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, especially 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 this subclass provides increased flexibility and accuracy in approximating the joint posterior density in a variety of 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.

翻译：高斯分布广泛用于贝叶斯变分推断中近似难以处理的后验密度，但捕捉偏态的能力可显著提升近似精度，尤其在数据或先验信息不足时。本文研究基于独立标准化单变量偏态正态分布仿射变换构造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近似的局限性，阐述该子类如何在多种应用中为联合后验密度的近似提供更强的灵活性与精度。证据下界采用随机梯度上升优化，其中推导了解析的自然梯度更新。我们还展示了偏态正态参数的最大似然估计问题如何在随机变分推断中类似出现，并可通过中心化参数化加以解决。