论文标题
精密矩阵上的歧管高斯差异贝叶斯
Manifold Gaussian Variational Bayes on the Precision Matrix
论文作者
论文摘要
我们提出了一种在复杂模型中的变异推理（VI）的优化算法。我们的方法依赖于自然梯度更新，其中变分空间是Riemann歧管。我们为高斯变异推断开发了一种有效的算法，其更新满足了对变异协方差矩阵的积极确定约束。我们在精密矩阵（MGVBP）解决方案上的歧管高斯变异贝叶斯提供了简单的更新规则，可以简单地实现，并且使用Precision矩阵参数化具有显着的计算优势。由于其黑盒性质，MGVBP在复杂模型中成为VI的现成解决方案。在五个数据集中，我们从经验上验证了我们在不同的统计和计量经济学模型上的可行方法，并讨论了其在基线方法方面的性能。
We propose an optimization algorithm for Variational Inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our Manifold Gaussian Variational Bayes on the Precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the use of the precision matrix parametrization has a significant computational advantage. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models. Over five datasets, we empirically validate our feasible approach on different statistical and econometric models, discussing its performance with respect to baseline methods.
