一种可统一处理多种场景的置信集构建方法，支持非独立同分布数据和任意时刻有效性。
Confidence Estimation via Sequential Likelihood Mixing
- 基于序列似然混合构造置信集，统一了多类最新研究
- 在序列线性回归中实现更紧的置信区间，证明过程简化
- 适用于变分推断等近似方法，模型误设下仍保覆盖概率
我们提出一种基于序列似然混合的通用置信集构建框架。该框架建立在序列分析的经典结果之上，统一了若干近期研究工作，并揭示了序列混合、贝叶斯推断与在线估计中的后悔不等式之间的基本联系。该方法适用于任意可实现的似然函数族，支持非独立同分布数据和任意时刻有效性。同时，框架可无缝集成变分推断、采样方法等标准近似推断技术，且在模型误设情形下仍保持可证明的覆盖保证。通过该框架，我们推导出经典场景（如序列线性回归和稀疏估计）中更紧的置信序列，并给出了简化的证明。
原文摘要 · Abstract (English)
We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and establish fundamental connections between sequential mixing, Bayesian inference and regret inequalities from online estimation. The framework applies to any realizable family of likelihood functions and allows for non-i.i.d. data and anytime validity. Moreover, the framework seamlessly integrates standard approximate inference techniques, such as variational inference and sampling-based methods, and extends to misspecified model classes, while preserving provable coverage guarantees. We illustrate the power of the framework by deriving tighter confidence sequences for classical settings, including sequential linear regression and sparse estimation, with simplified proofs.
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