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Monotone response surface of multi-factor condition: estimation and Bayes classifiers.

Ying Kuen Cheung1, Keith M Diaz2

  • 1Department of Biostatistics, Columbia University, New York, NY, 10032, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|March 11, 2024
PubMed
Summary

We introduce iPIPE, a novel method for estimating monotone response surfaces. This approach offers more precise and reliable credible intervals, especially in high-dimensional settings, outperforming traditional methods.

Keywords:
Clinical decision support toolpartial orderingposterior quantilessweep algorithmweighted posterior gain

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Area of Science:

  • Statistics
  • Machine Learning
  • Optimization

Background:

  • Estimating monotone response surfaces is crucial in various scientific fields.
  • Traditional methods like isotonic regression face challenges in high-dimensional spaces.
  • Bayes classifiers offer a flexible framework for complex data structures.

Purpose of the Study:

  • To develop a novel computational method for estimating monotone response surfaces in high-dimensional settings.
  • To establish the theoretical existence and computational feasibility of the proposed inverse method.
  • To compare the performance of the new method against existing techniques in simulation and analysis.

Main Methods:

  • Formulating response surface estimation as the inverse of partially ordered classifier ensembles (PIPE-classifiers).
  • Proving the existence of the inverse of PIPE-classifiers (iPIPE).
  • Developing efficient algorithms to compute iPIPE by reducing the optimization space.

Main Results:

  • Demonstrated the existence and efficient computation of iPIPE.
  • Applied iPIPE to analysis and simulation settings with surface dimensions exceeding typical isotonic regression literature.
  • iPIPE-based credible intervals achieved nominal coverage probability in simulations.
  • iPIPE-based credible intervals showed improved precision compared to unconstrained estimation.

Conclusions:

  • iPIPE provides a robust and efficient method for monotone response surface estimation, particularly in high-dimensional scenarios.
  • The method offers a valuable alternative to traditional techniques, enhancing precision and reliability.
  • Further applications in complex statistical modeling and machine learning are warranted.