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Related Concept Videos

Column Efficiency: Rate Theory01:12

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The rate theory of chromatography provides quantitative insight into the shapes and widths of elution bands. These bands are based on the random-walk mechanism governing molecular migration within a column. The Gaussian profile of chromatographic bands arises from the cumulative effect of random molecular motions as they progress through the column.
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Updated: Sep 13, 2025

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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A statistical view of column subset selection.

Anav Sood1, Trevor Hastie1

  • 1Department of Statistics, Stanford University, Sequoia Hall, 390 Jane Stanford Way, Stanford, CA 94305, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|July 28, 2025
PubMed
Summary
This summary is machine-generated.

This study unifies column subset selection (CSS) and principal variable identification, demonstrating their equivalence through maximum-likelihood estimation. It establishes conditions for consistent CSS in high dimensions and offers efficient methods for its application.

Keywords:
column subset selectionhigh-dimensional statisticsinterpretable dimensionality reductionprincipal components analysisprincipal variablesprobabilistic modelling

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Area of Science:

  • Statistics
  • Computer Science
  • Data Analysis

Background:

  • Dimensionality reduction is crucial for large datasets.
  • Column Subset Selection (CSS) and principal variable identification are common approaches.
  • These methods have traditionally been viewed separately.

Purpose of the Study:

  • To demonstrate the equivalence between CSS and principal variable identification.
  • To formalize both approaches within a unified semi-parametric maximum-likelihood model.
  • To develop efficient and robust methods for variable selection.

Main Methods:

  • Maximum-likelihood estimation within a semi-parametric model.
  • Analysis of consistency in high-dimensional data under the proportional asymptotic regime.
  • Development of methods utilizing summary statistics and handling missing/censored data.

Main Results:

  • Column Subset Selection (CSS) and principal variable identification are shown to be equivalent.
  • Conditions for consistent CSS in high dimensions are established.
  • Efficient algorithms for CSS are proposed, including those for incomplete datasets.

Conclusions:

  • A unified theoretical framework connects computer science and statistical approaches to variable selection.
  • The proposed methods offer efficient and consistent solutions for dimensionality reduction.
  • The findings facilitate practical application of variable selection in diverse data scenarios.