We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear predictor, eventually transformed using a bijective link, where the prediction misfit is measured using, possibly non-differentiable, loss functions. Examples include generalized linear models, quasi-likelihood models, and robust regression. To address the limitations of non-conjugate settings, we employ an efficient message passing optimization strategy under a Gaussian variational approximation of the posterior. The resulting algorithms automatically account for non-conjugate priors and non-smooth losses, without requiring model-specific data-augmented representations. Besides the general formulation, we provide closed-form updates for popular model specifications, including quantile regression and support vector machines. Overall, theoretical and empirical results highlight the effectiveness of the proposed method, demonstrating its computational efficiency and approximation accuracy as an alternative to existing Bayesian techniques.

翻译：本文提出了一种统一且易于编码的非共轭变分贝叶斯算法，用于通用贝叶斯广义混合效应模型的后验近似。具体而言，我们考虑通过线性预测变量（最终可通过双射链接函数进行变换）识别的回归模型，其中预测失配采用可能不可微的损失函数进行度量。示例包括广义线性模型、拟似然模型和稳健回归。为应对非共轭设置的限制，我们在后验的高斯变分近似下采用高效的消息传递优化策略。所得算法能自动处理非共轭先验与非光滑损失函数，无需依赖模型特定的数据增强表示。除一般性表述外，我们还为包括分位数回归和支持向量机在内的常用模型规范提供了闭式更新方案。总体而言，理论与实证结果均凸显了所提方法的有效性，其计算效率与近似精度证明了其作为现有贝叶斯技术替代方案的可行性。