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Machine learning applications on signals such as computer vision or biomedical data often face significant challenges due to the variability that exists across hardware devices or session recordings. This variability poses a Domain Adaptation (DA) problem, as training and testing data distributions often differ. In this work, we propose Spatio-Temporal Monge Alignment (STMA) to mitigate these variabilities. This Optimal Transport (OT) based method adapts the cross-power spectrum density (cross-PSD) of multivariate signals by mapping them to the Wasserstein barycenter of source domains (multi-source DA). Predictions for new domains can be done with a filtering without the need for retraining a model with source data (test-time DA). We also study and discuss two special cases of the method, Temporal Monge Alignment (TMA) and Spatial Monge Alignment (SMA). Non-asymptotic concentration bounds are derived for the mappings estimation, which reveals a bias-plus-variance error structure with a variance decay rate of $\mathcal{O}(n_\ell^{-1/2})$ with $n_\ell$ the signal length. This theoretical guarantee demonstrates the efficiency of the proposed computational schema. Numerical experiments on multivariate biosignals and image data show that STMA leads to significant and consistent performance gains between datasets acquired with very different settings. Notably, STMA is a pre-processing step complementary to state-of-the-art deep learning methods.

Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target domain with some data distribution shift. While many methods have been proposed in the literature, fair and realistic evaluation remains an open question, particularly due to methodological difficulties in selecting hyperparameters in the unsupervised setting. With SKADA-Bench, we propose a framework to evaluate DA methods and present a fair evaluation of existing shallow algorithms, including reweighting, mapping, and subspace alignment. Realistic hyperparameter selection is performed with nested cross-validation and various unsupervised model selection scores, on both simulated datasets with controlled shifts and real-world datasets across diverse modalities, such as images, text, biomedical, and tabular data with specific feature extraction. Our benchmark highlights the importance of realistic validation and provides practical guidance for real-life applications, with key insights into the choice and impact of model selection approaches. SKADA-Bench is open-source, reproducible, and can be easily extended with novel DA methods, datasets, and model selection criteria without requiring re-evaluating competitors. SKADA-Bench is available on GitHub at https://github.com/scikit-adaptation/skada-bench.

Electroencephalography (EEG) data is often collected from diverse contexts involving different populations and EEG devices. This variability can induce distribution shifts in the data $X$ and in the biomedical variables of interest $y$, thus limiting the application of supervised machine learning (ML) algorithms. While domain adaptation (DA) methods have been developed to mitigate the impact of these shifts, such methods struggle when distribution shifts occur simultaneously in $X$ and $y$. As state-of-the-art ML models for EEG represent the data by spatial covariance matrices, which lie on the Riemannian manifold of Symmetric Positive Definite (SPD) matrices, it is appealing to study DA techniques operating on the SPD manifold. This paper proposes a novel method termed Geodesic Optimization for Predictive Shift Adaptation (GOPSA) to address test-time multi-source DA for situations in which source domains have distinct $y$ distributions. GOPSA exploits the geodesic structure of the Riemannian manifold to jointly learn a domain-specific re-centering operator representing site-specific intercepts and the regression model. We performed empirical benchmarks on the cross-site generalization of age-prediction models with resting-state EEG data from a large multi-national dataset (HarMNqEEG), which included $14$ recording sites and more than $1500$ human participants. Compared to state-of-the-art methods, our results showed that GOPSA achieved significantly higher performance on three regression metrics ($R^2$, MAE, and Spearman's $\rho$) for several source-target site combinations, highlighting its effectiveness in tackling multi-source DA with predictive shifts in EEG data analysis. Our method has the potential to combine the advantages of mixed-effects modeling with machine learning for biomedical applications of EEG, such as multicenter clinical trials.

