Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning

• URL: http://arxiv.org/abs/2304.09154v1
• Date: Tue, 18 Apr 2023 17:49:02 GMT
• Title: Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning
• Authors: Tengyao Wang, Edgar Dobriban, Milana Gataric and Richard J. Samworth
• Abstract summary: We propose a new method for high-dimensional semi-supervised learning problems. It is based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data.
• Score: 16.673022545571566
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a new method for high-dimensional semi-supervised learning problems based on the careful aggregation of the results of a low-dimensional procedure applied to many axis-aligned random projections of the data. Our primary goal is to identify important variables for distinguishing between the classes; existing low-dimensional methods can then be applied for final class assignment. Motivated by a generalized Rayleigh quotient, we score projections according to the traces of the estimated whitened between-class covariance matrices on the projected data. This enables us to assign an importance weight to each variable for a given projection, and to select our signal variables by aggregating these weights over high-scoring projections. Our theory shows that the resulting Sharp-SSL algorithm is able to recover the signal coordinates with high probability when we aggregate over sufficiently many random projections and when the base procedure estimates the whitened between-class covariance matrix sufficiently well. The Gaussian EM algorithm is a natural choice as a base procedure, and we provide a new analysis of its performance in semi-supervised settings that controls the parameter estimation error in terms of the proportion of labeled data in the sample. Numerical results on both simulated data and a real colon tumor dataset support the excellent empirical performance of the method.

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