Spatially relaxed inference on high-dimensional linear models

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 $\delta$-FWER, that is the probability of making a false discovery at a distance greater than $\delta$ 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 $\delta$-FWER under standard assumptions for $\delta$ equal to the largest cluster diameter. We complement the theoretical analysis with empirical results, demonstrating accurate $\delta$-FWER control and decent power achieved by such inference algorithms.

Adaptive Multi-View ICA: Estimation of noise levels for optimal inference

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.

Statistical control for spatio-temporal MEG/EEG source imaging with desparsified multi-task Lasso

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.

Modeling Shared Responses in Neuroimaging Studies through MultiView ICA

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.

Fine-grain atlases of functional modes for fMRI analysis

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.

Aggregation of Multiple Knockoffs

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.

NeuroQuery: comprehensive meta-analysis of human brain mapping

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.

Multi-subject MEG/EEG source imaging with sparse multi-task regression

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.