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Variational Bayes for estimating the parameters of a hidden Potts model

机译：用于估计隐藏Potts模型参数的变分贝叶斯

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摘要

Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.
机译：隐藏的马尔可夫随机场模型提供了图像和其他空间问题的吸引人的表示形式。缺点是，对于这些模型，推论并非一帆风顺，因为除了很小的观测值集之外，对于可能性的归一化常数通常很难处理。变分方法是贝叶斯推理的新兴工具，并且已经在其他环境中成功应用。针对具有高斯噪声的隐藏Potts模型的特殊情况，我们展示了如何将变分贝叶斯方法应用于隐藏的Markov随机场推断。为了解决似然性难于归一化常数的障碍，我们探索了将可变贝叶斯算法纳入的替代估计方法。我们考虑了伪似然方法以及归一化常数的最近减少的依赖近似。为了说明这些方法的有效性，我们提供了对模拟数据集的分析得出的经验结果。我们还分析了一个真实的数据集，并将结果与​​以前的分析结果以及从最近开发的辅助变量MCMC方法和递归MCMC方法获得的结果进行比较。我们的结果表明，变分贝叶斯分析的执行速度比MCMC分析快得多，并且可以很好地估计模型参数。我们还发现，在我们对真实数据集和合成数据集的分析中，归一化常数的降低的依赖近似值优于伪似然近似值。

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