CAST：基于简单集的因果传输用于分布值时间序列
CAST: Causal Anchored Simplex Transport for Distribution-Valued Time Series
AI总结：
该研究提出CAST方法，通过因果锚定简单集传输来处理分布值时间序列的因果预测，解决了分布传输中的结构性失效问题，并在多个基准测试中表现出色。
摘要：
许多面向决策的随机系统是通过聚合分布而非标量轨迹观测的：队列占用、移动份额、公共卫生混合、发电源份额、生态组成和空气质量严重程度剖面都生活在概率简单集上并随时间演变。我们研究这些分布值时间序列的因果（在线）预测，并认为过渡算子本身应围绕简单集进行结构化。我们引入CAST（因果锚定简单集传输），一种 successor-local 操作符，它（i）从因果上下文中检索经验后继，（ii）通过持久锚稳定它们，（iii）在有序支持上应用有界的局部随机传输；每一步都通过构造保持简单集。我们识别出一种结构性失效模式，即潜在的转换核别名，其中相似的观测分布在不同的上下文制度下演变不同，且证明任何仅依赖于别名总结的预测者都会遭受不可约的加权Jensen-Shannon超额风险下界，而CAST假设类包含制度-aware的贝叶斯后继；对于有序支持，当传输后继位于无传输锚壳体外时，额外存在Pinsker分离。在覆盖生态、能源、饮食、死亡率、就业、空气质量、恶劣天气、移动和G/G/1，G_t/G/1队列占用的11个公共和模拟基准上，CAST在一步KL（1.27）和自回归滚动JSD（1.91）上获得最佳平均排名，战胜了广泛的统计、组成、递归、卷积和Transformer基线集，并在所有11个部分中取得前两名的离线KL。组件消融和受控合成别名实验验证了理论。
英文摘要：
Many decision-facing stochastic systems are observed through aggregate distributions rather than scalar trajectories: queue occupancies, mobility shares, public-health mixtures, generation-source shares, ecological compositions, and air-quality severity profiles all live on the probability simplex and evolve over time. We study causal (online) forecasting for these distribution-valued time series and argue that the transition operator itself should be structured around the simplex. We introduce CAST (Causal Anchored Simplex Transport), a successor-local operator that (i) retrieves empirical successors from causal context, (ii) stabilizes them with a persistence anchor, and (iii) applies a bounded local stochastic transport on ordered supports; every stage preserves the simplex by construction. We identify a structural failure mode, latent transition-kernel aliasing, where similar observed distributions evolve differently under different contextual regimes, and prove that any forecaster depending only on an aliased summary incurs an irreducible weighted Jensen-Shannon excess-risk lower bound, while the CAST hypothesis class contains the regime-aware Bayes successor; for ordered supports an additional Pinsker separation holds whenever the transported successor lies outside the no-transport anchor hull. On eleven public and simulated benchmarks spanning ecology, energy, diet, mortality, employment, air quality, severe weather, mobility, and G/G/1, G_t/G/1 queue occupancy, CAST attains the best average rank on both one-step KL (1.27) and autoregressive rollout JSD (1.91), winning 8/11 sections on each metric against a broad statistical, compositional, recurrent, convolutional, and Transformer baseline set, and top-2 on all 11 sections for offline KL. Component ablations and a controlled synthetic aliasing experiment corroborate the theory.
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