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On a Robust MaxEnt Process Regression Model with Sample-Selection.

Hea-Jung Kim1, Mihyang Bae1, Daehwa Jin1

  • 1Department of Statistics, Dongguk University-Seoul, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, Korea.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a robust sample-selection Gaussian process regression (RSGPR) model to address sample selection bias in regression analysis. The RSGPR model improves accuracy with non-normal data and demonstrates strong performance in simulations.

Keywords:
Gaussian process modelMarkov chain Monte Carlobias correctionhierarchical Bayesian methodologyrobust sample-selection MaxEnt process regression modelsample-selection bias

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Sample-selection bias occurs when dependent variables are partially observed.
  • Existing Gaussian process regression (GPR) models do not adequately handle non-normal data in sample selection.
  • Maximum Entropy (MaxEnt) process regression offers a flexible nonparametric approach.

Purpose of the Study:

  • Introduce a novel Maximum Entropy (MaxEnt) process regression model.
  • Generalize the GPR model to create a robust sample-selection Gaussian process regression (RSGPR) model.
  • Develop a hierarchical Bayesian methodology for estimating the RSGPR model.

Main Methods:

  • Developed a MaxEnt process regression model with a MaxEnt prior.
  • Generalized the GPR model to create the RSGPR model for non-normal sample selection data.
  • Employed a hierarchical Bayesian approach with a Markov chain Monte Carlo algorithm for model estimation.

Main Results:

  • The MaxEnt process regression model encompasses GPR as a special case.
  • Established key properties of the RSGPR model, including stochastic representation and bias magnitude.
  • Simulations confirmed the RSGPR model's effectiveness in bias correction, robustness, and prediction.

Conclusions:

  • The RSGPR model effectively corrects for sample-selection bias, even with non-normal data.
  • The proposed Bayesian estimation methodology is computationally feasible and avoids complex derivatives.
  • The RSGPR model shows excellent finite-sample performance, making it a valuable tool for regression analysis.