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

Split Conformal Prediction (SCP) provides a computationally efficient way to construct confidence intervals in prediction problems. Notably, most of the theory built around SCP is focused on the single test point setting. In real-life, inference sets consist of multiple points, which raises the question of coverage guarantees for many points simultaneously. While on average, the False Coverage Proportion (FCP) remains controlled, it can fluctuate strongly around its mean, the False Coverage Rate (FCR). We observe that when a dataset is split multiple times, classical SCP may not control the FCP in a majority of the splits. We propose CoJER, a novel method that achieves sharp FCP control in probability for conformal prediction, based on a recent characterization of the distribution of conformal $p$-values in a transductive setting. This procedure incorporates an aggregation scheme which provides robustness with respect to modeling choices. We show through extensive real data experiments that CoJER provides FCP control while standard SCP does not. Furthermore, CoJER yields shorter intervals than the state-of-the-art method for FCP control and only slightly larger intervals than standard SCP.

Causal machine learning (ML) promises to provide powerful tools for estimating individual treatment effects. While causal methods have placed some emphasis on heterogeneity in treatment response, it is of paramount importance to clarify the nature of this heterogeneity, by highlighting which variables drive it. 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) method and provides a reliable measure of variable importance. This property increases statistical power, which is crucial for causal inference applications with finite sample sizes. We empirically demonstrate the benefits of PermuCATE in simulated and real datasets, including complex settings with high-dimensional, correlated variables.

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

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.

Number sense, the ability to rapidly estimate object quantities in a visual scene without precise counting, is a crucial cognitive capacity found in humans and many other animals. Recent studies have identified artificial neurons tuned to numbers of items in biologically inspired vision models, even before training, and proposed these artificial neural networks as candidate models for the emergence of number sense in the brain. But real-world numerosity perception requires abstraction from the properties of individual objects and their contexts, unlike the simplified dot patterns used in previous studies. Using novel synthetically generated photorealistic stimuli, we show that deep convolutional neural networks optimized for object recognition encode information on approximate numerosity across diverse objects and scene types, which could be linearly read out from distributed activity patterns of later convolutional layers of different network architectures tested. In contrast, untrained networks with random weights failed to represent numerosity with abstractness to other visual properties and instead captured mainly low-level visual features. Our findings emphasize the importance of using complex, naturalistic stimuli to investigate mechanisms of number sense in both biological and artificial systems, and they suggest that the capacity of untrained networks to account for early-life numerical abilities should be reassessed. They further point to a possible, so far underappreciated, contribution of the brain's ventral visual pathway to representing numerosity with abstractness to other high-level visual properties.

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.

Reducing contributions from non-neuronal sources is a crucial step in functional magnetic resonance imaging (fMRI) connectivity analyses. Many viable strategies for denoising fMRI are used in the literature, and practitioners rely on denoising benchmarks for guidance in the selection of an appropriate choice for their study. However, fMRI denoising software is an ever-evolving field, and the benchmarks can quickly become obsolete as the techniques or implementations change. In this work, we present a denoising benchmark featuring a range of denoising strategies, datasets and evaluation metrics for connectivity analyses, based on the popular fMRIprep software. The benchmark prototypes an implementation of a reproducible framework, where the provided Jupyter Book enables readers to reproduce or modify the figures on the Neurolibre reproducible preprint server (https://neurolibre.org/). We demonstrate how such a reproducible benchmark can be used for continuous evaluation of research software, by comparing two versions of the fMRIprep. Most of the benchmark results were consistent with prior literature. Scrubbing, a technique which excludes time points with excessive motion, combined with global signal regression, is generally effective at noise removal. Scrubbing was generally effective, but is incompatible with statistical analyses requiring the continuous sampling of brain signal, for which a simpler strategy, using motion parameters, average activity in select brain compartments, and global signal regression, is preferred. Importantly, we found that certain denoising strategies behave inconsistently across datasets and/or versions of fMRIPrep, or had a different behavior than in previously published benchmarks. This work will hopefully provide useful guidelines for the fMRIprep users community, and highlight the importance of continuous evaluation of research methods.

