使用对数高斯Cox过程的分类
Classification using log Gaussian Cox processes
摘要：
McCullagh和Yang（2006）提出了一系列基于Cox过程的分类算法。我们进一步研究了对数高斯变量，它有一些吸引人的属性。在协变量的条件下，标签上的分布由一种条件马尔可夫随机场给出。在监督的情况下，单个测试点的预测概率的计算与训练点的数量成线性关系，并且多类泛化是直接的。我们展示了监督方法和经典非参数方法之间的新联系。我们给出了一个详细的分析的两两图表示的马尔可夫随机场，我们使用扩展模型的半监督学习问题，并提出了一种推理方法的基础上图最小割。我们给出了监督和半监督数据集上的第一个实验分析，并显示出良好的经验性能。
英文摘要：
McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.
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