Search arXivSearch

arXiv · 1907.08577

Learning Multimorbidity Patterns from Electronic Health Records Using Non-negative Matrix Factorisation

Abstract

Multimorbidity, or the presence of several medical conditions in the same individual, has been increasing in the population, both in absolute and relative terms. However, multimorbidity remains poorly understood, and the evidence from existing research to describe its burden, determinants and consequences has been limited. Previous studies attempting to understand multimorbidity patterns are often cross-sectional and do not explicitly account for multimorbidity patterns' evolution over time; some of them are based on small datasets and/or use arbitrary and narrow age ranges; and those that employed advanced models, usually lack appropriate benchmarking and validations. In this study, we (1) introduce a novel approach for using Non-negative Matrix Factorisation (NMF) for temporal phenotyping (i.e., simultaneously mining disease clusters and their trajectories); (2) provide quantitative metrics for the evaluation of disease clusters from such studies; and (3) demonstrate how the temporal characteristics of the disease clusters that result from our model can help mine multimorbidity networks and generate new hypotheses for the emergence of various multimorbidity patterns over time. We trained and evaluated our models on one of the world's largest electronic health records (EHR), with 7 million patients, from which over 2 million where relevant to this study.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Abdelaali Hassaine, Dexter Canoy, Jose Roberto Ayala Solares, Yajie Zhu, Shishir Rao, Yikuan Li, Mariagrazia Zottoli, Kazem Rahimi, Gholamreza Salimi-Khorshidi. 2019-11-18. Learning Multimorbidity Patterns from Electronic Health Records Using Non-negative Matrix Factorisation. https://arxiv.org/abs/1907.08577

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Optimal Learning Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay

We study optimal learning rate (LR) schedules under the functional scaling law (FSL) framework (Li et al., 2025), which decomposes training dynamics into signal learning and noise forgetting. In power-law kernel regression, these two components are governed by a source exponent $s>0$ and a capacity exponent $q>1$, respectively, with smaller $s$ corresponding to harder tasks. For a fixed training horizon $N$, we characterize the schedules that minimize the final-step loss under a stability constraint and reveal a sharp phase transition. In the easy-task regime $s>1-1/q$, the optimal schedule follows power decay from the beginning of training; in the hard-task regime $s<1-1/q$, it becomes warmup-stable-decay (WSD)-like (Hu et al., 2024), staying at the largest admissible LR for most of training before a final decay. In both regimes, the decay exponent is $2q-1$: task difficulty determines when to decay, while model capacity determines how to decay. Beyond the exact optimum, we study fractional schedules, whose shape is defined over relative training progress. We show that precise tuning of the decay shape is often unnecessary: a broad class of profiles attains the optimal convergence rate, while overly slow terminal decay leads to schedule-induced capacity saturation. Finally, for one-pass SGD in kernel regression, FSL-motivated power-decay schedules achieve optimal last-iterate rates. Experiments support the theoretical predictions and the task-dependent transition between early and delayed decay.

stat.ML

Differential Privacy of Gaussian Process Posterior Sampling

We study the privacy of releasing functional posterior sample paths from a Gaussian process (GP) when the entire training set including covariates and responses is private. Unlike standard differential-privacy (DP) mechanisms that inject external noise, posterior sampling is intrinsically random and we show that this randomness provides useful privacy guarantees. We derive Rényi-DP guarantees separating privacy leakage through the posterior mean from a distinct channel induced by the data-dependent posterior covariance. The analysis identifies effective ridge regularisation and covariance scale as the principal privacy-controlling quantities and yields sharper guarantees in several regimes of practical interest as well as extensions to repeated and adaptive releases. Membership inference attacks confirm the predicted dependence on regularisation, covariance scale and the number of released paths. Utility experiments on downstream posterior sampling tasks identify noisy observation regimes where privacy-compatible regularisation preserves useful samples. Finally we identify large-data asymptotic regime in which the privacy parameter and posterior mean-square risk vanish simultaneously, yielding privacy for free. Together, these results provide a comprehensive characterisation of privacy and utility of GP posterior sampling.

stat.ML

Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications

Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport computes both network dissimilarity and a transport plan that explains how one graph morphs into another. In this paper, we review how optimal transport compares undirected, unweighted simple graphs using three primary distances: the Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein distances. We examine the closed form of the Wasserstein distance in one dimension via node feature probability distributions, and show how the transport plans of the Wasserstein and Gromov-Wasserstein distances visualize how mass is shifted to transform one network into another. Beyond reviewing existing transport-based approaches, we establish new spectral lower and upper bounds for the Bures-Wasserstein distance and characterize the tightness of the lower bound under eigenbasis perturbations. Finally, we evaluate these distances using a synthetic network dataset for clustering and a real-world temporal network.

stat.ML