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

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.

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 time-courses 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 transformer-based 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 model-training choices, and suggest good practices for future studies aiming at explaining the human language system using neural language models.

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.

Individual brains vary in both anatomy and functional organization, even within a given species. Inter-individual variability is a major impediment when trying to draw generalizable conclusions from neuroimaging data collected on groups of subjects. Current co-registration procedures rely on limited data, and thus lead to very coarse inter-subject alignments. In this work, we present a novel method for inter-subject alignment based on Optimal Transport, denoted as Fused Unbalanced Gromov Wasserstein (FUGW). The method aligns two cortical surfaces based on the similarity of their functional signatures in response to a variety of stimuli, while penalizing large deformations of individual topographic organization.We demonstrate that FUGW is suited for whole-brain landmark-free alignment. The unbalanced feature allows to deal with the fact that functional areas vary in size across subjects. Results show that FUGW alignment significantly increases between-subject correlation of activity during new independent fMRI tasks and runs, and leads to more precise maps of fMRI results at the group level.

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 eachview 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 componentsthan alternatives.

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.

We develop an extension of the knockoff inference procedure, introduced by Barber & 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.

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 in this setting. Moreover, MEG/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.

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-sessions 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.

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. 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. Experiments on two real-world datasets demonstrate that the proposed approach produces models that generalize better than those trained with conventional regularizers, and also improves convergence speed, and has a linear computational cost.

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 then 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.

To map the neural substrate of mental function, cognitive neuroimaging relies on controlled psychological manipulations that engage brain systems associated with specific cognitive processes. In order to build comprehensive atlases of cognitive function in the brain, it must assemble maps for many different cognitive processes, which often evoke overlapping patterns of activation. Such data aggregation faces contrasting goals: on the one hand finding correspondences across vastly different cognitive experiments, while on the other hand precisely describing the function of any given brain region. Here we introduce a new analysis framework that tackles these difficulties and thereby enables the generation of brain atlases for cognitive function. The approach leverages ontologies of cognitive concepts and multi-label brain decoding to map the neural substrate of these concepts. We demonstrate the approach by building an atlas of functional brain organization based on 30 diverse functional neuroimaging studies, totaling 196 different experimental conditions. Unlike conventional brain mapping, this functional atlas supports robust reverse inference: predicting the mental processes from brain activity in the regions delineated by the atlas. To establish that this reverse inference is indeed governed by the corresponding concepts, and not idiosyncrasies of experimental designs, we show that it can accurately decode the cognitive concepts recruited in new tasks. These results demonstrate that aggregating independent task-fMRI studies can provide a more precise global atlas of selective associations between brain and cognition.

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.

We study the convergence of the ADMM (Alternating Direction Method of Multipliers) algorithm on a broad range of penalized regression problems including the Lasso, Group-Lasso and Graph-Lasso,(isotropic) TV-L1, Sparse Variation, and others. First, we establish a fixed-point iterationvia a nonlinear operator-which is equivalent to the ADMM iterates. We then show that this nonlinear operator is Fréchet-differentiable almost everywhere and that around each fixed point, Q-linear convergence is guaranteed, provided the spectral radius of the Jacobian of the operator at the fixed point is less than 1 (a classical result on stability). Moreover, this spectral radius is then a rate of convergence for the ADMM algorithm. Also, we show that the support of the split variable can be identified after finitely many iterations. In the anisotropic cases, we show that for sufficiently large values of the tuning parameter, we recover the optimal rates in terms of Friedrichs angles, that have appeared recently in the literature. Empirical results on various problems are also presented and discussed.

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 factorization method that scales gracefully to terabyte-scale datasets. Those 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.

