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From Observation to Orientation: an Adaptive Integer Programming Approach to Intervention Design

Abdelmonem Elrefaey, Rong Pan

TL;DR

The paper addresses budgeted causal discovery by learning a DAG from interventional data using an adaptive intervention design. It introduces a modular iterative integer programming framework (Adaptive_IP) that selects informative intervention sets to maximize edge orientation within a fixed budget and per-iteration limit, integrating Meek's rules to propagate orientations without extra experiments. The PKG representation tracks edge status across four sets (Unknown, Semi-directed, Adjacent, Known), and transition rules update this state as interventions yield outcomes. Empirical results on synthetic and real graphs show the adaptive approach reduces the number of intervention rounds and total manipulations compared to random baselines, with performance influenced by graph topology and intervention constraints; theoretical guarantees of finite convergence and correctness are provided under standard assumptions, and the framework is extensible to non-linear costs, batch experiments, and alternative objectives.

Abstract

Using both observational and experimental data, a causal discovery process can identify the causal relationships between variables. A unique adaptive intervention design paradigm is presented in this work, where causal directed acyclic graphs (DAGs) are for effectively recovered with practical budgetary considerations. In order to choose treatments that optimize information gain under these considerations, an iterative integer programming (IP) approach is proposed, which drastically reduces the number of experiments required. Simulations over a broad range of graph sizes and edge densities are used to assess the effectiveness of the suggested approach. Results show that the proposed adaptive IP approach achieves full causal graph recovery with fewer intervention iterations and variable manipulations than random intervention baselines, and it is also flexible enough to accommodate a variety of practical constraints.

From Observation to Orientation: an Adaptive Integer Programming Approach to Intervention Design

TL;DR

The paper addresses budgeted causal discovery by learning a DAG from interventional data using an adaptive intervention design. It introduces a modular iterative integer programming framework (Adaptive_IP) that selects informative intervention sets to maximize edge orientation within a fixed budget and per-iteration limit, integrating Meek's rules to propagate orientations without extra experiments. The PKG representation tracks edge status across four sets (Unknown, Semi-directed, Adjacent, Known), and transition rules update this state as interventions yield outcomes. Empirical results on synthetic and real graphs show the adaptive approach reduces the number of intervention rounds and total manipulations compared to random baselines, with performance influenced by graph topology and intervention constraints; theoretical guarantees of finite convergence and correctness are provided under standard assumptions, and the framework is extensible to non-linear costs, batch experiments, and alternative objectives.

Abstract

Using both observational and experimental data, a causal discovery process can identify the causal relationships between variables. A unique adaptive intervention design paradigm is presented in this work, where causal directed acyclic graphs (DAGs) are for effectively recovered with practical budgetary considerations. In order to choose treatments that optimize information gain under these considerations, an iterative integer programming (IP) approach is proposed, which drastically reduces the number of experiments required. Simulations over a broad range of graph sizes and edge densities are used to assess the effectiveness of the suggested approach. Results show that the proposed adaptive IP approach achieves full causal graph recovery with fewer intervention iterations and variable manipulations than random intervention baselines, and it is also flexible enough to accommodate a variety of practical constraints.

Paper Structure

This paper contains 41 sections, 3 theorems, 23 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. DAGs and Causal DAGs.
  3. Markov Equivalence and Essential Graphs.
  4. Types of Interventions.
  5. Strategies for Intervention Design.
  6. Our Contributions.
  7. Related Work
  8. Methodology
  9. Assumptions.
  10. Partially Known Graph.
  11. Meek's Rules
  12. IP Model Formulation
  13. Notation
  14. Objective Function
  15. Constraints
  16. ...and 26 more sections

Key Result

Theorem 1

Under Assumptions A1-A6, Algorithm alg:adaptiveip_meek terminates in a finite number of iterations.

Figures (5)

  • Figure 1: Meek Rules of Edge Orientation
  • Figure 2: Number of additional intervention rounds required when using method $r$ versus Adaptive_IP. Each panel corresponds to a graph-edge probability $p$; bars show the distribution of $r-\mathrm{IP}$ across seeds for different intervention limits $k_{\max}$ and network sizes $N$.
  • Figure 3: Number of additional intervention rounds required when using method $r$ versus Adaptive_IP. Each panel corresponds to one of 9 networks; bars show the distribution of $r-\mathrm{IP}$ across seeds for different intervention limits $k_{\max}$.
  • Figure 4: Number of additional variables manipulations required when using method $r$ versus Adaptive_IP. Each panel corresponds to a graph-edge probability $p$; bars show the distribution of $r-\mathrm{IP}$ across seeds for different intervention limits $k_{\max}$ and network sizes $N$.
  • Figure 5: Number of additional variable manipulations required when using method $r$ versus Adaptive_IP. Each panel corresponds to one of 9 networks; bars show the distribution of $r-\mathrm{IP}$ across seeds for different intervention limits $k_{\max}$.

Theorems & Definitions (6)

  • Theorem 1: Finite Convergence
  • proof
  • Theorem 2: Correctness
  • proof
  • Proposition 1: Single-Step Optimality
  • proof