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Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery
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Riesz Representers for the Rest of Us.

Nicholas T Williams1, Oliver J Hines, Kara E Rudolph

  • 1From the Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY.

Epidemiology (Cambridge, Mass.)
|May 21, 2026
PubMed
Summary

This paper introduces the Riesz representation theorem for epidemiologists. It explains the theorem and its utility in causal inference and machine learning, with practical examples.

Keywords:
Causal inferenceEfficient influence functionRiesz regressionRiesz representersSemiparametric estimators

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Area of Science:

  • Epidemiology
  • Causal Inference
  • Machine Learning

Background:

  • Semiparametric efficient estimators are increasingly used in epidemiology.
  • The Riesz representation theorem and Riesz regression are becoming more prevalent in this literature.

Purpose of the Study:

  • To introduce the Riesz representation theorem to epidemiologists.
  • To explain the theorem's concepts and practical applications.
  • To provide step-by-step examples for better understanding.

Main Methods:

  • Conceptual explanation of the Riesz representation theorem.
  • Demonstration of its utility in epidemiological contexts.
  • Worked examples illustrating its application.

Main Results:

  • The Riesz representation theorem provides a powerful tool for causal inference.
  • Machine learning integration enhances semiparametric estimation methods.
  • The paper clarifies the theorem's relevance and application.

Conclusions:

  • The Riesz representation theorem is a valuable concept for epidemiologic research.
  • Understanding this theorem can advance causal inference and machine learning applications in the field.
  • Practical examples facilitate adoption and understanding among epidemiologists.