Inference for max-linear Bayesian networks with noise

2025/05/01 by Adams, Mark, Ferry, Kamillo, Yoshida, Ruriko · 3 citations
#14T90 #62A09 #62H30 #90C20 #90C90 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2505.00229

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.

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• Minimum bounding polytropes for estimation of max-linear Bayesian networks
• A PC Algorithm for Max-Linear Bayesian Networks
• Structural Causal Models for Extremes: an Approach Based on Exponent Measures

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