论文标题
半监督回归的后验一致性
Posterior Consistency of Semi-Supervised Regression on Graphs
论文作者
论文摘要
基于图的半监督回归（SSR）是从其值（标签）上在顶点的一小部分上估算函数在加权图上的值的问题。本文与SSR在分类的背景下的一致性有关，在标签具有较小的噪声且底层图的加权与群集簇的节点一致的情况下。我们提出了SSR的贝叶斯公式，其中加权图使用图形laplacian定义了高斯先验，并且标记的数据定义了可能性。我们根据参数量化了图表中的小标签误差和固有的聚类，分析了地面真相围绕地面真相的收缩率。我们获得了收缩率的界限，并通过数值实验说明了它们的清晰度。该分析还可以深入了解输入先验定义的超参数的选择。
Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is consistent with well-clustered nodes. We present a Bayesian formulation of SSR in which the weighted graph defines a Gaussian prior, using a graph Laplacian, and the labeled data defines a likelihood. We analyze the rate of contraction of the posterior measure around the ground truth in terms of parameters that quantify the small label error and inherent clustering in the graph. We obtain bounds on the rates of contraction and illustrate their sharpness through numerical experiments. The analysis also gives insight into the choice of hyperparameters that enter the definition of the prior.
