Interpolating discriminant functions in high-dimensional Gaussian latent mixtures
本文研究高维特征二元分类问题，在低维潜在高斯混合模型下，使用广义最小二乘估计最优分离超平面方向，发现该超平面在训练数据上插值，并提出了一个需要独立保留样本的简单修正方法，使过程在多种场景下达到极小化最优。
Abstract This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in estimate fails to consistently estimate the intercept. A simple correction, which requires an independent hold-out sample, renders the procedure minimax optimal in many scenarios. The interpolation property of the latter procedure can be retained, but surprisingly depends on the way the labels are encoded.