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Pseudo-Marginal Bayesian Inference for Gaussian Processes

机译:高斯过程的伪边际贝叶斯推断

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摘要

The main challenges that arise when adopting Gaussian process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion.
机译:在概率建模中采用高斯过程先验时出现的主要挑战是,在对样本外数据进行基于模型的预测时,如何进行精确的贝叶斯推断以及如何考虑模型参数的不确定性。本文使用概率回归作为一个说明性的工作示例,提出了一种基于伪边际方法的马尔可夫链蒙特卡洛方法的通用有效方法,该方法有效地解决了这两个问题。本文提出的结果表明,在现有采样方法的改进下,可以从定义高斯过程先验协方差函数的参数的后验分布进行模拟。这一点特别重要,因为它提供了一个强大的工具来执行一般基于高斯过程的层次统计模型的完整贝叶斯推理。结果还表明,在此类模型中,基于蒙特卡洛的所有模型参数的集成实际上是可行的,从而提供了预测中不确定性的出色量化。关于最新的概率分类器的广泛比较证实了这一主张。

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