High-dimensional consistency in score-based and hybrid structure\n learning

2015/07/09 by Preetam Nandy, Nandy, Preetam, Alain Hauser +3 · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1507.02608

openalex publication_date 2015/07/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Main approaches for learning Bayesian networks can be classified as\nconstraint-based, score-based or hybrid methods. Although high-dimensional\nconsistency results are available for constraint-based methods like the PC\nalgorithm, such results have not been proved for score-based or hybrid methods,\nand most of the hybrid methods have not even shown to be consistent in the\nclassical setting where the number of variables remains fixed and the sample\nsize tends to infinity. In this paper, we show that consistency of hybrid\nmethods based on greedy equivalence search (GES) can be achieved in the\nclassical setting with adaptive restrictions on the search space that depend on\nthe current state of the algorithm. Moreover, we prove consistency of GES and\nadaptively restricted GES (ARGES) in several sparse high-dimensional settings.\nARGES scales well to sparse graphs with thousands of variables and our\nsimulation study indicates that both GES and ARGES generally outperform the PC\nalgorithm.\n

Cited by

• Causal Discovery on Higher-Order Interactions
• Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning
• Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models
• Optimal structure learning and conditional independence testing

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