We present a general methodology for using unlabeled data to design semi supervised learning (SSL) variants of the Empirical Risk Minimization (ERM) learning process. Focusing on generalized linear regression, we provide a careful treatment of the effectiveness of the SSL to improve prediction performance. The key ideas are carefully considering the null model as a competitor, and utilizing the unlabeled data to determine signal-noise combinations where the SSL outperforms both the ERM learning and the null model. In the special case of linear regression with Gaussian covariates, we show that the previously suggested semi-supervised estimator is in fact not capable of improving on both the supervised estimator and the null model simultaneously. However, the new estimator presented in this work, can achieve an improvement of $O(1/n)$ term over both competitors simultaneously. On the other hand, we show that in other scenarios, such as non-Gaussian covariates, misspecified linear regression, or generalized linear regression with non-linear link functions, having unlabeled data can derive substantial improvement in prediction by applying our suggested SSL approach. Moreover, it is possible to identify the usefulness of the SSL, by using the dedicated formulas we establish throughout this work. This is shown empirically through extensive simulations.

翻译：我们提出了一个使用未贴标签数据的一般方法,用于设计模拟风险最小化(ERM)学习过程的半监督学习变体。我们注重一般线性回归,对SSL的有效性进行仔细处理,以改进预测性能。主要想法正在仔细考虑作为竞争对手的无效模型,并利用未贴标签数据确定信号-噪音组合,使SSL在机构风险管理学习和无效模型方面都优于机构风险管理学习和无效模型。在与Gaussian 共变体进行线性回归的特殊情况下,我们表明,先前建议的半监督估计数字事实上无法同时改进受监督的估测器和无效模型。然而,这项工作中提出的新估计数字可以同时将美元(1/n)值用于改进两个竞争者之间的任期。另一方面,我们表明,在其他情景中,如非伽西文的共变法、误定线性回归或非线性联系功能的普通线性回归,如果未贴标签的估算数据能够同时改进受监督的估测的估算器和无效的模型。通过我们建议的SSSL的模拟方法,在预测中可以确定这一可能的实用性方法。