Quadratic distances on probabilities: A unified foundation

在无限域上度量离散风险：理论基础、条件五数概括与数据分析

Measuring Discrete Risks on Infinite Domains: Theoretical Foundations, Conditional Five Number Summaries, and Data Analyses

本文将平滑分位数估计量的统计推断从有限域扩展至无限域，提出新截断方法和基于bootstrap的灵活策略，利用汽车事故数据计算尾部风险条件五数概括（C5NS），证明该方法比线性插值法更准确且变异系数更低。

高斯变量二次型分布的高效且精确的近似方法

An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables

本文提出一种基于矩匹配框架的矩比率方法（MR），用于高效精确近似高斯变量二次型分布，显著提升远右尾概率精度，并适用于大数据分析中的小p值计算。

风险测度与上概率：一致性与分层

Risk Measures and Upper Probabilities: Coherence and Stratification

该研究突破经典概率论框架，系统研究谱风险测度等替代聚合泛函，借助重排不变Banach空间理论，以上概率为依据实现一致风险测度的自然分层，并验证其在实际机器学习问题中的应用价值。

On complex Gaussian random fields, Gaussian quadratic forms and sample distance multivariance

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian random fields (with possibly dependent real and complex part) and derive representation results, which allow to find efficient estimators for the moments of the associated Gaussian quadratic form. Finally, we apply these results to sample distance multivariance, which is the test statistic corresponding to distance multivariance -- a recently introduced multivari…

语言模型中Top-k解码的基础理论

Foundations of Top-$k$ Decoding For Language Models

本研究提出了一种理论框架，解释并推广了Top-k解码，展示了其在稀疏分布恢复中的有效性，并提出了新的解码策略。