Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic Gaussian processes. The partition is created using a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The Markov chain Monte Carlo algorithm is made possible through a Laplace approximation on the latent variables of the logistic Gaussian process model. This approximation marginalizes the parameters in each partition element, allowing an efficient search of the posterior distribution of the tessellation. The method has desirable consistency properties. In simulation and applications, the model successfully estimates the partition structure and conditional distribution of y.

中文翻译：

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使用逻辑高斯过程的条件密度估计分区模型

条件密度估计（密度回归）以协变量 x 为条件估计响应变量 y 的分布。利用分区模型框架，提出了使用逻辑高斯过程的条件密度估计方法。分区是使用 Voronoi 细分创建的，并使用可逆跳跃马尔可夫链蒙特卡罗算法从数据中学习。马尔可夫链蒙特卡罗算法是通过对逻辑高斯过程模型的潜在变量进行拉普拉斯近似来实现的。这种近似将每个分区元素中的参数边缘化，从而允许对细分的后验分布进行有效搜索。该方法具有理想的一致性特性。在仿真和应用中，