Determining which parameters of a non-linear model best describe a set of experimental data is a fundamental problem in science and it has gained much traction lately with the rise of complex large-scale simulators. The likelihood of such models is typically intractable, which is why classical MCMC methods can not be used. Simulation-based inference (SBI) stands out in this context by only requiring a dataset of simulations to train deep generative models capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. The proposed method is built upon recent developments from the flourishing score-based diffusion literature and allows to estimate the tall data posterior distribution, while simply using information from a score network trained for a single context observation. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost., Comment: 49 pages, 24 figures, 3 tables, 2 algorithms, 12 appendices, in proceedings

Most scientists need software to perform their research (Barker et al., 2020; Carver et al., 2022; Hettrick, 2014; Hettrick et al., 2014; Switters and Osimo, 2019), and neuroscientists are no exception. Whether we work with reaction times, electrophysiological signals, or magnetic resonance imaging data, we rely on software to acquire, analyze, and statistically evaluate the raw data we obtain - or to generate such data if we work with simulations. In recent years there has been a shift toward relying on free, open-source scientific software (FOSSS) for neuroscience data analysis (Poldrack et al., 2019), in line with the broader open science movement in academia (McKiernan et al., 2016) and wider industry trends (Eghbal, 2016). Importantly, FOSSS is typically developed by working scientists (not professional software developers) which sets up a precarious situation given the nature of the typical academic workplace (wherein academics, especially in their early careers, are on short and fixed term contracts). In this paper, we will argue that the existing ecosystem of neuroscientific open source software is brittle, and discuss why and how the neuroscience community needs to come together to ensure a healthy growth of our software landscape to the benefit of all.

Combining electroencephalogram (EEG) datasets for supervised machine learning (ML) is challenging due to session, subject, and device variability. ML algorithms typically require identical features at train and test time, complicating analysis due to varying sensor numbers and positions across datasets. Simple channel selection discards valuable data, leading to poorer performance, especially with datasets sharing few channels. To address this, we propose an unsupervised approach leveraging EEG signal physics. We map EEG channels to fixed positions using field interpolation, facilitating source-free domain adaptation. Leveraging Riemannian geometry classification pipelines and transfer learning steps, our method demonstrates robust performance in brain-computer interface (BCI) tasks and potential biomarker applications. Comparative analysis against a statistical-based approach known as Dimensionality Transcending, a signal-based imputation called ComImp, source-dependent methods, as well as common channel selection and spherical spline interpolation, was conducted with leave-one-dataset-out validation on six public BCI datasets for a right-hand/left-hand classification task. Numerical experiments show that in the presence of few shared channels in train and test, the field interpolation consistently outperforms other methods, demonstrating enhanced classification performance across all datasets. When more channels are shared, field interpolation was found to be competitive with other methods and faster to compute than source-dependent methods.

This paper introduces a novel domain adaptation technique for time series data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the challenge of limited labeled signals in the target dataset. Leveraging a domain-dependent mixing model and the optimal transport domain adaptation assumption, we exploit abundant unlabeled data in the target domain to ensure effective prediction by establishing pairwise correspondence with equivalent signal variances between domains. Theoretical foundations are laid for identifying crucial Stiefel matrices, essential for recovering underlying signal variances from a Riemannian representation of observed signal covariances. We propose an integrated cost function that simultaneously learns these matrices, pairwise domain relationships, and a predictor, classifier, or regressor, depending on the task. Applied to neuroscience problems, MSA outperforms recent methods in brain-age regression with task variations using magnetoencephalography (MEG) signals from the Cam-CAN dataset.

Linear Independent Component Analysis (ICA) is a blind source separation technique that has been used in various domains to identify independent latent sources from observed signals. In order to obtain a higher signal-to-noise ratio, the presence of multiple views of the same sources can be used. In this work, we present MultiView Independent Component Analysis with Delays (MVICAD). This algorithm builds on the MultiView ICA model by allowing sources to be delayed versions of some shared sources: sources are shared across views up to some unknown latencies that are view- and source-specific. Using simulations, we demonstrate that MVICAD leads to better unmixing of the sources. Moreover, as ICA is often used in neuroscience, we show that latencies are age-related when applied to Cam-CAN, a large-scale magnetoencephalography (MEG) dataset. These results demonstrate that the MVICAD model can reveal rich effects on neural signals without human supervision.

