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Provable Boolean interaction recovery from tree ensemble obtained via random forests.

Merle Behr1, Yu Wang1, Xiao Li1

  • 1Department of Statistics, University of California, Berkeley, CA 94720.

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|May 24, 2022
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Summary
This summary is machine-generated.

Iterative Random Forests (iRFs) can discover Boolean biological interactions. A new model and method, LSSFind, theoretically guarantees consistent discovery of these feature interactions.

Keywords:
consistencydecision treesensemble methodsinteraction selectioninterpretable machine learning

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Area of Science:

  • Genomics
  • Machine Learning
  • Computational Biology

Background:

  • Random Forests (RFs) excel in prediction, particularly in genomics.
  • Iterative RFs (iRFs) show promise for discovering Boolean biological interactions, crucial for functional genomics and precision medicine.
  • Theoretical understanding of how tree-based methods find Boolean interactions is lacking.

Purpose of the Study:

  • Introduce a novel discontinuous nonlinear regression model (Locally Spiky Sparse - LSS) inspired by biological thresholding.
  • Define Depth-Weighted Prevalence (DWP) to quantify feature co-occurrence in RF ensembles.
  • Establish a theoretically sound method (LSSFind) for consistent Boolean interaction discovery.

Main Methods:

  • Developed the Locally Spiky Sparse (LSS) regression model.
  • Defined Depth-Weighted Prevalence (DWP) for feature sets in RF ensembles.
  • Proposed LSSFind, a tractable iRF procedure for interaction discovery.

Main Results:

  • Proved that DWP attains a universal upper bound for Boolean interactions under the LSS model.
  • Demonstrated that LSSFind consistently discovers interactions as sample size increases.
  • Simulation results confirm LSSFind's ability to recover interactions, even with violated assumptions.

Conclusions:

  • The LSS model provides a theoretical framework for understanding Boolean interactions in RFs.
  • LSSFind offers a statistically grounded approach to identifying critical biological feature interactions.
  • This work advances functional genomics and precision medicine through improved interaction discovery.