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 Pólya-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.

翻译：本文提出了一种适用于贝叶斯计数响应回归类模型的变分推断方法，该方法具有凸优化与闭式更新等优良特性。凸优化特性保证了拟合算法的数值稳定性，而闭式更新特性使该方法兼具快速计算与易于实现的优势。该方法的本质在于：对负二项似然函数采用Pólya-Gamma数据增强技术，对形状参数采用有限值先验分布，并采用结构化平均场变分贝叶斯框架。本方法适用于广义计数响应场景，为具体说明，我们聚焦于半参数回归模型类中的广义线性混合模型，并阐述了实时拟合的实现方案。