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Updated: Jun 19, 2026
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Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
Published on: September 4, 2015
Feature selection by higher criticism thresholding achieves the optimal phase diagram
1Department of Statistics, Stanford University, Stanford, CA 94305, USA.
Summary
Feature selection for high-dimensional data is improved by higher criticism thresholding (HCT). HCT performs as well as ideal thresholding in the rare/weak model, outperforming false discovery rate methods.
Area of Science:
- Statistics
- Machine Learning
- Bioinformatics
Background:
- High-dimensional data with few samples presents challenges for classification.
- The rare/weak (RW) model describes scenarios where only a few features are informative and their effects are small.
- Previous work showed higher criticism thresholding (HCT) is close to ideal for RW models.
Purpose of the Study:
- To formalize an asymptotic framework for the RW model.
- To evaluate the performance of HCT in this framework.
- To compare HCT with ideal thresholding and other methods like false discovery rate (FDR).
Main Methods:
- Developing an asymptotic framework for the RW model with increasing features and decreasing samples.
- Analyzing feature selection by thresholding Z-scores using higher criticism (HC).
- Defining HC thresholding (HCT) based on p-value order statistics.
- Mapping performance in a two-dimensional phase space of 'rare' and 'weak' features.
Main Results:
- Asymptotically, HCT achieves performance comparable to ideal thresholding in the RW model.
- A two-dimensional phase space partitions success and failure regions for ideal thresholding and HCT.
- HCT and ideal thresholding succeed in a larger region of the phase space than FDR methods.
Conclusions:
- HCT is a robust feature selection method for high-dimensional, small-sample, rare/weak data.
- The performance of HCT asymptotically matches ideal thresholding.
- HCT offers superior performance over FDR methods in challenging feature selection scenarios.
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