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Leveraging independence in high-dimensional mixed linear regression.

Ning Wang1, Kai Deng2, Qing Mai2

  • 1Department of Statistics, Beijing Normal University, Zhuhai, 519000, China.

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|September 24, 2024

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel penalized expectation-maximization (EM) algorithm for high-dimensional mixed linear regression, improving regression coefficient estimation and variable selection. The method efficiently handles numerous predictors, outperforming existing approaches in complex datasets.

Keywords:
EM algorithmfinite mixture modelgroup lassolatent variable model

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • High-dimensional data presents challenges for mixed linear regression.
  • Existing methods often oversimplify predictor variability and lack synergistic selection.
  • The expectation-maximization (EM) algorithm is a common approach for likelihood maximization.

Purpose of the Study:

  • To develop an efficient method for estimating regression coefficients and selecting predictors in high-dimensional mixed linear regression.
  • To address limitations of existing EM-based procedures by accounting for predictor variability.
  • To achieve synergistic variable selection across mixture components.

Main Methods:

  • Leveraging the independence between predictors and latent indicator variables for efficient computation.
  • Incorporating fast group-penalized EM estimation.
  • Establishing non-asymptotic convergence rates for the proposed estimator.

    • Main Results:

    • The proposed method facilitates efficient computation and synergistic variable selection.
    • Non-asymptotic convergence rates to true regression parameters are established.
    • Demonstrated effectiveness through extensive simulations and real-world data analysis.

    Conclusions:

    • The novel penalized EM algorithm offers a robust solution for high-dimensional mixed linear regression.
    • The method enhances both parameter estimation and variable selection accuracy.
    • Applicable to biological data, such as predicting anticancer drug sensitivity.