用在线学习方法构建广义线性模型的置信集，统一已有成果并提出新类型。
Confidence Sequences for Generalized Linear Models via Regret Analysis
- 将参数置信集问题转化为在线概率预测中的低遗憾问题。
- 通过算法输出构造中心在最大似然估计的置信集，保证高概率上界。
- 适用于需要动态置信区间或新置信集形式的研究者。
我们提出一种通过减少到序列预测来构建统计模型参数置信集的方法。核心观察是：对任意广义线性模型（GLM），可构造一个相应的序列概率分配博弈，使得在该博弈中实现低遗憾，即意味着真实参数的超额似然具有高概率上界。这促使我们发展出称为‘在线转置信集’的方案，将统计证明问题转化为算法设计问题。研究了两种转换方式：1）分析型转换，仅需证明存在低遗憾算法，置信集以最大似然估计为中心；2）算法型转换，主动利用在线算法输出构造置信集（可中心于自适应构造的点估计）。该方法统一了现有最优置信集构造，并首次提出了若干文献中未见的新类型置信集。
原文摘要 · Abstract (English)
We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any generalized linear model (GLM), one can construct an associated game of sequential probability assignment such that achieving low regret in the game implies a high-probability upper bound on the excess likelihood of the true parameter of the GLM. This allows us to develop a scheme that we call online-to-confidence-set conversions, which effectively reduces the problem of proving the desired statistical claim to an algorithmic question. We study two varieties of this conversion scheme: 1) analytical conversions that only require proving the existence of algorithms with low regret and provide confidence sets centered at the maximum-likelihood estimator 2) algorithmic conversions that actively leverage the output of the online algorithm to construct confidence sets (and may be centered at other, adaptively constructed point estimators). The resulting methodology recovers all state-of-the-art confidence set constructions within a single framework, and also provides several new types of confidence sets that were previously unknown in the literature.
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