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HIGH-DIMENSIONAL FACTOR REGRESSION FOR HETEROGENEOUS SUBPOPULATIONS.

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Summary
This summary is machine-generated.

This study introduces a novel factor regression model to effectively analyze complex, heterogeneous data by balancing global and group-specific approaches. The model demonstrates improved estimation and prediction consistency, offering a competitive and interpretable solution for diverse datasets.

Keywords:
Factor modelsheterogeneitypenalized regressionprediction

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • Scientific research frequently encounters data heterogeneity due to complex data structures.
  • Existing models often fail to adequately address this heterogeneity, either by ignoring it (global models) or by over-fitting (group-specific models).

Purpose of the Study:

  • To propose a novel factor regression model designed to handle data heterogeneity across subpopulations.
  • To provide a balanced approach that integrates both common and subpopulation-specific variations.

Main Methods:

  • Developed a factor regression model decomposing data into heterogeneous (latent factor-driven) and homogeneous (common variation) terms.
  • Proved estimation and prediction consistency of the proposed estimators.
  • Analyzed convergence rates compared to global and group-specific models.

Main Results:

  • The proposed model achieves better convergence rates than traditional global and group-specific models.
  • Estimation of latent factors is asymptotically negligible, maintaining the minimax rate.
  • Demonstrated robustness to model mis-specification and superior performance on real-world datasets (Alzheimer's Disease Neuroimaging Initiative, microarray data).

Conclusions:

  • The factor regression model offers a competitive and interpretable solution for analyzing heterogeneous data.
  • It effectively balances the trade-offs between global and group-specific modeling approaches.
  • The method shows promise for applications in various scientific research fields dealing with complex data structures.