用新模型直接学习时间序列间的相互影响，提升预测精度。
A Set-Sequence Model for Time Series
- 用集合-序列结构同时捕捉个体动态与整体关系
- 在真实金融数据上实现更高夏普比率和更优分类性能
- 适合处理数量可变、对齐不严的多序列预测任务
科学与工程中的许多预测问题，如金融与经济领域，涉及大量个体时间序列，每个单位（如贷款、股票或客户）受自身特征和潜在跨单元动态影响。尽管序列模型已提升单个单位的时序预测能力，跨单元效应通常仍依赖人工设计的汇总特征。我们提出Set-Sequence模型，直接学习跨单元结构，增强表达能力并避免手工特征工程。在每个时间步，一个排列不变的集合模块对单位集合进行总结；随后，序列模块基于单位特征和学习到的摘要，建模每个单位的动态。该架构支持非对齐序列，推理时可处理不同数量的单位，能与标准序列骨干（如Transformer）集成，且跨单元规模呈线性扩展。在合成传染任务及两个大规模真实应用——股权组合优化与贷款风险预测中，Set-Sequence显著优于强基线，带来更高的夏普比率、更优的AUC值，并生成可解释的跨单元摘要。
原文摘要 · Abstract (English)
Many prediction problems across science and engineering, especially in finance and economics, involve large cross-sections of individual time series, where each unit (e.g., a loan, stock, or customer) is driven by unit-level features and latent cross-sectional dynamics. While sequence models have advanced per-unit temporal prediction, capturing cross-sectional effects often still relies on hand-crafted summary features. We propose Set-Sequence, a model that learns cross-sectional structure directly, enhancing expressivity and eliminating manual feature engineering. At each time step, a permutation-invariant Set module summarizes the unit set; a Sequence module then models each unit's dynamics conditioned on both its features and the learned summary. The architecture accommodates unaligned series, supports varying numbers of units at inference, integrates with standard sequence backbones (e.g., Transformers), and scales linearly in cross-sectional size. Across a synthetic contagion task and two large-scale real-world applications, equity portfolio optimization and loan risk prediction, Set-Sequence significantly outperforms strong baselines, delivering higher Sharpe ratios, improved AUCs, and interpretable cross-sectional summaries.
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