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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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An Algorithmic Treatment of Causal Unit Selection.

Haiying Huang1, Adnan Darwiche1

  • 1Computer Science Department, University of California, Los Angeles (UCLA), Los Angeles, CA 90095, USA.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new computational framework for causal unit selection, optimizing general benefit functions using counterfactual probabilities. The research presents an efficient algorithm using arithmetic circuits for faster computation of optimal units.

Keywords:
counterfactual reasoningknowledge compilationmaximum a posteriori inferencestructural causal modelunit selection

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Area of Science:

  • Causal inference
  • Computational social science
  • Artificial intelligence

Background:

  • Optimizing causal objective functions involves interventional or counterfactual probabilities.
  • The unit selection problem aims to identify individuals maximizing a benefit function using counterfactuals.

Purpose of the Study:

  • To develop a general theory and computational methods for causal unit selection.
  • To propose an exact algorithm for finding optimal units under a fully specified causal model.

Main Methods:

  • A novel reduction transforms causal objective functions into associational probabilities on an objective model.
  • Variable Elimination (VE) is applied to the objective model for exact unit selection.
  • Objective models are compiled into tractable arithmetic circuits for efficient computation.

Main Results:

  • Causal unit selection is NPPP-complete, requiring exponential time in the objective model's treewidth.
  • The circuit-based method achieves linear time complexity relative to circuit size.
  • Experimental results show significant speedups over VE and baseline search methods.

Conclusions:

  • The proposed framework provides an efficient and exact method for causal unit selection.
  • Arithmetic circuits offer a tractable approach to complex causal optimization problems.
  • The methods are validated through experiments and a real-world ecology case study.