Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for EMA data, as it is irregularly sampled, noisy, and partially observed. But SDE-based models suffer from two key limitations. (a) These models often violate domain constraints, undermining scientific validity and clinical trust of the model. (b) Training is numerically unstable without ad hoc fixes (e.g. oversimplified dynamics) that are ill-suited for high-stakes applications. Here, we develop a novel class of expressive SDEs whose solutions are provably confined to a prescribed compact polyhedral state space, matching the domains of EMA data. In this work, (1) we show why chain-rule based constructions of SDEs on compact domains fail, theoretically and empirically; (2) we derive constraints on drift and diffusion for general and stationary SDEs so their solutions remain in the desired state space; and (3), we introduce a parameterization that maps arbitrary (neural or expert-given) dynamics into constraint-satisfying SDEs. On several real EMA datasets, including a large suicide-risk study, our parameterization improves forecasts and optimization dynamics over standard latent neural SDE baselines. These contributions pave the way for principled, trustworthy continuous-time models of suicide risk and other clinical time series and extend applications of SDE-based methods (e.g. diffusion models) to domains with hard state constraints.

翻译：生态瞬时评估（EMA）研究能够通过智能手机收集关于自杀想法和行为（STBs）的高频自我报告数据。潜在随机微分方程（SDEs）是处理EMA数据的一类有前景的模型，因为这类数据通常具有不规则采样、含噪声且部分可观测的特点。然而，基于SDE的模型存在两个关键局限性：（a）模型常违反状态空间的域约束，损害了模型的科学有效性和临床可信度；（b）训练过程在数值上不稳定，除非采用针对高风险应用场景不适用的事后修正（例如过度简化的动力学）。为此，我们发展了一类新型表达性SDEs，其解可被严格约束在预定义的紧致多面体状态空间内，恰好匹配EMA数据的域特性。本文中，（1）我们从理论和实证角度揭示了基于链式法则构造紧致域上的SDEs为何失败；（2）推导了一般SDE和平稳SDE的漂移项与扩散项需满足的约束条件，以确保其解始终处于目标状态空间；（3）提出了一种参数化方法，可将任意（基于神经网络的或专家定义的）动力学映射为满足约束的SDEs。在多个真实EMA数据集（包括一项大规模自杀风险研究）上，我们的参数化方法在预测性能和优化动力学方面均优于标准潜在神经SDE基线模型。这些贡献为构建原则性、可信赖的自杀风险及其他临床时间序列连续时间模型铺平了道路，并拓展了基于SDE的方法（如扩散模型）在具有硬状态约束领域的应用。