Fusion, propagation, and structuring in belief networks
Artificial Intelligence
Estimation of multinomial probabilities under a model constraint
Journal of Multivariate Analysis
Machine Learning - Special issue on learning with probabilistic representations
Improving Text Classification by Shrinkage in a Hierarchy of Classes
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Relational Markov models and their application to adaptive web navigation
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Learning Bayesian network classifiers by maximizing conditional likelihood
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Learning class-discriminative dynamic Bayesian networks
ICML '05 Proceedings of the 22nd international conference on Machine learning
Functional Brain Imaging of Young, Nondemented, and Demented Older Adults
Journal of Cognitive Neuroscience
Learning bayesian networks from hierarchically related data with a neuroimaging application
Learning bayesian networks from hierarchically related data with a neuroimaging application
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
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Maximum likelihood estimates (MLEs) are commonly used to parameterize Bayesian networks. Unfortunately, these estimates frequently have unacceptably high variance and often overfit the training data. Laplacian correction can be used to smooth the MLEs towards a uniform distribution. However, the uniform distribution may represent an unrealistic relationships in the domain being modeled and can add an unreasonable bias. We present a shrinkage estimator for domains with hierarchically related random variables that smoothes MLEs towards other distributions found in the training data. Our methods are quick enough to be performed during Bayesian network structure searches. On both a simulated and a real-world neuroimaging domain, we empirically demonstrate that our estimator yields superior parameters in the presence of noise and greater likelihoods on left-out data.