用神经微分方程建模血糖分布随时间变化，捕捉细微动态变化。
Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data
- 基于高斯混合与最大均值差异的非参数分布估计
- 在26周临床试验中检测到治疗组与对照组的分布差异
- 适合关注长期动态变化的数字健康研究者
从时序数据中建模概率分布的动态变化是多个领域（包括数字健康）的基础问题。目标是分析生物标志物（如血糖）分布如何随时间演变，以及这些变化是否反映慢性病（如糖尿病）进展。本文提出一种基于高斯混合的概率模型，捕捉连续时间随机过程的演化。方法结合最大均值差异（MMD）获得的非参数分布估计与神经常微分方程（Neural ODE），控制混合权重的时序演化。该模型具有高度可解释性，能检测细微分布偏移，且计算高效。我们在一项26周的临床试验中，将所有连续血糖监测（CGM）时间序列作为主要结果，验证了该方法在治疗组与对照组之间进行严格纵向比较的能力，揭示了传统基于汇总统计的方法通常无法捕捉的特征。
原文摘要 · Abstract (English)
Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over time and how these changes may reflect the progression of chronic diseases such as diabetes. We introduce a probabilistic model based on a Gaussian mixture that captures the evolution of a continuous-time stochastic process. Our approach combines a nonparametric estimate of the distribution, obtained with Maximum Mean Discrepancy (MMD), and a Neural Ordinary Differential Equation (Neural ODE) that governs the temporal evolution of the mixture weights. The model is highly interpretable, detects subtle distribution shifts, and remains computationally efficient. We illustrate the broad utility of our approach in a 26-week clinical trial that treats all continuous glucose monitoring (CGM) time series as the primary outcome. This method enables rigorous longitudinal comparisons between the treatment and control arms and yields characterizations that conventional summary-based clinical trials analytical methods typically do not capture.
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