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Wavelet-Based Scalar-on-Function Finite Mixture Regression Models.

Adam Ciarleglio1, R Todd Ogden2

  • 1Department of Child and Adolescent Psychiatry, Division of Biostatistics, New York University, United States.

Computational Statistics & Data Analysis
|October 30, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel wavelet-based finite mixture regression model for analyzing functional predictor data. The method effectively handles high-dimensional data, enabling feature selection and accurate estimation in complex relationships.

Keywords:
EM algorithmFunctional data analysisLassoWavelets

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Finite mixture regression models are valuable for analyzing data from distinct subpopulations with varying predictor-response associations.
  • Classical models face challenges when incorporating functional predictors, which are common in fields like neuroimaging and bioinformatics.
  • Existing methods often struggle with the high dimensionality introduced by functional data, necessitating advanced statistical techniques.

Purpose of the Study:

  • To extend finite mixture regression to accommodate functional predictors using a wavelet-based approach.
  • To develop a method capable of handling situations with more predictors than observations, a common issue with functional data.
  • To enable simultaneous feature selection and parameter estimation in complex regression settings.

Main Methods:

  • A wavelet-based representation is used to convert functional predictors into a set of scalar predictors.
  • Lasso-type penalization is employed to address the high-dimensional nature of the transformed data, facilitating feature selection.
  • A fitting algorithm is developed for the proposed wavelet-based finite mixture regression model.

Main Results:

  • The wavelet-based approach effectively incorporates functional predictors into finite mixture regression models.
  • Lasso penalization successfully performs feature selection and estimation, even when the number of predictors exceeds the number of observations.
  • The model demonstrates robust performance on both synthetic datasets and a real-world application.

Conclusions:

  • The proposed wavelet-based finite mixture regression model offers a powerful tool for analyzing complex relationships involving functional predictors.
  • This methodology is particularly useful in fields such as neuroimaging, where functional data and high dimensionality are prevalent.
  • The approach provides a statistically sound framework for feature selection and estimation in mixture models with functional covariates.