic characteristics. Phenotype predictions facilitated by Variational Autoencoder manifolds typically scaled better with increasing unlabeled data than dimensionality reduction by PCA or Isomap. Performances gains from semisupervison approaches will probably become an important ingredient for various medical data science applications.

Badr Tajini, Hugo Richard, Bertrand Thirion

Advances in computational cognitive neuroimaging research are related to the availability of large amounts of labeled brain imaging data, but such data are scarce and expensive to generate. While powerful data generation mechanisms, such as Generative Adversarial Networks (GANs), have been designed in the last decade for computer vision, such improvements have not yet carried over to brain imaging. A likely reason is that GANs training is ill-suited to the noisy, high-dimensional and small-sample data available in functional neuroimaging. In this paper, we introduce Conditional Independent Components Analysis (Conditional ICA): a fast functional Magnetic Resonance Imaging (fMRI) data augmentation technique, that leverages abundant resting-state data to create images by sampling from an ICA decomposition. We then propose a mechanism to condition the generator on classes observed with few samples. We first show that the generative mechanism is successful at synthesizing data indistinguishable from observations, and that it yields gains in classification accuracy in brain decoding problems. In particular it outperforms GANs while being much easier to optimize and interpret. Lastly, Conditional ICA enhances classification accuracy in eight datasets without further parameters tuning.

Jérôme-Alexis Chevalier, Tuan-Binh Nguyen, Bertrand Thirion et al.

We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which neighboring pixels are usually very similar. Accurate point and confidence intervals estimation is not possible in this context with many more covariates than samples, furthermore with high correlation between covariates. This calls for a reformulation of the statistical inference problem, that takes into account the underlying spatial structure: if covariates are locally correlated, it is acceptable to detect them up to a given spatial uncertainty. We thus propose to rely on the $δ$-FWER, that is the probability of making a false discovery at a distance greater than $δ$ from any true positive. With this target measure in mind, we study the properties of ensembled clustered inference algorithms which combine three techniques: spatially constrained clustering, statistical inference, and ensembling to aggregate several clustered inference solutions. We show that ensembled clustered inference algorithms control the $δ$-FWER under standard assumptions for $δ$ equal to the largest cluster diameter. We complement the theoretical analysis with empirical results, demonstrating accurate $δ$-FWER control and decent power achieved by such inference algorithms.

Hugo Richard, Pierre Ablin, Aapo Hyvärinen et al.

We consider a multi-view learning problem known as group independent component analysis (group ICA), where the goal is to recover shared independent sources from many views. The statistical modeling of this problem requires to take noise into account. When the model includes additive noise on the observations, the likelihood is intractable. By contrast, we propose Adaptive multiView ICA (AVICA), a noisy ICA model where each view is a linear mixture of shared independent sources with additive noise on the sources. In this setting, the likelihood has a tractable expression, which enables either direct optimization of the log-likelihood using a quasi-Newton method, or generalized EM. Importantly, we consider that the noise levels are also parameters that are learned from the data. This enables sources estimation with a closed-form Minimum Mean Squared Error (MMSE) estimator which weights each view according to its relative noise level. On synthetic data, AVICA yields better sources estimates than other group ICA methods thanks to its explicit MMSE estimator. On real magnetoencephalograpy (MEG) data, we provide evidence that the decomposition is less sensitive to sampling noise and that the noise variance estimates are biologically plausible. Lastly, on functional magnetic resonance imaging (fMRI) data, AVICA exhibits best performance in transferring information across views.

Jérôme-Alexis Chevalier, Alexandre Gramfort, Joseph Salmon et al.