The Brain Imaging Data Structure (BIDS) is a community-driven standard for the organization of data and metadata from a growing range of neuroscience modalities. This paper is meant as a history of how the standard has developed and grown over time. We outline the principles behind the project, the mechanisms by which it has been extended, and some of the challenges being addressed as it evolves. We also discuss the lessons learned through the project, with the aim of enabling researchers in other domains to learn from the success of BIDS.

Electroencephalography (EEG) decoding is a challenging task due to the limited availability of labelled data. While transfer learning is a promising technique to address this challenge, it assumes that transferable data domains and task are known, which is not the case in this setting. This study investigates the transferability of deep learning representations between different EEG decoding tasks. We conduct extensive experiments using state-of-the-art decoding models on two recently released EEG datasets, ERP CORE and M$^3$CV, containing over 140 subjects and 11 distinct cognitive tasks. We measure the transferability of learned representations by pre-training deep neural networks on one task and assessing their ability to decode subsequent tasks. Our experiments demonstrate that, even with linear probing transfer, significant improvements in decoding performance can be obtained, with gains of up to 28% compare with the pure supervised approach. Additionally, we discover evidence that certain decoding paradigms elicit specific and narrow brain activities, while others benefit from pre-training on a broad range of representations. By revealing which tasks transfer well and demonstrating the benefits of transfer learning for EEG decoding, our findings have practical implications for mitigating data scarcity in this setting. The transfer maps generated also provide insights into the hierarchical relations between cognitive tasks, hence enhancing our understanding of how these tasks are connected from a neuroscientific standpoint., Comment: 19 pages, 9 figures

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, L-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, L-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of L-C2ST on a challenging application from computational neuroscience., Comment: 27 pages, 6 figures, 3 tables, 6 appendices, NeurIPS 2023

In many machine learning applications on signals and biomedical data, especially electroencephalogram (EEG), one major challenge is the variability of the data across subjects, sessions, and hardware devices. In this work, we propose a new method called Convolutional Monge Mapping Normalization (CMMN), which consists in filtering the signals in order to adapt their power spectrum density (PSD) to a Wasserstein barycenter estimated on training data. CMMN relies on novel closed-form solutions for optimal transport mappings and barycenters and provides individual test time adaptation to new data without needing to retrain a prediction model. Numerical experiments on sleep EEG data show that CMMN leads to significant and consistent performance gains independent from the neural network architecture when adapting between subjects, sessions, and even datasets collected with different hardware. Notably our performance gain is on par with much more numerically intensive Domain Adaptation (DA) methods and can be used in conjunction with those for even better performances.

Self-supervised learning is an increasingly popular approach to unsupervised learning, achieving state-of-the-art results. A prevalent approach consists in contrasting data points and noise points within a classification task: this requires a good noise distribution which is notoriously hard to specify. While a comprehensive theory is missing, it is widely assumed that the optimal noise distribution should in practice be made equal to the data distribution, as in Generative Adversarial Networks (GANs). We here empirically and theoretically challenge this assumption. We turn to Noise-Contrastive Estimation (NCE) which grounds this self-supervised task as an estimation problem of an energy-based model of the data. This ties the optimality of the noise distribution to the sample efficiency of the estimator, which is rigorously defined as its asymptotic variance, or mean-squared error. In the special case where the normalization constant only is unknown, we show that NCE recovers a family of Importance Sampling estimators for which the optimal noise is indeed equal to the data distribution. However, in the general case where the energy is also unknown, we prove that the optimal noise density is the data density multiplied by a correction term based on the Fisher score. In particular, the optimal noise distribution is different from the data distribution, and is even from a different family. Nevertheless, we soberly conclude that the optimal noise may be hard to sample from, and the gain in efficiency can be modest compared to choosing the noise distribution equal to the data's., Comment: arXiv admin note: text overlap with arXiv:2203.01110

