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Summary of Greedy Equivalence Search For Nonparametric Graphical Models, by Bryon Aragam


Greedy equivalence search for nonparametric graphical models

by Bryon Aragam

First submitted to arxiv on: 25 Jun 2024

Categories

  • Main: Machine Learning (stat.ML)
  • Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)

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Summary difficulty Written by Summary
High Paper authors High Difficulty Summary
Read the original abstract here
Medium GrooveSquid.com (original content) Medium Difficulty Summary
Medium Difficulty summary: The paper revisits the greedy equivalence search (GES) algorithm, a cornerstone in graphical modeling and Bayesian model selection. Initially developed by Chickering and Meek, GES efficiently estimates the structure of directed acyclic graph (DAG) models in specific scenarios like Gaussian and discrete models. However, this theory lacks a general framework for non-parametric DAG models that don’t necessarily belong to curved exponential families or parametric models. This paper bridges this gap by establishing the consistency of GES for general DAG models satisfying smoothness conditions on the Markov factorization. The proof leverages recent advances in non-parametric Bayes, constructing a test for comparing misspecified DAG models without relying on Laplace approximations. When applicable, the paper recovers the classical result, providing a general consistency theorem for GES applied to general DAG models.
Low GrooveSquid.com (original content) Low Difficulty Summary
Low Difficulty summary: This paper is about improving an important tool called Greedy Equivalence Search (GES). GES helps us understand complex systems by building simple models that fit real data. The original version of GES worked well for specific types of data, but it didn’t cover all possible scenarios. This new study makes GES work better for more general cases by using recent advancements in a field called non-parametric Bayes. The result is a reliable way to compare different models and find the best one that fits the data.

Keywords

» Artificial intelligence