Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Knowledge representation and inference in similarity networks and Bayesian multinets
Artificial Intelligence
A tutorial on learning with Bayesian networks
Learning in graphical models
Learning Recursive Bayesian Multinets for Data Clustering by Means of Constructive Induction
Machine Learning - Special issue: Unsupervised learning
Learning Probabilistic Relational Models
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
An Introduction to the Kalman Filter
An Introduction to the Kalman Filter
Dynamic bayesian networks: representation, inference and learning
Dynamic bayesian networks: representation, inference and learning
Separating Style and Content with Bilinear Models
Neural Computation
Learning Bayesian network parameters under order constraints
International Journal of Approximate Reasoning
Object-oriented Bayesian networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Learning Bayesian network parameters under incomplete data with domain knowledge
Pattern Recognition
Bayesian networks and the imprecise Dirichlet model applied to recognition problems
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Tutorial and selected approaches on parameter learning in bayesian network with incomplete data
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
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The task of learning models for many real-world problems requires incorporating domain knowledge into learning algorithms, to enable accurate learning from a realistic volume of training data. Domain knowledge can come in many forms. For example, expert knowledge about the relevance of variables relative to a certain problem can help perform better feature selection. Domain knowledge about the conditional independence relationships among variables can help learning of the Bayesian Network structure. This paper considers a different type of domain knowledge for constraining parameter estimates when learning Bayesian Networks. In particular, we consider domain knowledge that comes in the form of inequality constraints among subsets of parameters in a Bayesian Network with known structure. These parameter constraints are incorporated into learning procedures for Bayesian Networks, by formulating this task as a constrained optimization problem. The main contribution of this paper is the derivation of closed form Maximum Likelihood parameter estimators in the above setting.