Building on the recent trend of new deep generative models known as Normalizing Flows (NF), simulation-based inference (SBI) algorithms can now efficiently accommodate arbitrary complex and high-dimensional data distributions. The development of appropriate validation methods however has fallen behind. Indeed, most of the existing metrics either require access to the true posterior distribution, or fail to provide theoretical guarantees on the consistency of the inferred approximation beyond the one-dimensional setting. This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. The proposed workflow can be used to check, analyse and guarantee consistent behavior of the estimator. The method is illustrated with a challenging example that involves tightly coupled parameters in the context of computational neuroscience. This work should help the design of better specified models or drive the development of novel SBI-algorithms, hence allowing to build up trust on their ability to address important questions in experimental science., Comment: 7 pages, 2 figures, 1 appendix, published at "Machine Learning and the Physical Sciences" workshop (NeurIPS 2022): https://ml4physicalsciences.github.io/2022/

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast $\ell_2$ gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

Objective: The use of deep learning for electroencephalography (EEG) classification tasks has been rapidly growing in the last years, yet its application has been limited by the relatively small size of EEG datasets. Data augmentation, which consists in artificially increasing the size of the dataset during training, can be employed to alleviate this problem. While a few augmentation transformations for EEG data have been proposed in the literature, their positive impact on performance is often evaluated on a single dataset and compared to one or two competing augmentation methods. This work proposes to better validate the existing data augmentation approaches through a unified and exhaustive analysis. Approach: We compare quantitatively 13 different augmentations with two different predictive tasks, datasets and models, using three different types of experiments. Main results: We demonstrate that employing the adequate data augmentations can bring up to 45% accuracy improvements in low data regimes compared to the same model trained without any augmentation. Our experiments also show that there is no single best augmentation strategy, as the good augmentations differ on each task. Significance: Our results highlight the best data augmentations to consider for sleep stage classification and motor imagery brain-computer interfaces. More broadly, it demonstrates that EEG classification tasks benefit from adequate data augmentation, Comment: Accepted in Journal of Neural Engineering

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: $\ell_2$-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings., Comment: Accepted in proceedings of NeurIPS 22; Benchopt library documentation is available at https://benchopt.github.io/

Several deep neural networks have recently been shown to generate activations similar to those of the brain in response to the same input. These algorithms, however, remain largely implausible: they require (1) extraordinarily large amounts of data, (2) unobtainable supervised labels, (3) textual rather than raw sensory input, and / or (4) implausibly large memory (e.g. thousands of contextual words). These elements highlight the need to identify algorithms that, under these limitations, would suffice to account for both behavioral and brain responses. Focusing on the issue of speech processing, we here hypothesize that self-supervised algorithms trained on the raw waveform constitute a promising candidate. Specifically, we compare a recent self-supervised architecture, Wav2Vec 2.0, to the brain activity of 412 English, French, and Mandarin individuals recorded with functional Magnetic Resonance Imaging (fMRI), while they listened to ~1h of audio books. Our results are four-fold. First, we show that this algorithm learns brain-like representations with as little as 600 hours of unlabelled speech -- a quantity comparable to what infants can be exposed to during language acquisition. Second, its functional hierarchy aligns with the cortical hierarchy of speech processing. Third, different training regimes reveal a functional specialization akin to the cortex: Wav2Vec 2.0 learns sound-generic, speech-specific and language-specific representations similar to those of the prefrontal and temporal cortices. Fourth, we confirm the similarity of this specialization with the behavior of 386 additional participants. These elements, resulting from the largest neuroimaging benchmark to date, show how self-supervised learning can account for a rich organization of speech processing in the brain, and thus delineate a path to identify the laws of language acquisition which shape the human brain., Comment: Accepted to NeurIPS 2022

