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Updated: May 27, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Estimating Tree-Structured Covariance Matrices via Mixed-Integer Programming.

Héctor Corrada Bravo1, Stephen Wright, Kevin H Eng

  • 1Department of Biostatistics, Johns Hopkins Bloomberg, School of Public Health, Baltimore, MD 21205.

Journal of Machine Learning Research : JMLR
|November 15, 2011
PubMed
Summary
This summary is machine-generated.

We developed a new method to estimate tree-structured covariance matrices from continuous data. This approach uses optimization techniques to find the nearest tree-structured matrix, improving phylogenetic analysis.

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Last Updated: May 27, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Statistics
  • Computational Biology
  • Phylogenetics

Background:

  • Estimating covariance matrices is crucial for understanding relationships in continuous data.
  • Tree-structured covariance matrices model dependencies in hierarchical data, common in biological systems.
  • Existing methods may not efficiently handle the complexity of tree-structured dependencies.

Purpose of the Study:

  • To introduce a novel method for direct estimation of tree-structured covariance matrices from continuous data.
  • To formulate the estimation problem as a mixed-integer program (MIP) solvable by existing optimization tools.
  • To evaluate the method's performance in phylogenetic analysis and compare it with existing procedures.

Main Methods:

  • Representing tree-structured covariance matrices as linear combinations of rank-one matrices.
  • Formulating the estimation as a projection problem: finding the nearest tree-structured matrix to a sample covariance matrix.
  • Solving the estimation problem using linear or quadratic mixed-integer programming (MIP) solvers.

Main Results:

  • The proposed method successfully estimates tree-structured covariance matrices.
  • The MIP formulation allows for optimal solutions by leveraging existing solvers.
  • Case studies in phylogenetic analysis of gene expression demonstrate the method's utility and competitive performance.

Conclusions:

  • The novel projection-based MIP approach provides an efficient and robust method for estimating tree-structured covariance matrices.
  • This method offers a valuable tool for analyzing complex dependencies in continuous data, particularly in phylogenetics.
  • The approach integrates statistical estimation with powerful numerical optimization techniques.