Detecting where and when brain regions activate in a cognitive task or in a given clinical condition is the promise of non-invasive techniques like magnetoencephalography (MEG) or electroencephalography (EEG). This problem, referred to as source localization, or source imaging, poses however a high-dimensional statistical inference challenge. While sparsity promoting regularizations have been proposed to address the regression problem, it remains unclear how to ensure statistical control of false detections. Moreover, M/EEG source imaging requires to work with spatio-temporal data and autocorrelated noise. To deal with this, we adapt the desparsified Lasso estimator -- an estimator tailored for high dimensional linear model that asymptotically follows a Gaussian distribution under sparsity and moderate feature correlation assumptions -- to temporal data corrupted with autocorrelated noise. We call it the desparsified multi-task Lasso (d-MTLasso). We combine d-MTLasso with spatially constrained clustering to reduce data dimension and with ensembling to mitigate the arbitrary choice of clustering; the resulting estimator is called ensemble of clustered desparsified multi-task Lasso (ecd-MTLasso). With respect to the current procedures, the two advantages of ecd-MTLasso are that i)it offers statistical guarantees and ii)it allows to trade spatial specificity for sensitivity, leading to a powerful adaptive method. Extensive simulations on realistic head geometries, as well as empirical results on various MEG datasets, demonstrate the high recovery performance of ecd-MTLasso and its primary practical benefit: offer a statistically principled way to threshold MEG/EEG source maps.

Kamalaker Dadi, Gaël Varoquaux, Antonia Machlouzarides-Shalit et al.

Population imaging markedly increased the size of functional-imaging datasets, shedding new light on the neural basis of inter-individual differences. Analyzing these large data entails new scalability challenges, computational and statistical. For this reason, brain images are typically summarized in a few signals, for instance reducing voxel-level measures with brain atlases or functional modes. A good choice of the corresponding brain networks is important, as most data analyses start from these reduced signals. We contribute finely-resolved atlases of functional modes, comprising from 64 to 1024 networks. These dictionaries of functional modes (DiFuMo) are trained on millions of fMRI functional brain volumes of total size 2.4TB, spanned over 27 studies and many research groups. We demonstrate the benefits of extracting reduced signals on our fine-grain atlases for many classic functional data analysis pipelines: stimuli decoding from 12,334 brain responses, standard GLM analysis of fMRI across sessions and individuals, extraction of resting-state functional-connectomes biomarkers for 2,500 individuals, data compression and meta-analysis over more than 15,000 statistical maps. In each of these analysis scenarii, we compare the performance of our functional atlases with that of other popular references, and to a simple voxel-level analysis. Results highlight the importance of using high-dimensional "soft" functional atlases, to represent and analyse brain activity while capturing its functional gradients. Analyses on high-dimensional modes achieve similar statistical performance as at the voxel level, but with much reduced computational cost and higher interpretability. In addition to making them available, we provide meaningful names for these modes, based on their anatomical location. It will facilitate reporting of results.

Tuan-Binh Nguyen, Jérôme-Alexis Chevalier, Bertrand Thirion et al.

We develop an extension of the Knockoff Inference procedure, introduced by Barber and Candes (2015). This new method, called Aggregation of Multiple Knockoffs (AKO), addresses the instability inherent to the random nature of Knockoff-based inference. Specifically, AKO improves both the stability and power compared with the original Knockoff algorithm while still maintaining guarantees for False Discovery Rate control. We provide a new inference procedure, prove its core properties, and demonstrate its benefits in a set of experiments on synthetic and real datasets.

Jérôme Dockès, Russell Poldrack, Romain Primet et al.

Reaching a global view of brain organization requires assembling evidence on widely different mental processes and mechanisms. The variety of human neuroscience concepts and terminology poses a fundamental challenge to relating brain imaging results across the scientific literature. Existing meta-analysis methods perform statistical tests on sets of publications associated with a particular concept. Thus, large-scale meta-analyses only tackle single terms that occur frequently. We propose a new paradigm, focusing on prediction rather than inference. Our multivariate model predicts the spatial distribution of neurological observations, given text describing an experiment, cognitive process, or disease. This approach handles text of arbitrary length and terms that are too rare for standard meta-analysis. We capture the relationships and neural correlates of 7 547 neuroscience terms across 13 459 neuroimaging publications. The resulting meta-analytic tool, neuroquery.org, can ground hypothesis generation and data-analysis priors on a comprehensive view of published findings on the brain.

