Overlapping peaks and sample-dependent chemical shift variability prevent reliable metabolite recovery from complex biological spectra. This problem is critical in one-dimensional proton (1D 1H) NMR which has become the standard method providing fast acquisition and information-rich spectra in metabolomics and foodomics. This study demonstrates how chemical shifts can be utilised as a strength in 1D 1H NMR, when suitably modeled through the proposed Bayesian Shift-Invariant Non-negative Matrix Factorization (BSI-NMF) procedure. We find that BSI-NMF accurately recovers the underlying chemical signals in 1D 1H NMR spectra missed by existing analyses approaches across simulations, laboratory created datasets, and a large urine dataset obtained from 2439 people across Europe. Our study highlights how shifts in the chemical signatures - until now perceived as a nuisance - can in fact when suitably modelled be instrumental for unique recovery of metabolites. This creates an opportunity to experimentally induce chemical shifts changes to facilitate unique recovery of spectra.

Central to machine learning and signal processing is the ability to perform universal function approximation and learn complex input-output relationships from limited numbers of observations. Multivariate polynomial models offer a natural way to express such relationships through multiplicative feature interactions, but their coefficient tensors grow exponentially in size with the polynomial degree. Existing tensorized polynomial models reduce this cost, yet canonical polyadic decompositions have rank-limited expressivity, and tensor train formulations are feature order dependent. We introduce Multivariate Polynomial Optimization based on Matrix Product Operators (MPO)^2, a framework that combines learned MPO feature embeddings with compact polynomial weight tensors. This yields feature order independent polynomial representations that can incorporate structured operators such as projections, convolutions, and masks for weight tensor symmetries. Across regression and classification benchmarks, (MPO)^2 improves over existing tensor decomposition based polynomial models and provides a flexible alternative for efficient polynomial function approximation.

Multiplex social networks capture multiple types of relations among the same people. Their structure reflects how exchanges arise from individual attributes related to independence, the status or resources of others related to dependence, and mutual influence related to interdependence. Understanding these systems is challenging because layers can play distinct yet complementary roles. We introduce the Multiplex Latent Trade-off Model, MLT, a framework for identifying roles in multiplex networks that incorporates independence, dependence, and interdependence. MLT represents roles as trade-offs, requiring each node to distribute source and target roles across layers while allocating community memberships within hierarchical structures. Applying MLT to 176 multiplex networks, including social, health, and economic layers from villages in western Honduras, we identify core principles of social exchange and reveal multi-scale communities. Link-prediction analyses show that modeling interdependence most improves predictions for social ties, whereas health and economic ties are shaped more strongly by individual status and behavior.

In recent years, deep learning-based single-channel speech separation has improved considerably, in large part driven by increasingly compute- and parameter-efficient neural network architectures. Most such architectures are, however, designed with a fixed compute and parameter budget, and consequently cannot scale to varying compute demands or resources, which limits their use in embedded and heterogeneous devices such as mobile phones and hearables. To enable such use-cases we design a neural network architecture for speech separation capable of early-exit, and we propose an uncertainty-aware probabilistic framework to jointly model the clean speech signal and error variance which we use to derive probabilistic early-exit conditions in terms of desired signal-to-noise ratios. We evaluate our methods on both speech separation and enhancement tasks, and we show that a single early-exit model can be competitive with state-of-the-art models trained at many compute and parameter budgets. Our framework enables fine-grained dynamic compute-scaling of speech separation networks while achieving state-of-the-art performance and interpretable exit conditions.

Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.

Complex cognitive functions rely on coordinated communication between distributed brain regions, yet capturing these interactions as they evolve over time remains challenging. Traditional analyses of functional brain connectivity largely rely on correlations in signal amplitude, which are sensitive to noise and artifacts such as head motion. Here, we introduce a mixture modeling approach that focuses on the phase of brain signals, allowing dynamic patterns of large-scale synchronization in brain phase coherence networks to be studied directly and in their entirety. We lay the mathematical and conceptual groundwork for phase modeling and introduce the complex angular central Gaussian mixture model, providing a principled way to analyze phase-based interactions across the brain. Applied to functional MRI data, the model identifies recurring states of brain-wide synchronized activity that reliably distinguish cognitive tasks and generalize across previously unseen individuals, without requiring any task labels during training. These results show that modeling signal phase offers a clean and informative view of brain synchronization dynamics, opening avenues for studying large-scale neural coordination.

