Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 34 of its 96 references that are in the map. First posted on arXiv 18 Apr 2023.
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34 of 96 references.
References · 34
- 2018GANomaly: Semi-Supervised Anomaly Detection via Adversarial Trainingcited by 409
- 2018Not-so-supervised: a survey of semi-supervised, multi-instance, and transfer learning in medical image analysiscited by 178
- 2020A Semi-supervised Graph Attentive Network for Financial Fraud Detectioncited by 150
- 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 131
- 2016Statistical and Computational Guarantees of Lloyd's Algorithm and its Variantscited by 52
- 2019Optimality of Spectral Clustering in the Gaussian Mixture Modelcited by 42
- 2016Ten Steps of EM Suffice for Mixtures of Two Gaussianscited by 40
- 2016Semi-supervised Inference: General Theory and Estimation of Meanscited by 38
- 2018Singularity, Misspecification, and the Convergence Rate of EMcited by 38
- 2016Global analysis of Expectation Maximization for mixtures of two Gaussianscited by 31
- 2015Random-projection ensemble classificationcited by 29
- 2017Efficient and Adaptive Linear Regression in Semi-Supervised Settingscited by 29
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- 2016Clustering Algorithms: A Comparative Approachcited by 28
- 2019Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in O(√n) iterationscited by 27
- 2019Sharp Analysis of Expectation-Maximization for Weakly Identifiable Modelscited by 23
- 2017Local nearest neighbour classification with applications to semi-supervised learningcited by 17
- 2018High-dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm, and Missing Datacited by 17
- 2017Recent progress in log-concave density estimationcited by 15
- 2021Clustering a Mixture of Gaussians with Unknown Covariancecited by 14
- 2022Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clusteringcited by 14
- 2014Influential Feature PCA for high dimensional clusteringcited by 13
- 2020Computationally efficient sparse clusteringcited by 12
- 2020Instability, Computational Efficiency and Statistical Accuracycited by 12
- 2013Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separationcited by 11
- 2020Statistical and Algorithmic Insights for Semi-supervised Learning with Self-trainingcited by 11
- 2019Minimax rates in sparse, high-dimensional changepoint detectioncited by 9
- 2019Random projections: data perturbation for classification problemscited by 7
- 2014Detection and Feature Selection in Sparse Mixture Modelscited by 6
- 2014Efficient Sparse Clustering of High-Dimensional Non-spherical Gaussian Mixturescited by 6
- 2017Statistical properties of sketching algorithmscited by 6
- 2021Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: A new take on Robust Interpolationcited by 6
- 2017On Principal Components Regression, Random Projections, and Column Subsamplingcited by 4
- 2019High-dimensional clustering via Random Projectionscited by 4
- 2014Feature Selection For High-Dimensional Clusteringcited by 1
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2 papers.