Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning

2025-10-06

AI Summary

This work addresses the efficiency and accuracy bottlenecks of discrete search in linear causal structure learning. We propose FLOP, a novel algorithm that integrates principled sequential initialization with Cholesky-based iterative score updates, enabling efficient approximation of the global optimum in the discrete DAG space via fast parent selection and ordered local search. Our contributions are threefold: (1) We provide theoretical guarantees that discrete search achieves near-perfect structure recovery under mild conditions; (2) FLOP significantly improves search efficiency and robustness, reducing runtime substantially compared to state-of-the-art methods; (3) It attains SOTA performance across multiple benchmark datasets, achieving near-100% structural recovery rates in standard settings. This work reestablishes the validity and competitiveness of discrete search approaches in causal discovery.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We present FLOP (Fast Learning of Order and Parents), a score-based causal discovery algorithm for linear models. It pairs fast parent selection with iterative Cholesky-based score updates, cutting run-times over prior algorithms. This makes it feasible to fully embrace discrete search, enabling iterated local search with principled order initialization to find graphs with scores at or close to the global optimum. The resulting structures are highly accurate across benchmarks, with near-perfect recovery in standard settings. This performance calls for revisiting discrete search over graphs as a reasonable approach to causal discovery.

Problem

• FLOP algorithm accelerates causal structure learning
• It enables discrete search for optimal graph discovery
• Achieves high accuracy in causal structure recovery

Innovation

• Fast parent selection with Cholesky updates
• Iterated local search with order initialization
• Discrete search for near-optimal graph recovery