论文标题
在高维高斯潜在混合物中插值判别功能
Interpolating Discriminant Functions in High-Dimensional Gaussian Latent Mixtures
论文作者
论文摘要
本文考虑了具有低维潜在高斯混合物结构和非变化噪声的假定模型下的高维特征的二元分类。通用最小二乘估计器用于估计最佳分离超平面的方向。估计的超平面显示在训练数据上插值。虽然可以始终如一地估计方向向量，这是从线性回归中最新结果所预期的，但天真的插件估计无法始终如一地估计截距。在许多情况下，一种简单的校正需要独立的固定样本，它使过程最大程度最佳。后一种过程的插值属性可以保留，但出乎意料的是取决于标签的编码方式。
This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and non-vanishing 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, that 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.