Abstract Scientists have for decades attempted to automate the manual sleep staging problem not only for human polysomnography data but also for rodent data. No model has, however, succeeded in fully replacing the manual procedure across clinics and laboratories. We hypothesize that this is due to the models’ limited ability to generalize to data from unseen laboratories. Our findings show that despite the high performance of four state-of-the-art models reported in initial publications, the published models struggle to generalize to other laboratories. We further show a significant improvement in model performance across labs by re-training them on a diverse dataset from five different sites. To assess the contribution of variability in manual scoring, ten experts from five laboratories all labelled the same nine mouse sleep recordings. The result revealed substantial scoring variability, particularly for rapid eye movement (REM) sleep, both within and between labs. In conclusion our study demonstrates that key challenges in the generalizability of state-of-the-art sleep scoring models are signal variability and label noise. Our study highlights the need for a standardized set of mouse sleep scoring guidelines to enable consistency and collaboration across the field. Until such a consensus is reached, we present four sufficiently robust models trained on diverse datasets that can serve as standardized tools across labs.

Abstract Diffusion-weighted magnetic resonance imaging (dMRI) is used to study white matter microstructure and to delineate pathways by estimating fiber orientation distributions (FODs). Symmetric FODs represent the conventional model assuming antipodal symmetry in water diffusion. However, in complex regions with bending, branching or fanning fibers, this assumption is not guaranteed. To better capture such underlying fibers geometries, asymmetric FODs (A-FODs), derived from neighboring FODs, have been introduced. Here, we propose an Encoder-based Curvature-Aware Regularization (EnCAR) method for estimating A-FODs. Incorporating curvature features into the regularization weight applied to neighboring voxels improves reconstruction of A-FODs. A self-supervised Transformer network, combined with a Spherical Harmonics Semantic Encoder, learns region-specific regularization parameters from this local neighborhood to capture the diversity of fiber geometries across the brain. The EnCAR method was verified on the DiSCo challenge phantom, and applied to in vivo multi-shell Human data. The model estimated sharp, high-angular-resolution A-FODs that were well aligned with local fiber pathway. Compared with established FOD and A-FOD methods, it performed on par in regions dominated by symmetric FODs and outperformed them in complex asymmetric regions. Quantitative evaluation using the Asymmetry Index (ASI) and Model Discrepancy Index (MDI) confirmed improved consistency with the underlying diffusion signals. By ensuring smooth directional transitions, this work enhances the visibility of continuous fiber segments.

Functional neuroimaging has become a central window into our working mind and how it changes by aging and disease. However, the different measurement modalities in functional neuroimaging are challenged by high dimensionality when compared with sample sizes. Furthermore, they exhibit high degrees of variability across individuals when analyzing multiset functional neuroimaging datasets. Whereas the multiple functional neuroimaging modalities currently available provide complementary views of brain function, their joint analysis remains an important challenge in neuroscience. This survey article highlights prominent modeling methodologies for the discovery of interpretable patterns in such multiset and multimodal functional neuroimaging datasets. The survey highlights prominent modeling strategies from hard to soft coupling for the modeling of these high-dimensional multiset and multimodal functional neuroimaging datasets while emphasizing the importance of model uniqueness as a prerequisite for reliable and reproducible pattern discovery. We also provide future directions of research for interpretable pattern discovery in functional neuroimaging that ultimately can further our understanding of perhaps one of nature’s most intriguing organs, the human brain.

Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure for extracting distinct aspects, so-called archetypes, from observations, with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data and enabling wide applications across the sciences. However, AA also faces challenges, particularly as the associated optimization problem is non-convex. This is the first survey that provides researchers and data mining practitioners with an overview of the methodologies and opportunities that AA offers, surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data with AA and its limitations. The survey concludes by explaining crucial future research directions concerning AA.

Partially observed and heterogeneous data pose significant challenges in machine learning and statistical analysis, often leading to biased results or reduced model performance. While various imputation methods exist, they typically struggle with high-dimensional and mixed data types. To address these limitations, we introduce a flexible framework that leverages tensor network structures and probabilistic circuits (TNSPC) to provide an analytically tractable and scalable solution for imputing high-dimensional and mixed data types. Within the TNSPC framework, we systematically contrast the canonical polyadic (CP), tensor train (TT), and tensor tree network (TTN) structures to prominent probabilistic circuit structures not relying on tensor networks and find that the considered TNSPCs in general provide comparable performance and on some of the considered datasets even best performance. We further highlight the versatility of the TNSPC framework and its limitations.

