标题： 变分推断用于计数响应半参数回归：一种凸解 显示英文标题

标题： Variational Inference for Count Response Semiparametric Regression: A Convex Solution

摘要： 我们开发了一种用于贝叶斯计数响应回归型模型的变分推断版本，该版本具有凸性和闭式更新等优点。 凸性方面意味着数值稳定的拟合算法，而闭式方面使该方法快速且易于实现。 该方法的核心是使用负二项似然的Polya-Gamma扩充，形状参数的有限值先验以及结构化均场变分贝叶斯范式。 该方法适用于一般的计数响应情况。 为了具体起见，我们专注于半参数回归模型类别中的广义线性混合模型。 还描述了实时拟合。 显示英文摘要

摘要： We develop a version of variational inference for Bayesian count response regression-type models that possesses attractive attributes such as convexity and closed form updates. The convex solution aspect entails numerically stable fitting algorithms, whilst the closed form aspect makes the methodology fast and easy to implement. The essence of the approach is the use of P\'olya-Gamma augmentation of a Negative Binomial likelihood, a finite-valued prior on the shape parameter and the structured mean field variational Bayes paradigm. The approach applies to general count response situations. For concreteness, we focus on generalized linear mixed models within the semiparametric regression class of models. Real-time fitting is also described.