密度敏感半监督推理
Density-sensitive semisupervised inference
摘要：
半监督方法是使用标记数据$(X_1,Y_1),\ldots,(X_n,Y_n)$和未标记数据$X_{n+1},\ldots,X_N$进行预测的技术。这些方法调用了将X的边缘分布$P_X$与回归函数f（x）联系起来的一些假设。例如，通常假设f在$P_X$的高密度区域上非常平滑。许多方法是特设的，并已被证明在特定的例子中工作，但缺乏理论基础。我们提供了一个分析半监督方法的极大极小框架。特别是，我们研究的方法是敏感的分布$P_X$的指标的基础上。我们的模型包括一个参数$α$，它控制半监督假设的强度。然后，我们使用这些数据来适应$α$。
英文摘要：
Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$ of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of $P_X$. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a minimax framework for analyzing semisupervised methods. In particular, we study methods based on metrics that are sensitive to the distribution $P_X$. Our model includes a parameter $α$ that controls the strength of the semisupervised assumption. We then use the data to adapt to $α$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