Hicham Janati, Thomas Bazeille, Bertrand Thirion et al.

Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Estimating the location and magnitude of the current sources that generated these electromagnetic fields is a challenging ill-posed regression problem known as \emph{source imaging}. When considering a group study, a common approach consists in carrying out the regression tasks independently for each subject. An alternative is to jointly localize sources for all subjects taken together, while enforcing some similarity between them. By pooling all measurements in a single multi-task regression, one makes the problem better posed, offering the ability to identify more sources and with greater precision. The Minimum Wasserstein Estimates (MWE) promotes focal activations that do not perfectly overlap for all subjects, thanks to a regularizer based on Optimal Transport (OT) metrics. MWE promotes spatial proximity on the cortical mantel while coping with the varying noise levels across subjects. On realistic simulations, MWE decreases the localization error by up to 4 mm per source compared to individual solutions. Experiments on the Cam-CAN dataset show a considerable improvement in spatial specificity in population imaging. Our analysis of a multimodal dataset shows how multi-subject source localization closes the gap between MEG and fMRI for brain mapping.

Hugo Richard, Lucas Martin, Ana Luısa Pinho et al.

The shared response model provides a simple but effective framework to analyse fMRI data of subjects exposed to naturalistic stimuli. However when the number of subjects or runs is large, fitting the model requires a large amount of memory and computational power, which limits its use in practice. In this work, we introduce the FastSRM algorithm that relies on an intermediate atlas-based representation. It provides considerable speed-up in time and memory usage, hence it allows easy and fast large-scale analysis of naturalistic-stimulus fMRI data. Using four different datasets, we show that our method matches the performance of the original SRM algorithm while being about 5x faster and 20x to 40x more memory efficient. Based on this contribution, we use FastSRM to predict age from movie watching data on the CamCAN sample. Besides delivering accurate predictions (mean absolute error of 7.5 years), FastSRM extracts topographic patterns that are predictive of age, demonstrating that brain activity during free perception reflects age.

Hicham Janati, Thomas Bazeille, Bertrand Thirion et al.

Magnetoencephalography (MEG) and electroencephalogra-phy (EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Inferring the location of the current sources that generated these magnetic fields is an ill-posed inverse problem known as source imaging. When considering a group study, a baseline approach consists in carrying out the estimation of these sources independently for each subject. The ill-posedness of each problem is typically addressed using sparsity promoting regularizations. A straightforward way to define a common pattern for these sources is then to average them. A more advanced alternative relies on a joint localization of sources for all subjects taken together, by enforcing some similarity across all estimated sources. An important advantage of this approach is that it consists in a single estimation in which all measurements are pooled together, making the inverse problem better posed. Such a joint estimation poses however a few challenges, notably the selection of a valid regularizer that can quantify such spatial similarities. We propose in this work a new procedure that can do so while taking into account the geometrical structure of the cortex. We call this procedure Minimum Wasserstein Estimates (MWE). The benefits of this model are twofold. First, joint inference allows to pool together the data of different brain geometries, accumulating more spatial information. Second, MWE are defined through Optimal Transport (OT) metrics which provide a tool to model spatial proximity between cortical sources of different subjects, hence not enforcing identical source location in the group. These benefits allow MWE to be more accurate than standard MEG source localization techniques. To support these claims, we perform source localization on realistic MEG simulations based on forward operators derived from MRI scans. On a visual task dataset, we demonstrate how MWE infer neural patterns similar to functional Magnetic Resonance Imaging (fMRI) maps.

Andre Manoel, Florent Krzakala, Gaël Varoquaux et al.