Several fields in science, from genomics to neuroimaging, require monitoring populations (measures) that evolve with time. These complex datasets, describing dynamics with both time and spatial components, pose new challenges for data analysis. We propose in this work a new framework to carry out averaging of these datasets, with the goal of synthesizing a representative template trajectory from multiple trajectories. We show that this requires addressing three sources of invariance: shifts in time, space, and total population size (or mass/amplitude). Here we draw inspiration from dynamic time warping (DTW), optimal transport (OT) theory and its unbalanced extension (UOT) to propose a criterion that can address all three issues. This proposal leverages a smooth formulation of DTW (Soft-DTW) that is shown to capture temporal shifts, and UOT to handle both variations in space and size. Our proposed loss can be used to define spatio-temporal barycenters as Fr\'echet means. Using Fenchel duality, we show how these barycenters can be computed efficiently, in parallel, via a novel variant of entropy-regularized debiased UOT. Experiments on handwritten letters and brain imaging data confirm our theoretical findings and illustrate the effectiveness of the proposed loss for spatio-temporal data.

Learning a parametric model of a data distribution is a well-known statistical problem that has seen renewed interest as it is brought to scale in deep learning. Framing the problem as a self-supervised task, where data samples are discriminated from noise samples, is at the core of state-of-the-art methods, beginning with Noise-Contrastive Estimation (NCE). Yet, such contrastive learning requires a good noise distribution, which is hard to specify; domain-specific heuristics are therefore widely used. While a comprehensive theory is missing, it is widely assumed that the optimal noise should in practice be made equal to the data, both in distribution and proportion. This setting underlies Generative Adversarial Networks (GANs) in particular. Here, we empirically and theoretically challenge this assumption on the optimal noise. We show that deviating from this assumption can actually lead to better statistical estimators, in terms of asymptotic variance. In particular, the optimal noise distribution is different from the data's and even from a different family.

Transfer learning and meta-learning offer some of the most promising avenues to unlock the scalability of healthcare and consumer technologies driven by biosignal data. This is because current methods cannot generalise well across human subjects' data and handle learning from different heterogeneously collected data sets, thus limiting the scale of training data. On the other side, developments in transfer learning would benefit significantly from a real-world benchmark with immediate practical application. Therefore, we pick electroencephalography (EEG) as an exemplar for what makes biosignal machine learning hard. We design two transfer learning challenges around diagnostics and Brain-Computer-Interfacing (BCI), that have to be solved in the face of low signal-to-noise ratios, major variability among subjects, differences in the data recording sessions and techniques, and even between the specific BCI tasks recorded in the dataset. Task 1 is centred on the field of medical diagnostics, addressing automatic sleep stage annotation across subjects. Task 2 is centred on Brain-Computer Interfacing (BCI), addressing motor imagery decoding across both subjects and data sets. The BEETL competition with its over 30 competing teams and its 3 winning entries brought attention to the potential of deep transfer learning and combinations of set theory and conventional machine learning techniques to overcome the challenges. The results set a new state-of-the-art for the real-world BEETL benchmark., Comment: PrePrint of the NeurIPS2021 BEETL Competition Submitted to Proceedings of Machine Learning Research (PMLR)

Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g. using convolutions for translations, or using data augmentation. Yet, enforcing true invariance in the network can be difficult, and data invariances are not always known a piori. State-of-the-art methods for learning data augmentation policies require held-out data and are based on bilevel optimization problems, which are complex to solve and often computationally demanding. In this work we investigate new ways of learning invariances only from the training data. Using learnable augmentation layers built directly in the network, we demonstrate that our method is very versatile. It can incorporate any type of differentiable augmentation and be applied to a broad class of learning problems beyond computer vision. We provide empirical evidence showing that our approach is easier and faster to train than modern automatic data augmentation techniques based on bilevel optimization, while achieving comparable results. Experiments show that while the invariances transferred to a model through automatic data augmentation are limited by the model expressivity, the invariance yielded by our approach is insensitive to it by design., Comment: Accepted to NeurIPS 2022