We propose a multivariate online dictionary-learning method for obtaining decompositions of brain images with structured and sparse components (aka atoms). Sparsity is to be understood in the usual sense: the dictionary atoms are constrained to contain mostly zeros. This is imposed via an $\ell_1$-norm constraint. By "structured", we mean that the atoms are piece-wise smooth and compact, thus making up blobs, as opposed to scattered patterns of activation. We propose to use a Sobolev (Laplacian) penalty to impose this type of structure. Combining the two penalties, we obtain decompositions that properly delineate brain structures from functional images. This non-trivially extends the online dictionary-learning work of Mairal et al. (2010), at the price of only a factor of 2 or 3 on the overall running time. Just like the Mairal et al. (2010) reference method, the online nature of our proposed algorithm allows it to scale to arbitrarily sized datasets. Experiments on brain data show that our proposed method extracts structured and denoised dictionaries that are more intepretable and better capture inter-subject variability in small medium, and large-scale regimes alike, compared to state-of-the-art models.

Systems neuroscience has identified a set of canonical large-scale networks in humans. These have predominantly been characterized by resting-state analyses of the task-unconstrained, mind-wandering brain. Their explicit relationship to defined task performance is largely unknown and remains challenging. The present work contributes a multivariate statistical learning approach that can extract the major brain networks and quantify their configuration during various psychological tasks. The method is validated in two extensive datasets (n = 500 and n = 81) by model-based generation of synthetic activity maps from recombination of shared network topographies. To study a use case, we formally revisited the poorly understood difference between neural activity underlying idling versus goal-directed behavior. We demonstrate that task-specific neural activity patterns can be explained by plausible combinations of resting-state networks. The possibility of decomposing a mental task into the relative contributions of major brain networks, the "network co-occurrence architecture" of a given task, opens an alternative access to the neural substrates of human cognition.

There is a recent interest in using functional magnetic resonance imaging (fMRI) for decoding more naturalistic, cognitive states, in which subjects perform various tasks in a continuous, self-directed manner. In this setting, the set of brain volumes over the entire task duration is usually taken as a single sample with connectivity estimates, such as Pearson's correlation, employed as features. Since covariance matrices live on the positive semidefinite cone, their elements are inherently inter-related. The assumption of uncorrelated features implicit in most classifier learning algorithms is thus violated. Coupled with the usual small sample sizes, the generalizability of the learned classifiers is limited, and the identification of significant brain connections from the classifier weights is nontrivial. In this paper, we present a Riemannian approach for connectivity-based brain decoding. The core idea is to project the covariance estimates onto a common tangent space to reduce the statistical dependencies between their elements. For this, we propose a matrix whitening transport, and compare it against parallel transport implemented via the Schild's ladder algorithm. To validate our classification approach, we apply it to fMRI data acquired from twenty four subjects during four continuous, self-driven tasks. We show that our approach provides significantly higher classification accuracy than directly using Pearson's correlation and its regularized variants as features. To facilitate result interpretation, we further propose a non-parametric scheme that combines bootstrapping and permutation testing for identifying significantly discriminative brain connections from the classifier weights. Using this scheme, a number of neuro-anatomically meaningful connections are detected, whereas no significant connections are found with pure permutation testing.

Imaging neuroscience links human behavior to aspects of brain biology in ever-increasing datasets. Existing neuroimaging methods typically perform either discovery of unknown neural structure or testing of neural structure associated with mental tasks. However, testing hypotheses on the neural correlates underlying larger sets of mental tasks necessitates adequate representations for the observations. We therefore propose to blend representation modelling and task classification into a unified statistical learning problem. A multinomial logistic regression is introduced that is constrained by factored coefficients and coupled with an autoencoder. We show that this approach yields more accurate and interpretable neural models of psychological tasks in a reference dataset, as well as better generalization to other datasets.