Sleep in mice is a heterogeneous state where the currently used three main sleep stages may not adequately capture underlying sleep-wake dynamics, which are believed to be a continuum as opposed to be defined by discrete states. We presently explore how archetypal analysis (AA) can be used to extract distinct characteristics in sleep data and to represent the sleep as a continuum. For the analyses, we consider relative EEG power of six frequency bands and EMG RMS in 4 s epochs as obtained from 36 unique mice (18 wild-type (WT) and 18 narcolepsy (NT) from a diphtheria toxin A (DTA) mouse model). Specifically, we investigate how the AA extracted sample-specific profiles defined by a continuum of the archetypes reflect sleep stages, mice type (WT/NT) as well as inherent mouse variability (mice ID) as quantified by their normalized mutual information (NMI). We find that the AA robustly extracts distinct characteristics reflecting specific aspects of frequency band and RMS activity of the sleep data. We further observe that the extracted sample specific profiles defining a continuum between these distinct characteristics share correspondence to sleep stages, mouse type and mouse ID with the most pronounced correspondence being to sleep stages. Whereas these correspondences are significant when compared using permutation testing by randomly shuffling the sample specific labels, the correspondence is relatively low (NMI≤0.2), pointing to the distinct aspects identified in the data reflecting richer properties of the sleep data. AA is a promising framework for the analysis of sleep data providing easily interpretable characterizations of the distinct aspects in the data notably also representing samples as a continuum of these identified aspects. The approach readily generalizes to higher-dimensional sleep data providing an interesting versatile tool to further our understand of the properties and structure of sleep.Clinical relevance Archetypal analysis provides a novel and interpretable characterization of sleep data in terms of their distinct aspects. Additionally, each observation can be defined as a continuum enabling further understanding of sleep characteristics in health and disease.

The manual evaluation of mouse sleep studies is labor-intensive and time-consuming. Although several approaches for automatic sleep stage classification have been proposed, no automatic pipeline for detecting a specific mouse phenotype has yet been developed. Here, we present a fully automated pipeline for estimating the probability of Narcolepsy Type 1 (NT1) in the hypocretin-tTA;TetO-Diphteria toxin A (DTA) mouse model using unlabeled electroencephalographic (EEG) and electromyographic (EMG) data. The pipeline is divided into three modules: (1) automatic sleep stage classification, (2) feature extraction, and (3) phenotype classification. We trained two automatic sleep stage classifiers, UsleepEEG and UsleepEMG, using data from 83 wild-type (WT) mice. We next computed features such as EEG spectral power bands, EMG root mean square, and bout metrics from 11 WT and 19 DTA mice. The features were used to train an L1-penalized logistic regression classifier in a Leave-One-Subject-Out approach, achieving an accuracy of 97%. Finally, we validated the pipeline in a held-out dataset of EEG/EMG recordings at four different timepoints during disease development in seven DTA mice, finding that the pipeline captured disease progression in all mice. While our pipeline generalizes well to data from other laboratories, it is sensitive to artifacts, which should be considered in its application. With this study, we present a pipeline that facilitates a fast assessment of NT1 probability in the DTA model and thus can accelerate large-scale evaluations of NT1 treatments.

Event-related potentials (ERP) are measurements of brain activity with wide applications in basic and clinical neuroscience, that are typically estimated using the average of many trials of electroencephalography signals (EEG) to sufficiently reduce noise and signal variability. We introduce EEG2ERP, a novel uncertainty-aware autoencoder approach that maps an arbitrary number of EEG trials to their associated ERP. To account for the ERP uncertainty we use bootstrapped training targets and introduce a separate variance decoder to model the uncertainty of the estimated ERP. We evaluate our approach in the challenging zero-shot scenario of generalizing to new subjects considering three different publicly available data sources; i) the comprehensive ERP CORE dataset that includes over 50,000 EEG trials across six ERP paradigms from 40 subjects, ii) the large P300 Speller BCI dataset, and iii) a neuroimaging dataset on face perception consisting of both EEG and magnetoencephalography (MEG) data. We consistently find that our method in the few trial regime provides substantially better ERP estimates than commonly used conventional and robust averaging procedures. EEG2ERP is the first deep learning approach to map EEG signals to their associated ERP, moving toward reducing the number of trials necessary for ERP research. Code is available at https://github.com/andersxa/EEG2ERP

This study is concerned with establishing a means to generate better methods to analyse and learn about task design for digital learning environments. Specifically, we utilise data consisting of over 2 million unique answers from a popular Danish digital learning environment, matematikfessor.dk, to solve 892 unique tasks dealing with linear equations. Utilising the Multinomial Infinite Relational Model (MIRM), which can account for extensive didactical coding of the five most popular answers to each of the 892 tasks, we successfully co-clustered students and tasks into groups for further analysis. The results showed that the analysis of these clusters of tasks can provide access to valuable information on the difficulties students in four respective groups face and what kind of specific tasks and knowledge pertinent to what types of tasks actually affect students' problems or difficulties anticipated by the task designer.