The quantitative analysis of non-invasive electrophysiology signals from electroencephalography (EEG) and magnetoencephalography (MEG) boils down to the identification of temporal patterns such as evoked responses, transient bursts of neural oscillations but also blinks or heartbeats for data cleaning. Several works have shown that these patterns can be extracted efficiently in an unsupervised way, e.g., using Convolutional Dictionary Learning. This leads to an event-based description of the data. Given these events, a natural question is to estimate how their occurrences are modulated by certain cognitive tasks and experimental manipulations. To address it, we propose a point process approach. While point processes have been used in neuroscience in the past, in particular for single cell recordings (spike trains), techniques such as Convolutional Dictionary Learning make them amenable to human studies based on EEG/MEG signals. We develop a novel statistical point process model-called driven temporal point processes (DriPP)-where the intensity function of the point process model is linked to a set of point processes corresponding to stimulation events. We derive a fast and principled expectation-maximization (EM) algorithm to estimate the parameters of this model. Simulations reveal that model parameters can be identified from long enough signals. Results on standard MEG datasets demonstrate that our methodology reveals event-related neural responses-both evoked and induced-and isolates non-task specific temporal patterns.

Deep learning has recently made remarkable progress in natural language processing. Yet, the resulting algorithms remain far from competing with the language abilities of the human brain. Predictive coding theory offers a potential explanation to this discrepancy: while deep language algorithms are optimized to predict adjacent words, the human brain would be tuned to make long-range and hierarchical predictions. To test this hypothesis, we analyze the fMRI brain signals of 304 subjects each listening to 70min of short stories. After confirming that the activations of deep language algorithms linearly map onto those of the brain, we show that enhancing these models with long-range forecast representations improves their brain-mapping. The results further reveal a hierarchy of predictions in the brain, whereby the fronto-parietal cortices forecast more abstract and more distant representations than the temporal cortices. Overall, this study strengthens predictive coding theory and suggests a critical role of long-range and hierarchical predictions in natural language processing.

Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologically-relevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector $\theta$ that best describes a given observed data point $x_0$, but also a full posterior distribution $p(\theta|x_0)$ over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.

While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex high-dimensional space composed by thousands of hyperparameters. On the other hand, the latest progress with high-dimensional hyperparameter optimization (HD-HPO) methods for black-box functions demonstrates that high-dimensional applications can indeed be efficiently optimized. Despite this initial success, HD-HPO approaches are mostly applied to synthetic problems with a moderate number of dimensions, which limits its impact in scientific and engineering applications. We propose LassoBench, the first benchmark suite tailored for Weighted Lasso regression. LassoBench consists of benchmarks for both well-controlled synthetic setups (number of samples, noise level, ambient and effective dimensionalities, and multiple fidelities) and real-world datasets, which enables the use of many flavors of HPO algorithms to be studied and extended to the high-dimensional Lasso setting. We evaluate 6 state-of-the-art HPO methods and 3 Lasso baselines, and demonstrate that Bayesian optimization and evolutionary strategies can improve over the methods commonly used for sparse regression while highlighting limitations of these frameworks in very high-dimensional and noisy settings., Comment: 21 pages, 13 figures, Accepted as a conference paper at AutoML2022

Estimators based on non-convex sparsity-promoting penalties were shown to yield state-of-the-art solutions to the magneto-/electroencephalography (M/EEG) brain source localization problem. In this paper we tackle the model selection problem of these estimators: we propose to use a proxy of the Stein's Unbiased Risk Estimator (SURE) to automatically select their regularization parameters. The effectiveness of the method is demonstrated on realistic simulations and $30$ subjects from the Cam-CAN dataset. To our knowledge, this is the first time that sparsity promoting estimators are automatically calibrated at such a scale. Results show that the proposed SURE approach outperforms cross-validation strategies and state-of-the-art Bayesian statistics methods both computationally and statistically.

