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Causal machine learning (ML) promises to provide powerful tools for estimating individual treatment effects. Although causal ML methods are now well established, they still face the significant challenge of interpretability, which is crucial for medical applications. In this work, we propose a new algorithm based on the Conditional Permutation Importance (CPI) method for statistically rigorous variable importance assessment in the context of Conditional Average Treatment Effect (CATE) estimation. Our method termed PermuCATE is agnostic to both the meta-learner and the ML model used. Through theoretical analysis and empirical studies, we show that this approach provides a reliable measure of variable importance and exhibits lower variance compared to the standard Leave-One-Covariate-Out (LOCO) method. We illustrate how this property leads to increased statistical power, which is crucial for the application of explainable ML in small sample sizes or high-dimensional settings. We empirically demonstrate the benefits of our approach in various simulation scenarios, including previously proposed benchmarks as well as more complex settings with high-dimensional and correlated variables that require advanced CATE estimators.

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.

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.

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.

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.

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

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

The supervised learning paradigm is limited by the cost - and sometimes the impracticality - of data collection and labeling in multiple domains. Self-supervised learning, a paradigm which exploits the structure of unlabeled data to create learning problems that can be solved with standard supervised approaches, has shown great promise as a pretraining or feature learning approach in fields like computer vision and time series processing. In this work, we present self-supervision strategies that can be used to learn informative representations from multivariate time series. One successful approach relies on predicting whether time windows are sampled from the same temporal context or not. As demonstrated on a clinically relevant task (sleep scoring) and with two electroencephalography datasets, our approach outperforms a purely supervised approach in low data regimes, while capturing important physiological information without any access to labels.

Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal dynamics non-invasively in real-time and are therefore appreciated methods in medicine and neuroscience. Recent advances in modeling brain-behavior relationships have highlighted the effectiveness of Riemannian geometry for summarizing the spatially correlated time-series from M/EEG in terms of their covariance. However, after artefact-suppression, M/EEG data is often rank deficient which limits the application of Riemannian concepts. In this article, we focus on the task of regression with rank-reduced covariance matrices. We study two Riemannian approaches that vectorize the M/EEG covariance between-sensors through projection into a tangent space. The Wasserstein distance readily applies to rank-reduced data but lacks affine-invariance. This can be overcome by finding a common subspace in which the covariance matrices are full rank, enabling the affine-invariant geometric distance. We investigated the implications of these two approaches in synthetic generative models, which allowed us to control estimation bias of a linear model for prediction. We show that Wasserstein and geometric distances allow perfect out-of-sample prediction on the generative models. We then evaluated the methods on real data with regard to their effectiveness in predicting age from M/EEG covariance matrices. The findings suggest that the data-driven Riemannian methods outperform different sensor-space estimators and that they get close to the performance of biophysics-driven source-localization model that requires MRI acquisitions and tedious data processing. Our study suggests that the proposed Riemannian methods can serve as fundamental building-blocks for automated large-scale analysis of M/EEG.

We present an automated algorithm for unified rejection and repair of bad trials in magnetoencephalography (MEG) and electroencephalography (EEG) signals. Our method capitalizes on cross-validation in conjunction with a robust evaluation metric to estimate the optimal peak-to-peak threshold -- a quantity commonly used for identifying bad trials in M/EEG. This approach is then extended to a more sophisticated algorithm which estimates this threshold for each sensor yielding trial-wise bad sensors. Depending on the number of bad sensors, the trial is then repaired by interpolation or by excluding it from subsequent analysis. All steps of the algorithm are fully automated thus lending itself to the name Autoreject. In order to assess the practical significance of the algorithm, we conducted extensive validation and comparison with state-of-the-art methods on four public datasets containing MEG and EEG recordings from more than 200 subjects. Comparison include purely qualitative efforts as well as quantitatively benchmarking against human supervised and semi-automated preprocessing pipelines. The algorithm allowed us to automate the preprocessing of MEG data from the Human Connectome Project (HCP) going up to the computation of the evoked responses. The automated nature of our method minimizes the burden of human inspection, hence supporting scalability and reliability demanded by data analysis in modern neuroscience.

Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didactic overview of the relevant theoretical considerations. Practical aspects are highlighted with an extensive empirical study of the common decoders in within-and across-subject predictions, on multiple datasets --anatomical and functional MRI and MEG-- and simulations. Theory and experiments outline that the popular " leave-one-out " strategy leads to unstable and biased estimates, and a repeated random splits method should be preferred. Experiments outline the large error bars of cross-validation in neuroimaging settings: typical confidence intervals of 10%. Nested cross-validation can tune decoders' parameters while avoiding circularity bias. However we find that it can be more favorable to use sane defaults, in particular for non-sparse decoders., Comment: NeuroImage, Elsevier, 2016

Large-scale transitions in societies are associated with both individual behavioural change and restructuring of the social network. These two factors have often been considered independently, yet recent advances in social network research challenge this view. Here we show that common features of societal marginalization and clustering emerge naturally during transitions in a co-evolutionary adaptive network model. This is achieved by explicitly considering the interplay between individual interaction and a dynamic network structure in behavioural selection. We exemplify this mechanism by simulating how smoking behaviour and the network structure get reconfigured by changing social norms. Our results are consistent with empirical findings: The prevalence of smoking was reduced, remaining smokers were preferentially connected among each other and formed increasingly marginalised clusters. We propose that self-amplifying feedbacks between individual behaviour and dynamic restructuring of the network are main drivers of the transition. This generative mechanism for co-evolution of individual behaviour and social network structure may apply to a wide range of examples beyond smoking., Comment: 16 pages, 5 figures