Bayesian inference via projections
Bayesian inference via projections
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DOI：
10.1007/s11222-015-9557-6
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发表时间：
2015-06
影响因子：
2.2
通讯作者：
Ricardo Silva;Freddie Kalaitzis
中科院分区：
文献类型：
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作者：
Ricardo Silva;Freddie Kalaitzis
贝叶斯推理通常会带来复杂的计算问题。即使现成的马尔可夫链蒙特卡罗（MCMC）方法可用来解决手头的问题，混合问题可能会损害结果的质量。我们为模型空间可以自然地分为两个部分的情况引入了一个框架：(i)观察变量的基线黑箱概率分布和（ii）对该概率分布的函数施加的约束。推理是通过从第一个分量隐含的后验中采样，并在第二个分量定义的空间上找到投影来完成的。我们在潜在变量模型的先验、模型选择和MCMC混合方面讨论了这种分离的含义。案例研究包括概率主成分分析、边际独立性模型和可解释的结构化有序概率模型。
Bayesian inference often poses difficult computational problems. Even when off-the-shelf Markov chain Monte Carlo (MCMC) methods are available to the problem at hand, mixing issues might compromise the quality of the results. We introduce a framework for situations where the model space can be naturally divided into two components: (i) a baseline black-box probability distribution for the observed variables and (ii) constraints enforced on functionals of this probability distribution. Inference is performed by sampling from the posterior implied by the first component, and finding projections on the space defined by the second component. We discuss the implications of this separation in terms of priors, model selection, and MCMC mixing in latent variable models. Case studies include probabilistic principal component analysis, models of marginal independence, and a interpretable class of structured ordinal probit models.