论文标题
伪可能混合效应模型的非偶联变异贝叶斯
Non-conjugate variational Bayes for pseudo-likelihood mixed effect models
论文作者
论文摘要
我们提出了一种统一但简单的编码非偶联贝叶斯算法，用于通用贝叶斯通用混合效应模型的后近似。具体而言，我们考虑了由线性预测变量确定的回归模型，最终使用双线链接进行了转换，在该链接中，预测失调是使用，可能是非差异的损失函数来衡量的。示例包括通用线性模型，准类模型和鲁棒回归。为了解决非轭设置的局限性，我们采用有效的消息传递优化策略，在后部的高斯变分近似下。所得算法自动考虑了非偶联的先验和非平滑损失，而无需特定于模型的数据调节表示。除了一般公式外，我们还为流行模型规格（包括分位数回归和支持向量机）提供封闭式更新。总体而言，理论和经验结果突出了所提出的方法的有效性，证明了其计算效率和近似准确性，可作为现有贝叶斯技术的替代方法。
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.
