Interpolating discriminant functions in high-dimensional Gaussian latent mixtures

Xin Bing and Marten Wegkamp

Biometrika, 2024, vol. 111, issue 1, 291-308

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.

Keywords: Benign overfitting; Discriminant analysis; Generalized least-squares estimate; High-dimensional classification; Minimax optimal rate of convergence; Overparameterization (search for similar items in EconPapers)
Date: 2024
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