Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our article develops a flexible variational approximation based on a copula of a mixture, which is implemented by combining boosting, natural gradient, and a variance reduction method. The efficacy of the approach is illustrated by using simulated and real datasets to approximate multimodal, skewed and heavy-tailed posterior distributions, including an application to Bayesian deep feedforward neural network regression models.

翻译：变分贝叶斯方法通过一族易于处理的分布族来近似后验密度，这些分布的参数通过优化进行估计。当精确推断难以实现或计算成本过高时，变分近似尤为有用。本文提出了一种基于混合分布连接函数的灵活变分近似方法，该方法结合了Boosting、自然梯度和方差缩减技术。通过使用模拟数据集和真实数据集对多模态、偏态及重尾后验分布进行近似，包括在贝叶斯深度前馈神经网络回归模型中的应用，验证了该方法的有效性。