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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Capturing the Curve: Functional Data Analysis for Validat...
[Submitted on 27 May 2026] · 2026-05-28 · via stat updates on arXiv.org

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Abstract:Digital health technologies enable high-frequency collection of data in near-continuous time and capture rich information about the health of individuals. The raw data collected by these devices often have a hierarchical functional structure: repeated physiological functions are observed over time and on multiple time scales (seconds, days, weeks). While many summaries can be derived from digital data, typically, only a small subset of pre-defined scalars is validated as outcome measures in clinical trials. We explore data-driven summaries based on between-subject scores from Multilevel Functional Principal Component Analysis (MFPCA), which are low-dimensional representations of functional data with robust statistical properties. Specifically, we compute MFPCA projection scores with respect to a reference population, summarising how individuals differ from the dominant directions of variation at each hierarchical level. Through a simulation study based on smartwatch electrocardiogram (ECG) signals, we compare MFPCA scores with pre-specified summaries in terms of validation criteria, including test-retest reliability and known-groups discrimination. We demonstrate that MFPCA scores generally have high reliability and can discriminate between groups across simulated scenarios of change. This offers an advantage when digital tools enable the measurement of novel physiological signals and the characteristics of the change are not yet defined. Finally, using knee flexion-extension data from individuals living with Parkinson's disease, we demonstrate that one of the MFPCA scores more strongly correlates with established gold-standard metrics and can detect clinical change, compared to a pre-specified scalar. We conclude that MFPCA-derived scores retain more information than typical outcome measures and open the door to using learning representation strategies in clinical trial settings.

Submission history

From: Mia Tackney [view email]
[v1] Wed, 27 May 2026 11:48:45 UTC (3,597 KB)