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the variable to be determined, a notable example being total variation (TV). We describe the connection between message-passing algorithms -- typically used for approximate inference -- and proximal methods for optimization, and show that our scheme is, as VAMP, similar in nature to the Peaceman-Rachford splitting, with the important difference that stepsizes are set adaptively. Finally, we benchmark the performance of our VAMP-like iteration in problems where TV penalties are useful, namely classification in task fMRI and reconstruction in tomography, and show faster convergence than that of state-of-the-art approaches such as FISTA and ADMM in most settings.

Arthur Mensch, Julien Mairal, Bertrand Thirion et al.

Cognitive brain imaging is accumulating datasets about the neural substrate of many different mental processes. Yet, most studies are based on few subjects and have low statistical power. Analyzing data across studies could bring more statistical power; yet the current brain-imaging analytic framework cannot be used at scale as it requires casting all cognitive tasks in a unified theoretical framework. We introduce a new methodology to analyze brain responses across tasks without a joint model of the psychological processes. The method boosts statistical power in small studies with specific cognitive focus by analyzing them jointly with large studies that probe less focal mental processes. Our approach improves decoding performance for 80% of 35 widely-different functional-imaging studies. It finds commonalities across tasks in a data-driven way, via common brain representations that predict mental processes. These are brain networks tuned to psychological manipulations. They outline interpretable and plausible brain structures. The extracted networks have been made available; they can be readily reused in new neuro-imaging studies. We provide a multi-study decoding tool to adapt to new data.

Hugo Richard, Ana Pinho, Bertrand Thirion et al.

The comparison of observed brain activity with the statistics generated by artificial intelligence systems is useful to probe brain functional organization under ecological conditions. Here we study fMRI activity in ten subjects watching color natural movies and compute deep representations of these movies with an architecture that relies on optical flow and image content. The association of activity in visual areas with the different layers of the deep architecture displays complexity-related contrasts across visual areas and reveals a striking foveal/peripheral dichotomy.

Sergul Aydore, Bertrand Thirion, Gael Varoquaux

In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. It is challenging in this setting to train expressive, non-linear models without overfitting. These datasets call for intelligent regularization that exploits known structure, such as correlations between the features arising from the measurement device. However, existing structured regularizers need specially crafted solvers, which are difficult to apply to complex models. We propose a new regularizer specifically designed to leverage structure in the data in a way that can be applied efficiently to complex models. Our approach relies on feature grouping, using a fast clustering algorithm inside a stochastic gradient descent loop: given a family of feature groupings that capture feature covariations, we randomly select these groups at each iteration. We show that this approach amounts to enforcing a denoising regularizer on the solution. The method is easy to implement in many model architectures, such as fully connected neural networks, and has a linear computational cost. We apply this regularizer to a real-world fMRI dataset and the Olivetti Faces datasets. Experiments on both datasets demonstrate that the proposed approach produces models that generalize better than those trained with conventional regularizers, and also improves convergence speed.

Jérôme Dockès, Demian Wassermann, Russell Poldrack et al.

Despite the digital nature of magnetic resonance imaging, the resulting observations are most frequently reported and stored in text documents. There is a trove of information untapped in medical health records, case reports, and medical publications. In this paper, we propose to mine brain medical publications to learn the spatial distribution associated with anatomical terms. The problem is formulated in terms of minimization of a risk on distributions which leads to a least-deviation cost function. An efficient algorithm in the dual then learns the mapping from documents to brain structures. Empirical results using coordinates extracted from the brain-imaging literature show that i) models must adapt to semantic variation in the terms used to describe a given anatomical structure, ii) voxel-wise parameterization leads to higher likelihood of locations reported in unseen documents, iii) least-deviation cost outperforms least-square. As a proof of concept for our method, we use our model of spatial distributions to predict the distribution of specific neurological conditions from text-only reports.

Arthur Mensch, Julien Mairal, Danilo Bzdok et al.

