The Variational Gaussian Approximation Revisited
The Variational Gaussian Approximation Revisited
复制标题
DOI：
10.1162/neco.2008.08-07-592
复制
发表时间：
2009-03-01
影响因子：
2.9
通讯作者：
Archambeau, Cedric
中科院分区：
文献类型：
--
作者：
Opper, Manfred;Archambeau, Cedric
在机器学习社区中，多变量高斯的后验分布的变分近似与因子分解分布的相应近似相比要少得多。这是一个很好的理由：高斯近似通常受到O（N-2）个待优化的变分参数的困扰，N是随机变量的数目。在这封信中，我们讨论了拉普拉斯和变分近似之间的关系，我们表明，对于高斯先验和因子分解似然模型，变分参数的数量实际上是O（N）。该方法被应用到高斯过程回归与非高斯似然。
The variational approximation of posterior distributions by multivariate gaussians has been much less popular in the machine learning community compared to the corresponding approximation by factorizing distributions. This is for a good reason: the gaussian approximation is in general plagued by an O(N-2) number of variational parameters to be optimized, N being the number of random variables. In this letter, we discuss the relationship between the Laplace and the variational approximation, and we show that for models with gaussian priors and factorizing likelihoods, the number of variational parameters is actually O(N). The approach is applied to gaussian process regression with nongaussian likelihoods.