Data Analysis with Bayesian Networks: A Bootstrap Approach

By Nir Friedman, Moisés Goldszmidt, Abraham J. Wyner. 1999

In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high scores. We need to provide confidence measures on features of these networks: Is the existence of an edge between two nodes warranted? Is the Markov blanket of a given node robust? Can we say something about the ordering of the variables? We should be able to address these questions, even when the amount of data is not enough to induce a high scoring network. In this paper we propose Efron's Bootstrap as a computationally efficient approach for answering these questions. In addition, we propose to use these confidence measures to induce better structures from the data, and to detect the presence of latent variables.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Bayesian Structure Learning with Generative Flow Networks (2022, methodology): “, 2020)), non-parametric DAG Bootstrapping (Friedman et al., 1999) with PC (Spirtes et al.”
DAG-GNN: DAG Structure Learning with Graph Neural Networks (2019, background): “Many bootstrap (Friedman et al., 1999) and sampling-based structure learning algorithms (Madigan et al.”
DiBS: Differentiable Bayesian Structure Learning (2021, methodology): “We compare DiBS with the nonparametric DAG bootstrap [42] using the constraint-based PC [7] and the score-based GES [6] algorithms (BPC and BGES).”
Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification Part I: Algorithms and Empirical Evaluation (2010, methodology): “We note that SCA has greatly different inductive bias from the GLL variants and thus the comparison (provided that the causal generative model is a Bayesian network) is not unduly biased toward them, while still allowing induction of a credible causal graphical model.”
Being Bayesian about Network Structure (2000, methodology): “to the tradeoff curve of the non-parametric Bootstrap approach of [5], a non-Bayesian simulation approach to estimate “confidence” in features.”
Learning Bayesian networks: approaches and issues (2011, methodology): “Geiger et al. (1996) showed how the BIC scoring function could be used to score structures with missing data and hidden variables.”
Determining the Number of Non-Spurious Arcs in a Learned DAG Model: Investigation of a Bayesian and a Frequentist Approach (2007, methodology): “compute confidence measures on arcs (and other features) of induced Bayesian networks by using the bootstrap [11, 12] (or parametric bootstrap).”
Inferring subnetworks from perturbed expression profiles (2001, methodology): “We can generate such networks using non-parametric bootstrap (Friedman et al., 1999) or using more exact but costly MCMC simulations (Friedman and Koller, 2001).”
From vital signs to clinical outcomes for patients with sepsis: a machine learning basis for a clinical decision support system (2014, methodology): “Finally, the strength of the arcs within the networks was calculated using the bootstrap-based inference method 31 to provide a comparison between the BN1 and BN2 structures, in which the arc strengths ranged between 1 (strongest) and 0 (weakest).”