Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In this paper we propose a hybrid approximate method called Low-Rank Variational Bayes correction (VBC), that uses the Laplace method and subsequently a Variational Bayes correction in a lower dimension, to the joint posterior mean. The cost is essentially that of the Laplace method which ensures scalability of the method, in both model complexity and data size. Models with fixed and unknown hyperparameters are considered, for simulated and real examples, for small and large datasets.

翻译：近似推断方法如拉普拉斯方法、拉普拉斯近似以及变分方法等，在模型复杂或数据量庞大导致精确推断不可行时被广泛采用。本文提出一种名为低秩变分贝叶斯校正（Low-Rank Variational Bayes correction, VBC）的混合近似方法，该方法利用拉普拉斯方法后，在低维空间中对联合后验均值进行变分贝叶斯校正。其计算成本本质上与拉普拉斯方法相当，从而确保该方法在模型复杂度和数据规模两方面均具有良好的可扩展性。本文针对固定与未知超参数的模型，在模拟与真实案例中，对小规模及大规模数据集均进行了考察。