Deep Recurrent Encoder: A scalable end-to-end network to model brain signals

Understanding how the brain responds to sensory inputs is challenging: brain recordings are partial, noisy, and high dimensional; they vary across sessions and subjects and they capture highly nonlinear dynamics. These challenges have led the community to develop a variety of preprocessing and analytical (almost exclusively linear) methods, each designed to tackle one of these issues. Instead, we propose to address these challenges through a specific end-to-end deep learning architecture, trained to predict the brain responses of multiple subjects at once. We successfully test this approach on a large cohort of magnetoencephalography (MEG) recordings acquired during a one-hour reading task. Our Deep Recurrent Encoding (DRE) architecture reliably predicts MEG responses to words with a three-fold improvement over classic linear methods. To overcome the notorious issue of interpretability of deep learning, we describe a simple variable importance analysis. When applied to DRE, this method recovers the expected evoked responses to word length and word frequency. The quantitative improvement of the present deep learning approach paves the way to better understand the nonlinear dynamics of brain activity from large datasets.

Decomposing lexical and compositional syntax and semantics with deep language models

The activations of language transformers like GPT2 have been shown to linearly map onto brain activity during speech comprehension. However, the nature of these activations remains largely unknown and presumably conflate distinct linguistic classes. Here, we propose a taxonomy to factorize the high-dimensional activations of language models into four combinatorial classes: lexical, compositional, syntactic, and semantic representations. We then introduce a statistical method to decompose, through the lens of GPT2's activations, the brain activity of 345 subjects recorded with functional magnetic resonance imaging (fMRI) during the listening of ~4.6 hours of narrated text. The results highlight two findings. First, compositional representations recruit a more widespread cortical network than lexical ones, and encompass the bilateral temporal, parietal and prefrontal cortices. Second, contrary to previous claims, syntax and semantics are not associated with separated modules, but, instead, appear to share a common and distributed neural substrate. Overall, this study introduces a general framework to isolate the distributed representations of linguistic constructs generated in naturalistic settings.

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.

Leveraging Global Parameters for Flow-based Neural Posterior Estimation

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference(SBI) based on normalizing flows to Bayesian hierarchical models. We validate quantitatively our proposal on a motivating example amenable to analytical solutions, and then apply it to invert a well known non-linear model from computational neuroscience.

Learning summary features of time series for likelihood free inference

There has been an increasing interest from the scientific community in using likelihood-free inference (LFI) to determine which parameters of a given simulator model could best describe a set of experimental data. Despite exciting recent results and a wide range of possible applications, an important bottleneck of LFI when applied to time series data is the necessity of defining a set of summary features, often hand-tailored based on domain knowledge. In this work, we present a data-driven strategy for automatically learning summary features from univariate time series and apply it to signals generated from autoregressive-moving-average (ARMA) models and the Van der Pol Oscillator. Our results indicate that learning summary features from data can compete and even outperform LFI methods based on hand-crafted values such as autocorrelation coefficients even in the linear case.

Model identification and local linear convergence of coordinate descent

For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough. Results concerning coordinate descent are scarcer and model identification has only been shown for specific estimators, the support-vector machine for instance. In this work, we show that cyclic coordinate descent achieves model identification in finite time for a wide class of functions. In addition, we prove explicit local linear convergence rates for coordinate descent. Extensive experiments on various estimators and on real datasets demonstrate that these rates match well empirical results.

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.

Uncovering the structure of clinical EEG signals with self-supervised learning

Objective. Supervised learning paradigms are often limited by the amount of labeled data that is available. This phenomenon is particularly problematic in clinically-relevant data, such as electroencephalography (EEG), where labeling can be costly in terms of specialized expertise and human processing time. Consequently, deep learning architectures designed to learn on EEG data have yielded relatively shallow models and performances at best similar to those of traditional feature-based approaches. However, in most situations, unlabeled data is available in abundance. By extracting information from this unlabeled data, it might be possible to reach competitive performance with deep neural networks despite limited access to labels. Approach. We investigated self-supervised learning (SSL), a promising technique for discovering structure in unlabeled data, to learn representations of EEG signals. Specifically, we explored two tasks based on temporal context prediction as well as contrastive predictive coding on two clinically-relevant problems: EEG-based sleep staging and pathology detection. We conducted experiments on two large public datasets with thousands of recordings and performed baseline comparisons with purely supervised and hand-engineered approaches. Main results. Linear classifiers trained on SSL-learned features consistently outperformed purely supervised deep neural networks in low-labeled data regimes while reaching competitive performance when all labels were available. Additionally, the embeddings learned with each method revealed clear latent structures related to physiological and clinical phenomena, such as age effects. Significance. We demonstrate the benefit of self-supervised learning approaches on EEG data. Our results suggest that SSL may pave the way to a wider use of deep learning models on EEG data.

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.