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
A study of smoothing methods for language models applied to Ad Hoc information retrieval
Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval
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
Clinical and financial outcomes analysis with existing hospital patient records
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Learning to Decode Cognitive States from Brain Images
Machine Learning
Dependent Dirichlet priors and optimal linear estimators for belief net parameters
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Separating Style and Content with Bilinear Models
Neural Computation
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
ICML '06 Proceedings of the 23rd international conference on Machine learning
The Interplay of Optimization and Machine Learning Research
The Journal of Machine Learning Research
Classification in Very High Dimensional Problems with Handfuls of Examples
PKDD 2007 Proceedings of the 11th European conference on Principles and Practice of Knowledge Discovery in Databases
Discovering Constrained Substructures in Bayesian Trees Using the E.M. Algorithm
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Bayesian Inference Under Probability Constraints
Proceedings of the 2008 conference on Tenth Scandinavian Conference on Artificial Intelligence: SCAI 2008
A conditional independence algorithm for learning undirected graphical models
Journal of Computer and System Sciences
Domain knowledge uncertainty and probabilistic parameter constraints
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A modular design of Bayesian networks using expert knowledge: Context-aware home service robot
Expert Systems with Applications: An International Journal
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
Combining subjective probabilities and data in training markov logic networks
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Confidence estimation of feedback information for logicdiagnosis
Engineering Applications of Artificial Intelligence
Incorporating expert judgement into Bayesian network machine learning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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. This paper considers a variety of types of domain knowledge for constraining parameter estimates when learning Bayesian networks. In particular, we consider domain knowledge that constrains the values or relationships among subsets of parameters in a Bayesian network with known structure. We incorporate a wide variety of parameter constraints into learning procedures for Bayesian networks, by formulating this task as a constrained optimization problem. The assumptions made in module networks, dynamic Bayes nets and context specific independence models can be viewed as particular cases of such parameter constraints. We present closed form solutions or fast iterative algorithms for estimating parameters subject to several specific classes of parameter constraints, including equalities and inequalities among parameters, constraints on individual parameters, and constraints on sums and ratios of parameters, for discrete and continuous variables. Our methods cover learning from both frequentist and Bayesian points of view, from both complete and incomplete data. We present formal guarantees for our estimators, as well as methods for automatically learning useful parameter constraints from data. To validate our approach, we apply it to the domain of fMRI brain image analysis. Here we demonstrate the ability of our system to first learn useful relationships among parameters, and then to use them to constrain the training of the Bayesian network, resulting in improved cross-validated accuracy of the learned model. Experiments on synthetic data are also presented.