Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior information is scarce. We study the properties of a subclass of closed skew normals constructed using affine transformation of independent standardized univariate skew normals as the variational density, and illustrate how it provides increased flexibility and accuracy in approximating the joint posterior in various applications, by overcoming limitations in existing skew normal variational approximations. The evidence lower bound is optimized using stochastic gradient ascent, where analytic natural gradient updates are derived. We also demonstrate how problems in maximum likelihood estimation of skew normal parameters occur similarly in stochastic variational inference, and can be resolved using the centered parametrization. Supplemental materials are available online.

翻译：高斯分布广泛应用于贝叶斯变分推断中以逼近难处理的后验密度，但在数据或先验信息稀缺时，容纳偏态的能力可显著提升逼近精度。本文研究了一类通过独立标准化单变量偏态正态的仿射变换构建的封闭偏态正态子类作为变分密度的性质，并通过克服现有偏态正态变分逼近的局限性，阐明其如何在各类应用中为联合后验逼近提供更强的灵活性与精度。证据下界通过随机梯度上升法进行优化，其中推导了解析自然梯度更新公式。我们同时证明了偏态正态参数极大似然估计中的问题在随机变分推断中同样存在，并可通过中心化参数化方法解决。补充材料已在线发布。