A Unified Dirichlet Framework for Spatial-Temporal Risk Assessment
中文标题: 时空风险评估的统一Dirichlet框架
英文摘要
The paper proposes a unified Dirichlet framework for spatial-temporal risk assessment, proving that a single Dirichlet posterior per cell with an additive evidence-update rule is the unique update–predictor pair satisfying four axioms and is limit-equivalent to seven classical methods (AHP, Dempster–Shafer, Hawkes, kernel density estimation, etc.). The framework simultaneously yields a severity score and threat characterization from the posterior. On a large-scale benchmark of 41 regions × 10,000 cells × 365 days, it achieves an one-vs-rest AUROC of 0.666 and severity AUROC of 0.725, statistically significantly outperforming 15 structured baselines (Holm-corrected p < 10⁻²⁶), while delivering threat characterization accuracy of 79.1%—compared to only 0–26% for competitors with comparable AUROC. Real-world transfer to 1.69M London and 119K Chicago crime events preserves the dual-output advantage, and a pre-registered specialization experiment confirms the operational configuration beats the matched specialist. The method requires 3.6× less memory than seven independent models (128 vs. 464 bytes/cell) at 41K signals/sec throughput.
中文摘要
本文提出了一种时空风险评估的统一Dirichlet框架，证明了每个空间单元维护的单个Dirichlet后验及其加性证据更新规则是满足四个公理的唯一更新-预测对，并与七种经典方法（AHP、Dempster–Shafer、Hawkes过程等）极限等价。该框架从后验中同时输出危险严重性评分和威胁特征描述。在大规模基准测试（41个区域×10,000单元×365天）中，它的one-vs-rest AUROC为0.666，严重度AUROC为0.725，统计显著优于15个结构化基线（Holm校正p < 10⁻²⁶），威胁特征描述准确率达到79.1%，而AUROC相当的竞争方法仅为0–26%。向169万伦敦和11.9万芝加哥犯罪事件的真实迁移保持了双重输出优势，预注册专业化实验证实运行配置优于匹配的专用方法。该方法仅需七个独立模型3.6分之一的内存（每单元128字节 vs 464字节），吞吐量达41K信号/秒。
关键要点
The Dirichlet posterior is theoretically proven to be the unique update–predictor pair satisfying linearity, scale-invariance, temporal continuity, and spatial locality axioms, and is limit-equivalent to AHP, Dempster–Shafer, Hawkes, kernel density, and three other classical methods.
理论上证明Dirichlet后验是满足线性性、尺度不变性、时间连续性、空间局部性四个公理的唯一更新-预测对，并与AHP、Dempster–Shafer、Hawkes、核密度等七种经典方法极限等价。
The unified model provides dual outputs: a severity score and threat characterization from a single posterior cell, addressing both 'how dangerous' and 'what threats dominate'.
统一模型从单一后验单元同时给出严重性评分和威胁特征描述两个输出，解答“多危险”和“主导威胁是什么”。
On a large benchmark with 5 random seeds and 205 total evaluations, it achieves one-vs-rest AUROC 0.666 and severity AUROC 0.725, significantly outperforming 15 structured baselines, with threat characterization accuracy 79.1% versus 0–26% for competitors.
在包含5个随机种子共205项评估的大规模基准上，取得one-vs-rest AUROC 0.666和严重度AUROC 0.725，显著优于15个结构化基线，威胁特征描述准确率79.1%，而竞争方法仅0–26%。
Real-world crime event datasets in London (1.69M) and Chicago (119K) validate the dual-output benefit; a pre-registered experiment shows the operational configuration significantly beats the specialist (p < 0.01).
伦敦（169万）和芝加哥（11.9万）犯罪事件真实数据验证了双输出优势；预注册实验显示运行配置显著优于专用方法（p < 0.01）。
The framework is memory-efficient, using 128 bytes per cell versus 464 bytes for seven independent models, and processes 41K signals per second.
框架内存占用低，每单元128字节 vs 七个独立模型需464字节，处理速度达41K信号/秒。