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An R-Based Landscape Validation of a Competing Risk Model
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Binary regression and classification with covariates in metric spaces.

Yinan Lin1, Zhenhua Lin2

  • 1National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, 401331, China.

Biometrics
|September 19, 2025
PubMed
Summary
This summary is machine-generated.

We developed a new regression model and classifier for binary data with covariates in metric spaces. Our methods offer optimal estimation and classification performance, demonstrated in simulations and fMRI data analysis.

Keywords:
Alexandrov geometryHadarmard spaceexcess risklogistic regressionmanifoldminimax optimality

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Traditional regression models assume vector space covariates.
  • Metric spaces lack inherent vector structures, posing challenges for standard statistical methods.
  • Analyzing binary responses with metric-space covariates requires novel approaches.

Purpose of the Study:

  • Introduce a novel regression model for binary responses with metric-space covariates.
  • Develop a binary classifier tailored for metric-space valued data.
  • Establish theoretical performance bounds and demonstrate practical utility.

Main Methods:

  • Proposed a logistic regression-inspired model for metric-space data.
  • Developed a maximum likelihood estimator for the regression coefficient.
  • Derived minimax upper and lower bounds on estimation error using metric entropy.
  • Established optimality for general metric spaces and Riemannian manifolds.

Main Results:

  • The proposed estimator achieves optimal performance in common metric spaces.
  • A refined bound demonstrates classifier optimality on Riemannian manifolds.
  • The methods are the first of their kind for binary response analysis in general metric spaces.
  • Simulation studies confirm the estimator and classifier's numerical performance.

Conclusions:

  • The novel regression model and classifier effectively handle binary data with metric-space covariates.
  • Theoretical bounds confirm the statistical efficiency and optimality of the proposed methods.
  • The approach shows promise for applications like neuroimaging analysis (fMRI).