Imaging neuroscience links brain activation maps to behavior and cognition via correlational studies. Due to the nature of the individual experiments, based on eliciting neural response from a small number of stimuli, this link is incomplete, and unidirectional from the causal point of view. To come to conclusions on the function implied by the activation of brain regions, it is necessary to combine a wide exploration of the various brain functions and some inversion of the statistical inference. Here we introduce a methodology for accumulating knowledge towards a bidirectional link between observed brain activity and the corresponding function. We rely on a large corpus of imaging studies and a predictive engine. Technically, the challenges are to find commonality between the studies without denaturing the richness of the corpus. The key elements that we contribute are labeling the tasks performed with a cognitive ontology, and modeling the long tail of rare paradigms in the corpus. To our knowledge, our approach is the first demonstration of predicting the cognitive content of completely new brain images. To that end, we propose a method that predicts the experimental paradigms across different studies.

Functional connections between brain regions are supported by structural connectivity. Both functional and structural connectivity are estimated from in vivo magnetic resonance imaging and offer complementary information on brain organization and function. However, imaging only provides noisy measures, and we lack a good neuroscientific understanding of the links between structure and function. Therefore, inter-subject joint modeling of structural and functional connectivity, the key to multimodal biomarkers, is an open challenge. We present a probabilistic framework to learn across subjects a mapping from structural to functional brain connectivity. Expanding on our previous work [1], our approach is based on a predictive framework with multiple sparse linear regression. We rely on the randomized LASSO to identify relevant anatomo-functional links with some confidence interval. In addition, we describe resting-state functional magnetic resonance imaging in the setting of Gaussian graphical models, on the one hand imposing conditional independences from structural connectivity and on the other hand parameterizing the problem in terms of multivariate autoregressive models. We introduce an intrinsic measure of prediction error for functional connectivity that is independent of the parameterization chosen and provides the means for robust model selection. We demonstrate our methodology with regions within the default mode and the salience network as well as, atlas-based cortical parcellation.

Reverse inference, or brain reading, is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Reverse inference takes into account the multivariate information between voxels and is currently the only way to assess how precisely some cognitive information is encoded by the activity of neural populations within the whole brain. However, it relies on a prediction function that is plagued by the curse of dimensionality, since there are far more features than samples, i.e., more voxels than fMRI volumes. To address this problem, different methods have been proposed, including univariate feature selection, feature agglomeration, and regularization techniques. In this paper, we consider a sparse hierarchical structured regularization. Specifically, the penalization we use is constructed from a tree that is obtained by spatially constrained agglomerative clustering. This approach encodes the spatial structure of the data at different scales into the regularization, which makes the overall prediction procedure more robust to intersubject variability. The regularization used induces the selection of spatially coherent predictive brain regions simultaneously at different scales. We test our algorithm on real data acquired to study the mental representation of objects, and we show that the proposed algorithm not only delineates meaningful brain regions but also yields better prediction accuracy than reference methods.

While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional magnetic resonance imaging (fMRI) data, that provide an indirect measure of task-related or spontaneous neuronal activity, are classically analyzed in a mass-univariate procedure yielding statistical parametric maps. This analysis framework disregards some important principles of brain organization: population coding, distributed and overlapping representations. Multivariate pattern analysis, i.e., the prediction of behavioral variables from brain activation patterns better captures this structure. To cope with the high dimensionality of the data, the learning method has to be regularized. However, the spatial structure of the image is not taken into account in standard regularization methods, so that the extracted features are often hard to interpret. More informative and interpretable results can be obtained with the l(1) norm of the image gradient, also known as its total variation (TV), as regularization. We apply for the first time this method to fMRI data, and show that TV regularization is well suited to the purpose of brain mapping while being a powerful tool for brain decoding. Moreover, this article presents the first use of TV regularization for classification.

