Propagation Algorithms for Variational Bayesian Learning
Propagation Algorithms for Variational Bayesian Learning
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发表时间：
2000
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通讯作者：
Zoubin Ghahramani;Matthew J. Beal
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作者：
Zoubin Ghahramani;Matthew J. Beal
变分近似正成为贝叶斯学习图形模型的一个广泛的工具。我们提供了一些理论结果的变分更新在一个非常普遍的家庭共轭指数图形模型。我们展示了如何在变分贝叶斯学习的推理步骤中使用置信传播和连接树算法。将这些结果应用于线性高斯状态空间模型的贝叶斯分析，我们得到了一个学习过程，利用卡尔曼平滑传播，同时集成在所有的模型参数。我们演示了如何可以用来推断隐藏的状态维度的状态空间模型在各种合成问题和一个真实的高维数据集。
Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these results to the Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smoothing propagation, while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimensionality of the state-space model in a variety of synthetic problems and one real high-dimensional data set.