Cognitive neuroscience is enjoying rapid increase in extensive public brain-imaging datasets. It opens the door to large-scale statistical models. Finding a unified perspective for all available data calls for scalable and automated solutions to an old challenge: how to aggregate heterogeneous information on brain function into a universal cognitive system that relates mental operations/cognitive processes/psychological tasks to brain networks? We cast this challenge in a machine-learning approach to predict conditions from statistical brain maps across different studies. For this, we leverage multi-task learning and multi-scale dimension reduction to learn low-dimensional representations of brain images that carry cognitive information and can be robustly associated with psychological stimuli. Our multi-dataset classification model achieves the best prediction performance on several large reference datasets, compared to models without cognitive-aware low-dimension representations, it brings a substantial performance boost to the analysis of small datasets, and can be introspected to identify universal template cognitive concepts.

Arthur Mensch, Julien Mairal, Bertrand Thirion et al.

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms.

Arthur Mensch, Julien Mairal, Gaël Varoquaux et al.

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low complexity per iteration andreasonable memory footprint. In contrast to previous online matrix factorization methods, our approach relies on low-dimensional statistics from past iterates to control the extra variance introduced by subsampling. We present a convergence analysis that guarantees us to reach a stationary point of the problem. Large speed-ups can be obtained compared to previous online algorithms that do not perform subsampling, thanks to the feature redundancy that often exists in high-dimensional settings.

Alexandre Abraham, Michael Milham, Adriana Di Martino et al.

Resting-state functional Magnetic Resonance Imaging (R-fMRI) holds the promise to reveal functional biomarkers of neuropsychiatric disorders. However, extracting such biomarkers is challenging for complex multi-faceted neuropatholo-gies, such as autism spectrum disorders. Large multi-site datasets increase sample sizes to compensate for this complexity, at the cost of uncontrolled heterogeneity. This heterogeneity raises new challenges, akin to those face in realistic diagnostic applications. Here, we demonstrate the feasibility of inter-site classification of neuropsychiatric status, with an application to the Autism Brain Imaging Data Exchange (ABIDE) database, a large (N=871) multi-site autism dataset. For this purpose, we investigate pipelines that extract the most predictive biomarkers from the data. These R-fMRI pipelines build participant-specific connectomes from functionally-defined brain areas. Connectomes are then compared across participants to learn patterns of connectivity that differentiate typical controls from individuals with autism. We predict this neuropsychiatric status for participants from the same acquisition sites or different, unseen, ones. Good choices of methods for the various steps of the pipeline lead to 67% prediction accuracy on the full ABIDE data, which is significantly better than previously reported results. We perform extensive validation on multiple subsets of the data defined by different inclusion criteria. These enables detailed analysis of the factors contributing to successful connectome-based prediction. First, prediction accuracy improves as we include more subjects, up to the maximum amount of subjects available. Second, the definition of functional brain areas is of paramount importance for biomarker discovery: brain areas extracted from large R-fMRI datasets outperform reference atlases in the classification tasks.

Andrés Hoyos-Idrobo, Gaël Varoquaux, Jonas Kahn et al.

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is that good clustering comes with large algorithmic costs. We address it by contributing a linear-time agglomerative clustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fast agglomerative schemes, it avoids the creation of giant clusters. We empirically validate that it approximates the data as well as traditional variance-minimizing clustering schemes that have a quadratic complexity. In addition, we analyze signal approximation with feature clustering and show that it can remove noise, improving subsequent analysis steps. As a consequence, data reduction by clustering features with ReNA yields very fast and accurate models, enabling to process large datasets on budget. Our theoretical analysis is backed by extensive experiments on publicly-available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme.

Gaël Varoquaux, Matthieu Kowalski, Bertrand Thirion

Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or graph-net, is computationally costly. Here we introduce sparsity in the local neighborhood of each voxel with social-sparsity, a structured shrinkage operator. We find that, on brain imaging classification problems, social-sparsity performs almost as well as total-variation models and better than graph-net, for a fraction of the computational cost. It also very clearly outlines predictive regions. We give details of the model and the algorithm.

Gaël Varoquaux, Pradeep Reddy Raamana, Denis Engemann et al.

Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within-and across-subject predictions, on multiple datasets --anatomical and functional MRI and MEG-- and simulations. Theory and experiments outline that the popular " leave-one-out " strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be more favorable to use sane defaults, in particular for non-sparse decoders.

Arthur Mensch, Julien Mairal, Bertrand Thirion et al.

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factoriza-tion method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.

Arthur Mensch, Gaël Varoquaux, Bertrand Thirion

We present a method for fast resting-state fMRI spatial decomposi-tions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest fMRI, we demonstrates that time-reduced dictionary learning produces result as reliable as non-reduced decompositions. We also show that this reduction significantly improves computational scalability.

Bertrand Thirion, Andrés Hoyos-Idrobo, Jonas Kahn et al.

The use of brain images as markers for diseases or behavioral differences is challenged by the small effects size and the ensuing lack of power, an issue that has incited researchers to rely more systematically on large cohorts. Coupled with resolution increases, this leads to very large datasets. A striking example in the case of brain imaging is that of the Human Connectome Project: 20 Terabytes of data and growing. The resulting data deluge poses severe challenges regarding the tractability of some processing steps (discriminant analysis, multivariate models) due to the memory demands posed by these data. In this work, we revisit dimension reduction approaches, such as random projections, with the aim of replacing costly function evaluations by cheaper ones while decreasing the memory requirements. Specifically, we investigate the use of alternate schemes, based on fast clustering, that are well suited for signals exhibiting a strong spatial structure, such as anatomical and functional brain images. Our contribution is twofold: i) we propose a linear-time clustering scheme that bypasses the percolation issues inherent in these algorithms and thus provides compressions nearly as good as traditional quadratic-complexity variance-minimizing clustering schemes, ii) we show that cluster-based compression can have the virtuous effect of removing high-frequency noise, actually improving subsequent estimations steps. As a consequence, the proposed approach yields very accurate models on several large-scale problems yet with impressive gains in computational efficiency, making it possible to analyze large datasets.

Alexandre Abraham, Elvis Dohmatob, Bertrand Thirion et al.

Functional Magnetic Resonance Images acquired during resting-state provide information about the functional organization of the brain through measuring correlations between brain areas. Independent components analysis is the reference approach to estimate spatial components from weakly structured data such as brain signal time courses; each of these components may be referred to as a brain network and the whole set of components can be conceptualized as a brain functional atlas. Recently, new methods using a sparsity prior have emerged to deal with low signal-to-noise ratio data. However, even when using sophisticated priors, the results may not be very sparse and most often do not separate the spatial components into brain regions. This work presents post-processing techniques that automatically sparsify brain maps and separate regions properly using geometric operations, and compares these techniques according to faithfulness to data and stability metrics. In particular, among threshold-based approaches, hysteresis thresholding and random walker segmentation, the latter improves significantly the stability of both dense and sparse models.

Alexandre Abraham, Fabian Pedregosa, Michael Eickenberg et al.

Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.

Fabian Pedregosa, Michael Eickenberg, Philippe Ciuciu et al.

Despite the common usage of a canonical, data-independent, hemodynamic response function (HRF), it is known that the shape of the HRF varies across brain regions and subjects. This suggests that a data-driven estimation of this function could lead to more statistical power when modeling BOLD fMRI data. However, unconstrained estimation of the HRF can yield highly unstable results when the number of free parameters is large. We develop a method for the joint estimation of activation and HRF using a rank constraint causing the estimated HRF to be equal across events/conditions, yet permitting it to be different across voxels. Model estimation leads to an optimization problem that we propose to solve with an efficient quasi-Newton method exploiting fast gradient computations. This model, called GLM with Rank-1 constraint (R1-GLM), can be extended to the setting of GLM with separate designs which has been shown to improve decoding accuracy in brain activity decoding experiments. We compare 10 different HRF modeling methods in terms of encoding and decoding score in two different datasets. Our results show that the R1-GLM model significantly outperforms competing methods in both encoding and decoding settings, positioning it as an attractive method both from the points of view of accuracy and computational efficiency.