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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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Measures of Variability for Bayesian Network Graphical Structures
Marco Scutari · 2010-05-24 · via math.ST updates on arXiv.org

The structure of a Bayesian network includes a great deal of information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study its variability, which can be used to compare the performance of different learning algorithms and to measure the strength of any arbitrary subset of arcs. In this paper we will introduce some descriptive statistics and the corresponding parametric and Monte Carlo tests on the undirected graph underlying the structure of a Bayesian network, modeled as a multivariate Bernoulli random variable. A simple numeric example and the comparison of the performance of some structure learning algorithm on small samples will then illustrate their use.

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