Spontaneous brain activity, as observed in functional neuroimaging, has been shown to display reproducible structure that expresses brain architecture and carries markers of brain pathologies. An important view of modern neuroscience is that such large-scale structure of coherent activity reflects modularity properties of brain connectivity graphs. However, to date, there has been no demonstration that the limited and noisy data available in spontaneous activity observations could be used to learn full-brain probabilistic models that generalize to new data. Learning such models entails two main challenges: i) modeling full brain connectivity is a difficult estimation problem that faces the curse of dimensionality and ii) variability between subjects, coupled with the variability of functional signals between experimental runs, makes the use of multiple datasets challenging. We describe subject-level brain functional connectivity structure as a multivariate Gaussian process and introduce a new strategy to estimate it from group data, by imposing a common structure on the graphical model in the population. We show that individual models learned from functional Magnetic Resonance Imaging (fMRI) data using this population prior generalize better to unseen data than models based on alternative regularization schemes. To our knowledge, this is the first report of a cross-validated model of spontaneous brain activity. Finally, we use the estimated graphical model to explore the large-scale characteristics of functional architecture and show for the first time that known cognitive networks appear as the integrated communities of functional connectivity graph.

Schizophrenia is a complex psychiatric disorder that has eluded a characterization in terms of local abnormalities of brain activity, and is hypothesized to affect the collective, ``emergent working of the brain. We propose a novel data-driven approach to capture emergent features using functional brain networks [Eguiluzet al] extracted from fMRI data, and demonstrate its advantage over traditional region-of-interest (ROI) and local, task-specific linear activation analyzes. Our results suggest that schizophrenia is indeed associated with disruption of global, emergent brain properties related to its functioning as a network, which cannot be explained by alteration of local activation patterns. Moreover, further exploitation of interactions by sparse Markov Random Field classifiers shows clear gain over linear methods, such as Gaussian Naive Bayes and SVM, allowing to reach 86% accuracy (over 50% baseline - random guess), which is quite remarkable given that it is based on a single fMRI experiment using a simple auditory task.

Group studies of functional magnetic resonance imaging datasets are usually based on the computation of the mean signal across subjects at each voxel (random effects analyses), assuming that all subjects have been set in the same anatomical space (normalization). Although this approach allows for a correct specificity (rate of false detections), it is not very efficient for three reasons: i) its underlying hypotheses, perfect coregistration of the individual datasets and normality of the measured signal at the group level are frequently violated; ii) the group size is small in general, so that asymptotic approximations on the parameters distributions do not hold; iii) the large size of the images requires some conservative strategies to control the false detection rate, at the risk of increasing the number of false negatives. Given that it is still very challenging to build generative or parametric models of intersubject variability, we rely on a rule based, bottom-up approach: we present a set of procedures that detect structures of interest from each subject's data, then search for correspondences across subjects and outline the most reproducible activation regions in the group studied. This framework enables a strict control on the number of false detections. It is shown here that this analysis demonstrates increased validity and improves both the sensitivity and reliability of group analyses compared with standard methods. Moreover, it directly provides information on the spatial position correspondence or variability of the activated regions across subjects, which is difficult to obtain in standard voxel-based analyses.

The acquisition of brain images in fMRI yields rich topographic information about the functional structure of the brain. However, these descriptions are limited by strong inter-subject variability. A recent approach to represent the gross functional architecture across the population as seen in fMRI consists in automatically defining accross-subjects brain parcels. This technique yields large-scale inter-subject correspondences while allowing some spatial relaxation in the alignment of the brains. We address here the open question of an optimal parameterization (number of parcels) of brain parcellations using information theoretic criteria and cross-validation. Moreover, a finer analysis of variance components enables us to better characterize intra- and inter-subject variability sources in parcellation models.

Image segmentation has traditionally been thought of us a low/mid-level vision process incorporating no high level constraints. However, in complex and uncontrolled environments, such bottom-up strategies have drawbacks that lead to large misclassification rates. Remedies to this situation include taking into account (1) contextual and application constraints, (2) user input and feedback to incrementally improve the performance of the system. We attempt to incorporate these in the context of pipeline segmentation in industrial images. This problem is of practical importance for the 3D reconstruction of factory environments. However it poses several fundamental challenges mainly due to shading. Highlights and textural variations, etc. Our system performs pipe segmentation by fusing methods from physics-based vision, edge and texture analysis, probabilistic learning and the use of the graph-cut formalism.