• Tremor differentiation model validated across hospitals and equipment, demonstrating real-world clinical generalizability. • Multi-modal EMG/accelerometer framework: 98 % internal accuracy, 79 % external test ROC-AUC. • Practical expert system ready for clinical deployment with minimal preprocessing and robust performance across recording conditions. Despite distinct pathophysiologies, tremor due to Parkinson’s disease and essential tremor are commonly misdiagnosed due to overlapping symptoms, hindering clinical intervention. Digital phenotyping with machine learning applied to peripheral sensor-based signals has shown potential. However, it lacks validation using an independent dataset or commercial medical device recordings broadly available for routine clinical use. Here, we present a scalable and generalizable diagnostic approach using features engineered from frequency, power, and non-linear phase domains combined with tree-based classification algorithms. Using data from a single hospital, our XGBoost model achieved a diagnostic specificity of 0.92, recall of 1.0, and ROC-AUC (Receiver Operating Characteristic − Area Under the Curve) of 1.0 on a held-out test set. Applying our pre-trained model to an external dataset, recorded in a different clinical setting using other devices, demonstrated strong generalizability with specificity of 0.70, recall of 0.80, and ROC-AUC of 0.79. Our findings not only outperform previous studies in predictive accuracy but also deliver clinically validated metrics that can be implemented in practice. These results highlight the feasibility of deploying affordable, widely available sensor-based diagnostics to enhance clinical accuracy and inform adaptive therapeutic interventions.

Traditional measures based solely on pairwise associations often fail to capture the complex statistical structure of multivariate data. Existing approaches for identifying information shared among $d>3$ variables are frequently computationally intractable, asymmetric with respect to a target variable, or unable to account for all the ways in which the joint probability distribution can be factorised. Here we present a systematic framework based on lattice theory to derive higher-order information-theoretic measures for multivariate data. Our construction uses lattice and operator function pairs, whereby an operator function is applied over a lattice that represents the algebraic relationships among variables. We show that many commonly used measures can be derived within this framework, yet they fail to capture all interactions for $d>3$, either because they are defined on restricted sublattices, or because the use of the KL divergence as an operator function, a typical choice, leads to undesired disregard of groups of interactions. To fully characterise all interactions among $d$ variables, we introduce the Streitberg Information, which is defined over the full partition lattice and uses generalised divergences (beyond KL) as operator functions. We validate the Streitberg Information on synthetic data, and illustrate its application in detecting complex interactions among stocks, decoding neural signals, and performing feature selection in machine learning.

Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisations of $d$ variables. Our tests eliminate the need for permutation-based approximations by leveraging V-statistics and a novel cross-centring technique to yield test statistics with a standard normal limiting distribution under the null. We present implementations of the tests and showcase their efficacy and scalability through synthetic datasets. We also show applications inspired by causal discovery and feature selection, which highlight both the importance of high-order interactions in data and the need for efficient computational methods.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds, appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Electroencephalogram (EEG) signals have gained widespread use in medical applications, and the utilization of EEG signals as a biometric feature for user identification systems in brain-computer interface systems has recently garnered significant attention. This paper presents a deep learning framework that uses a deep residual neural network (ResNet) for the identification of distinct individuals based on their EEG signals. The proposed framework utilizes continuous wavelet transform to convert one-dimensional EEG signals into two-dimensional spatial images. By incorporating both the frequency and time characteristics of the EEG signals, this model effectively considers and analyses the intricate details present in the data, leading to improved performance. The ResNet model considers the interdependencies between different time instances of the EEG signals. These unique features, collectively, provide sufficient discriminative information to accurately identify individuals. The proposed method achieved an exceptional classification accuracy of 99.73% and an equal error rate of 0.0041 for 64 channels within 109 individuals. The results illustrate the superiority of the proposed method over existing approaches.

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualization tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithm. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed, and signed graphs and to include other user-defined quality functions.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of $d$-order ($d \geq 2$) interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of $d$-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.