Inference for max-linear Bayesian networks with noise

2025-05-01

AI Summary

This paper addresses causal inference in noisy max-linear Bayesian networks (MLBNs) under extreme-value regimes, assuming a known DAG topology. Methodologically, it introduces a structured modeling framework based on logarithmic transformation and max-plus algebra, converting the original extremal model into a tractable linear form, and proposes a parameter estimation procedure integrating the EM algorithm with quadratic optimization. Theoretically, it establishes, for the first time, the asymptotic normality of edge-wise causal parameter estimators—providing an interpretable and testable foundation for statistical inference in extremal causal models. Empirical evaluations confirm the efficacy and stability of the proposed estimators. This work bridges a critical theoretical gap at the intersection of extreme-value statistics and causal inference, advancing structured causal modeling for heavy-tailed data.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then, we show that an estimator of a parameter for each edge in a directed acyclic graph (DAG) is distributed normally. We end this paper with computational experiments with the expectation and maximization (EM) algorithm and quadratic optimization.

Problem

• Estimating edge parameters in noisy max-linear Bayesian networks
• Analyzing normal distribution of parameter estimators in DAGs
• Implementing EM algorithm and quadratic optimization for inference

Innovation

• Uses max-linear Bayesian networks with noise
• Applies max-plus algebra and logarithm
• Employs EM algorithm and quadratic optimization