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., Comment: Accepted at NeurIPS 2021

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., Comment: Accepted at NIPS 2017 Workshop on Machine Learning for Health

A popular approach to decompose the neural bases of language consists in correlating, across individuals, the brain responses to different stimuli (e.g. regular speech versus scrambled words, sentences, or paragraphs). Although successful, this `model-free' approach necessitates the acquisition of a large and costly set of neuroimaging data. Here, we show that a model-based approach can reach equivalent results within subjects exposed to natural stimuli. We capitalize on the recently-discovered similarities between deep language models and the human brain to compute the mapping between i) the brain responses to regular speech and ii) the activations of deep language models elicited by modified stimuli (e.g. scrambled words, sentences, or paragraphs). Our model-based approach successfully replicates the seminal study of Lerner et al. (2011), which revealed the hierarchy of language areas by comparing the functional-magnetic resonance imaging (fMRI) of seven subjects listening to 7min of both regular and scrambled narratives. We further extend and precise these results to the brain signals of 305 individuals listening to 4.1 hours of narrated stories. Overall, this study paves the way for efficient and flexible analyses of the brain bases of language., Comment: Accepted to EMNLP 2021 (Findings)

Data augmentation is a key element of deep learning pipelines, as it informs the network during training about transformations of the input data that keep the label unchanged. Manually finding adequate augmentation methods and parameters for a given pipeline is however rapidly cumbersome. In particular, while intuition can guide this decision for images, the design and choice of augmentation policies remains unclear for more complex types of data, such as neuroscience signals. Besides, class-dependent augmentation strategies have been surprisingly unexplored in the literature, although it is quite intuitive: changing the color of a car image does not change the object class to be predicted, but doing the same to the picture of an orange does. This paper investigates gradient-based automatic data augmentation algorithms amenable to class-wise policies with exponentially larger search spaces. Motivated by supervised learning applications using EEG signals for which good augmentation policies are mostly unknown, we propose a new differentiable relaxation of the problem. In the class-agnostic setting, results show that our new relaxation leads to optimal performance with faster training than competing gradient-based methods, while also outperforming gradient-free methods in the class-wise setting. This work proposes also novel differentiable augmentation operations relevant for sleep stage classification.

Building machine learning models using EEG recorded outside of the laboratory setting requires methods robust to noisy data and randomly missing channels. This need is particularly great when working with sparse EEG montages (1-6 channels), often encountered in consumer-grade or mobile EEG devices. Neither classical machine learning models nor deep neural networks trained end-to-end on EEG are typically designed or tested for robustness to corruption, and especially to randomly missing channels. While some studies have proposed strategies for using data with missing channels, these approaches are not practical when sparse montages are used and computing power is limited (e.g., wearables, cell phones). To tackle this problem, we propose dynamic spatial filtering (DSF), a multi-head attention module that can be plugged in before the first layer of a neural network to handle missing EEG channels by learning to focus on good channels and to ignore bad ones. We tested DSF on public EEG data encompassing ~4,000 recordings with simulated channel corruption and on a private dataset of ~100 at-home recordings of mobile EEG with natural corruption. Our proposed approach achieves the same performance as baseline models when no noise is applied, but outperforms baselines by as much as 29.4% accuracy when significant channel corruption is present. Moreover, DSF outputs are interpretable, making it possible to monitor channel importance in real-time. This approach has the potential to enable the analysis of EEG in challenging settings where channel corruption hampers the reading of brain signals., Comment: 42 pages, 9 figures

Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but non-smooth. We show that the forward-mode differentiation of proximal gradient descent and proximal coordinate descent yield sequences of Jacobians converging toward the exact Jacobian. Using implicit differentiation, we show it is possible to leverage the non-smoothness of the inner problem to speed up the computation. Finally, we provide a bound on the error made on the hypergradient when the inner optimization problem is solved approximately. Results on regression and classification problems reveal computational benefits for hyperparameter optimization, especially when multiple hyperparameters are required.

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.

The activations of language transformers like GPT-2 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 GPT-2'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 versatile framework to isolate, in the brain activity, the distributed representations of linguistic constructs., Comment: Accepted to ICML 2021

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.

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 hierarchical neural posterior estimation (HNPE), a novel 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, using both simulated and real EEG data.

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.

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.

