Variational Bayes methods approximate the posterior density by a family of tractable distributions and use optimisation to estimate the unknown parameters of the approximation. 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 of normals, which is implemented using the 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. Each example shows that the proposed variational approximation is much more accurate than the corresponding Gaussian copula and a mixture of normals variational approximations.

翻译：易变贝亚斯方法与可移动分布式分布式组合的后方密度相近,并使用优化方法估计近似值的未知参数。当精确推论难以解决或非常昂贵时,易变近似值是有用的。我们的文章根据正常物混合物的交织体开发了灵活的变近值,采用自然梯度和减少差异的方法加以实施。该方法的功效通过使用模拟和真实数据集来模拟近似多式、斜形和重尾尾次分布式的近似数据集加以说明,包括对巴伊西亚深饲料向神经网络回归模型的应用。每个例子都显示,拟议的变近度比相应的高斯氏相和正常变近物混合法要精确得多。