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Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper, we provide a complete algebraic characterization of these models when the observed variables are discrete and no assumption is made about the state-space of the latent variables.
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We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular, these two models have the same dimension, differing only by inequality constraints for which there is no general description. The nested Markov model is therefore the closest possible description of the latent variable model that avoids consideration of inequalities.
A consequence of this is that the constraint finding algorithm of Tian and Pearl [In Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence —] is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and nonregular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.
Source Ann. Zentralblatt MATH identifier Subjects Primary: 62H None of the above, but in this section 62F Asymptotic properties of estimators. Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Get access to the full version of this article.wikbud.eu/wp-content/2020-01-28/4090.php
Probabilistic Graphical Models: Bayesian Networks
View access options below. You previously purchased this article through ReadCube. Institutional Login. Log in to Wiley Online Library. Purchase Instant Access. View Preview. Learn more Check out. Citing Literature. Volume 80 , Issue 1 April Pages Related Information. Python Machine Learning Second Edition takes a practical, hands-on coding approach so you can learn about machine learning by coding with Python.
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Top charts. New arrivals. This book is a thorough introduction to the formal foundations and practical applications of Bayesian networks. It provides an extensive discussion of techniques for building Bayesian networks that model real-world situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis.
Using Bayesian networks to manage uncertainty in student modeling — Arizona State University
It also treats exact and approximate inference algorithms at both theoretical and practical levels. The treatment of exact algorithms covers the main inference paradigms based on elimination and conditioning and includes advanced methods for compiling Bayesian networks, time-space tradeoffs, and exploiting local structure of massively connected networks. The treatment of approximate algorithms covers the main inference paradigms based on sampling and optimization and includes influential algorithms such as importance sampling, MCMC, and belief propagation.
The author assumes very little background on the covered subjects, supplying in-depth discussions for theoretically inclined readers and enough practical details to provide an algorithmic cookbook for the system developer. Reviews Review Policy. Published on.
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A Brief Introduction to Graphical Models and Bayesian Networks
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See more. Probability with Martingales. David Williams. Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions.
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The authors show how an IM produces meaning.