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., Comment: 21 pages

Background: Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix is a noiseless linear mixture of independent sources that are assumed non-Gaussian. A limitation is that it enforces to estimate as many sources as sensors or to rely on a detrimental PCA step. Methods: We present the Spectral Matching ICA (SMICA) model. Signals are modelled as a linear mixing of independent sources corrupted by additive noise, where sources and the noise are stationary Gaussian time series. Thanks to the Gaussian assumption, the negative log-likelihood has a simple expression as a sum of divergences between the empirical spectral covariance matrices of the signals and those predicted by the model. The model parameters can then be estimated by the expectation-maximization (EM) algorithm. Results: Experiments on phantom MEG datasets show that SMICA can recover dipole locations more precisely than usual ICA algorithms or Maxwell filtering when the dipole amplitude is low. Experiments on EEG datasets show that SMICA identifies a source subspace which contains sources that have less pairwise mutual information, and are better explained by the projection of a single dipole on the scalp. Comparison with existing methods: Noiseless ICA models lead to degenerate likelihood when there are fewer sources than sensors, while SMICA succeeds without resorting to prior dimension reduction. Conclusions: SMICA is a promising alternative to other noiseless ICA models based on non-Gaussian assumptions.

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., Comment: 32 pages, 9 figures

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., Comment: Accepted to NeurIPS 2020

Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized Wasserstein distance while having a significantly lower complexity thanks to Sinkhorn's algorithm. However, entropy brings some inherent smoothing bias, resulting for example in blurred barycenters. This side effect has prompted an increasing temptation in the community to settle for a slower algorithm such as log-domain stabilized Sinkhorn which breaks the parallel structure that can be leveraged on GPUs, or even go back to unregularized OT. Here we show how this bias is tightly linked to the reference measure that defines the entropy regularizer and propose debiased Wasserstein barycenters that preserve the best of both worlds: fast Sinkhorn-like iterations without entropy smoothing. Theoretically, we prove that the entropic OT barycenter of univariate Gaussians is a Gaussian and quantify its variance bias. This result is obtained by extending the differentiability and convexity of entropic OT to sub-Gaussian measures with unbounded supports. Empirically, we illustrate the reduced blurring and the computational advantage on various applications., Comment: ICML 2020

As data are generated more and more from multiple disparate sources, multiview data sets, where each sample has features in distinct views, have ballooned in recent years. However, no comprehensive package exists that enables non-specialists to use these methods easily. mvlearn is a Python library which implements the leading multiview machine learning methods. Its simple API closely follows that of scikit-learn for increased ease-of-use. The package can be installed from Python Package Index (PyPI) and the conda package manager and is released under the MIT open-source license. The documentation, detailed examples, and all releases are available at https://mvlearn.github.io/., Comment: 6 pages, 2 figures, 1 table

Setting regularization parameters for Lasso-type estimators is notoriously difficult, though crucial in practice. The most popular hyperparameter optimization approach is grid-search using held-out validation data. Grid-search however requires to choose a predefined grid for each parameter, which scales exponentially in the number of parameters. Another approach is to cast hyperparameter optimization as a bi-level optimization problem, one can solve by gradient descent. The key challenge for these methods is the estimation of the gradient with respect to the hyperparameters. Computing this gradient via forward or backward automatic differentiation is possible yet usually suffers from high memory consumption. Alternatively implicit differentiation typically involves solving a linear system which can be prohibitive and numerically unstable in high dimension. In addition, implicit differentiation usually assumes smooth loss functions, which is not the case for Lasso-type problems. This work introduces an efficient implicit differentiation algorithm, without matrix inversion, tailored for Lasso-type problems. Our approach scales to high-dimensional data by leveraging the sparsity of the solutions. Experiments demonstrate that the proposed method outperforms a large number of standard methods to optimize the error on held-out data, or the Stein Unbiased Risk Estimator (SURE).

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern techniques to solve these include smoothing the datafitting term, to benefit from fast efficient proximal algorithms. In this work we show minimax sup-norm convergence rates for non smoothed and smoothed, single task and multitask square-root Lasso-type estimators. Thanks to our theoretical analysis, we provide some guidelines on how to set the smoothing hyperparameter, and illustrate on synthetic data the interest of such guidelines.