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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Learning interactions via hierarchical group-lasso regularization.

Michael Lim1, Trevor Hastie1

  • 1Statistics Department, Stanford University.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|January 14, 2016
PubMed
Summary
This summary is machine-generated.

We developed a new method for learning pairwise interactions in regression models that ensures main effects are included when interactions are present. This approach simplifies model interpretability and works for categorical and continuous variables.

Keywords:
computer intensivehierarchicalinteractionlogisticregression

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Learning pairwise interactions is crucial for understanding complex relationships in regression models.
  • Existing methods often struggle with model identifiability and interpretability, especially with categorical variables.
  • Strong hierarchy, where main effects must be present if an interaction is, is a desirable property for interpretable models.

Purpose of the Study:

  • To introduce a novel method for learning hierarchical pairwise interactions in linear and logistic regression.
  • To develop a method that accommodates categorical variables with multiple levels and continuous variables.
  • To provide an interpretable interaction model without explicit constraints on main effects and interactions.

Main Methods:

  • Developed a method for estimating pairwise interactions that enforces strong hierarchy.
  • Extended the method to handle categorical variables with arbitrary levels and continuous variables.
  • Utilized an R package, glinternet, for implementation and comparison.

Main Results:

  • The proposed method successfully learns interpretable interaction models satisfying strong hierarchy.
  • Demonstrated effectiveness on both simulated and real-world data, including a genome-wide association study.
  • The glinternet package provides a practical tool for applying this method.

Conclusions:

  • The new method offers a robust and interpretable way to model pairwise interactions.
  • The approach simplifies model building by inherently satisfying hierarchical constraints.
  • This work facilitates more accurate and understandable analyses in various fields, including genetics.