Archetypal analysis (AA) is a matrix decomposition method that identifies distinct patterns using convex combinations of the data points denoted archetypes with each data point in turn reconstructed as convex combinations of the archetypes. AA thereby forms a polytope representing trade-offs of the distinct aspects in the data. Most existing methods for AA are designed for continuous data and do not exploit the structure of the data distribution. In this paper, we propose two new optimization frameworks for archetypal analysis for binary data. i) A second order approximation of the AA likelihood based on the Bernoulli distribution with efficient closed-form updates using an active set procedure for learning the convex combinations defining the archetypes, and a sequential minimal optimization strategy for learning the observation specific reconstructions. ii) A Bernoulli likelihood based version of the principal convex hull analysis (PCHA) algorithm originally developed for least squares optimization. We compare these approaches with the only existing binary AA procedure relying on multiplicative updates and demonstrate their superiority on both synthetic and real binary data. Notably, the proposed optimization frameworks for AA can easily be extended to other data distributions providing generic efficient optimization frameworks for AA based on tailored likelihood functions reflecting the underlying data distribution.

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.

Basal insulin has been and remains a common and cost-effective intensification step from insufficient oral antidiabetic drug (OAD) treatment for people with type 2 diabetes (T2D), but individualized intensification alternatives are rapidly increasing. Recently, decision support tools to assist healthcare professionals based on machine learning (ML) algorithms are becoming more popular. By means of ML, the aim of this pilot study is to explore to what extent patient characteristics and continuous glucose monitoring (CGM) data enhance the ability to predict a successful basal insulin treatment outcome beyond what can be predicted based on hemoglobin A1C (HbA1c) alone at treatment initiation. Clinical data were acquired from four different trials with a total of 222 poorly regulated (HbA1c ≥ 7% ) patients with T2D on OAD initiating basal insulin treatment. HbA1c, patient characteristics, and consensus CGM metrics (based on three days) were available and systematically added as input to three classification models, respectively, based on logistic regression and Gaussian process (GP) classification with linear and both linear and nonlinear kernels. Classification models predicted a binarized HbA1c value after six months as either acceptable (HbA1c < 7%) or suboptimal (HbA1c≥7%) using a repeated stratified cross-validation setup. The consensus metrics based on only three days of CGM show a trend towards slightly improved performance when added on top of HbA1c. However, it appears difficult to accurately predict a binarized HbA1c outcome based on the considered patient information to a satisfactory level for clinical use. Future research should consider the outlined limitations associated with this study and suggested considerations for improvement. However, this pilot study can be considered an initial attempt towards leveraging the potential of ML and CGM data for personalised and cost-effective treatment decision-support for basal insulin initiation.

Deep learning-based single-channel speaker separation has improved significantly in recent years largely due to the introduction of the transformer-based attention mechanism. However, these improvements come at the expense of intense computational demands, precluding their use in many practical applications. As a computationally efficient alternative with similar modeling capabilities, Mamba was recently introduced. We propose SepMamba, a U-Net-based architecture composed primarily of bidirectional Mamba layers. We find that our approach outperforms similarly-sized prominent models - including transformer-based models - on the WSJ0 2-speaker dataset while enjoying a significant reduction in computational cost, memory usage, and forward pass time. We additionally report strong results for causal variants of SepMamba. Our approach provides a computationally favorable alternative to transformer-based architectures for deep speech separation.

Complex behavioral and cognitive processes emerge from coordinated communication between sometimes disparate brain regions, implying a systems-level dynamic synchronization of underlying neural signals. This study presents approaches to multivariate mixture modeling of functional brain imaging data for analyzing phase coherence networks for human brain macroscale dynamic functional connectivity. We show that 1) the complex domain is required to analyze phase coherence in its entirety, 2) statistical models for complex-valued phase coherence, particularly the complex angular central gaussian (ACG) distribution, greatly exceeds performance over models for time-series data, rank-2 cosine phase coherence maps, or the leading eigenvector of cosine phase coherence maps (i.e., LEiDA), 3) methods should account for the inherent anisotropy of the brain's interconnections. We emphasize the need to utilize models that account for the manifold on which the data reside, and show that the proposed models provide valuable information about intrinsic functional connectivity networks and can easily distinguish task-related brain function. We provide an open-source, Python-based toolbox ("Phase Coherence Mixture Modeling" (PCMM): github.com/anders-s-olsen/PCMM) to facilitate and promote implementation of these models. ### Competing Interest Statement The authors have declared no competing interest.