标签定义时间尺度：模型表现受限于数据采集方式而非自身能力
The Label Defines the Timescale: Trait-State Limits of Temporal-Aggregate Learning
- 用贝叶斯风险分解标签方差，区分个体特质与短期状态影响
- 发现均值标签依赖普通相关时间，占用时间标签依赖多阶相关时间
- 重复采样快速饱和，分散观测更有效，适合长期追踪研究
机器学习基准常将长期时间窗口的标签与单次或少数短时输入配对。其性能上限可能源于数据采集协议而非模型容量。本文研究形式为 $Θ_{g,T}=T^{-1}igint_0^T g\{Z(t)\}\mathrm{d}t$ 的标签，当潜在高斯过程包含稳定个体特质和相关个体内状态时，推导出协议相关的贝叶斯风险恒等式。首先，标签方差分解为 $O(1)$ 的特质分量与 $O(T^{-1})$ 的状态分量，解释为何快照可预测横断面差异但难追踪个体变化。其次，任务决定的有效时间跨度不同：均值标签取决于普通相关时间，而占用时间标签依赖整个高阶相关时间谱。第三，当特质处于阈值时，状态驱动的占用标签方差最大；远离该边界时，窗口效率衰减缓慢。在相同段数预算下，精确风险与蒙特卡洛实验显示，单一时点重复采样迅速饱和，而时间分散的观测持续提升状态可解释性。特质上限仅需常规重测数据，状态上限则需短延迟时间校准。结果揭示架构限制与协议限制的区别，表明标签本身而非时长或片段数定义了关键时间尺度。
原文摘要 · Abstract (English)
Machine-learning benchmarks often pair a label that aggregates a long temporal horizon with input observed through one or a few short windows. Their apparent performance ceiling may therefore be an acquisition-protocol ceiling rather than a model-capacity ceiling. We study labels of the form $Θ_{g,T}=T^{-1}\int_0^T g\{Z(t)\}\,\mathrm{d}t$ when the latent Gaussian process contains both a stable individual trait and a correlated within-individual state. An exact protocol-conditioned Bayes-risk identity provides a common tool. First, we decompose label variance into an $O(1)$ trait component and an $O(T^{-1})$ state component, explaining why a snapshot can retain cross-sectional predictability while poorly tracking within-person change. Second, we derive task-dependent effective temporal spans: mean labels depend on the ordinary correlation time, whereas occupation-time labels depend on an entire spectrum of higher-order correlation times. Third, state-driven occupation-label variance is maximal when the stable trait lies at the threshold; window efficiency decays much more slowly away from that boundary. Under an equal segment budget, exact risks and Monte Carlo experiments show that repeated segments at one time rapidly saturate, whereas temporally dispersed observations continue to increase state explainability. The trait ceiling uses quantities available from ordinary test-retest data; only the state ceiling requires short-lag temporal calibration. The results distinguish architectural limits from protocol limits and show that the label, rather than duration or segment count alone, defines the relevant timescale.
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