The premise of semi-supervised learning (SSL) is that combining labeled and unlabeled data yields significantly more accurate models. Despite empirical successes, the theoretical understanding of SSL is still far from complete. In this work, we study SSL for high dimensional sparse Gaussian classification. To construct an accurate classifier a key task is feature selection, detecting the few variables that separate the two classes. % For this SSL setting, we analyze information theoretic lower bounds for accurate feature selection as well as computational lower bounds, assuming the low-degree likelihood hardness conjecture. % Our key contribution is the identification of a regime in the problem parameters (dimension, sparsity, number of labeled and unlabeled samples) where SSL is guaranteed to be advantageous for classification. Specifically, there is a regime where it is possible to construct in polynomial time an accurate SSL classifier. However, % any computationally efficient supervised or unsupervised learning schemes, that separately use only the labeled or unlabeled data would fail. Our work highlights the provable benefits of combining labeled and unlabeled data for {classification and} feature selection in high dimensions. We present simulations that complement our theoretical analysis.

本研究解决了半监督学习在高维稀疏高斯分类中的理论不足。通过信息论下界和计算下界的分析，我们识别了特定参数区间，在该区间内，结合标记和未标记数据可以有效构建准确的分类器，显示出半监督学习在特征选择中的显著优势。

半监督稀疏高斯分类：未标记数据的可证明优势