标题： 广义线性模型的信心序列通过遗憾分析得到 显示英文标题

标题： Confidence Sequences for Generalized Linear Models via Regret Analysis

摘要： 我们提出了一种通过归约为顺序预测来构建统计模型参数置信集的方法。我们的关键观察是，对于任何广义线性模型（GLM），可以构造一个相关的顺序概率分配博弈，使得在博弈中获得低遗憾意味着GLM的真实参数的超额似然性的高概率上界。这使我们能够开发一种称为“在线到置信集转换”的方案，该方案有效地将证明所需统计断言的问题归结为算法问题。我们研究了这种转换方案的两种类型：1）分析转换，只需要证明存在具有低遗憾的算法，并提供以最大似然估计为中心的置信集；2）算法转换，主动利用在线算法的输出来构造置信集（并且可能以其他自适应构造的点估计为中心）。由此产生的方法在一个框架内恢复了所有最先进的置信集构造，并提供了文献中之前未知的几种新类型的置信集。 显示英文摘要

摘要： 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.