Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Learning equivalence classes of bayesian-network structures
The Journal of Machine Learning Research
Limitations of learning via embeddings in euclidean half spaces
The Journal of Machine Learning Research
Inner Product Spaces for Bayesian Networks
The Journal of Machine Learning Research
Learning Bayesian Networks
Compression-Based Averaging of Selective Naive Bayes Classifiers
The Journal of Machine Learning Research
Induction of multiple fuzzy decision trees based on rough set technique
Information Sciences: an International Journal
Max-margin Classification of Data with Absent Features
The Journal of Machine Learning Research
Discriminative Learning of Max-Sum Classifiers
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Pattern recognition with a Bayesian kernel combination machine
Pattern Recognition Letters
A simple graphical approach for understanding probabilistic inference in Bayesian networks
Information Sciences: an International Journal
Bayesian classifiers based on kernel density estimation: Flexible classifiers
International Journal of Approximate Reasoning
VC dimension and inner product space induced by Bayesian networks
International Journal of Approximate Reasoning
Data mining based Bayesian networks for best classification
Computational Statistics & Data Analysis
Improving generalization of fuzzy IF-THEN rules by maximizing fuzzy entropy
IEEE Transactions on Fuzzy Systems
Operations for inference in continuous Bayesian networks with linear deterministic variables
International Journal of Approximate Reasoning
Learning Bayesian network parameters under order constraints
International Journal of Approximate Reasoning
Bayesian network classification using spline-approximated kernel density estimation
Pattern Recognition Letters
A driver fatigue recognition model based on information fusion and dynamic Bayesian network
Information Sciences: an International Journal
Empirical analysis of an on-line adaptive system using a mixture of Bayesian networks
Information Sciences: an International Journal
| Hi-index | 0.07 |
The concept class C"N induced by a Bayesian network N can be embedded into some Euclidean inner product space. The Vapnik-Chervonenkis (VC)-dimension of the concept class and the minimum dimension of the inner product space are very important indicators for evaluating the classification capability of the Bayesian network. In this paper, we investigate the properties of the concept class C"N"^"k induced by a multivalued Bayesian network N^k, where each node X"i of N^k is a k-valued variable. We focus on the values of two dimensions: (i) the VC-dimension of the concept class C"N"^"k, denoted as VCdim(N^k), and (ii) the minimum dimension of the inner product space into which C"N"^"k can be embedded. We show that the values of these two dimensions are k^n-1 for fully connected k-valued Bayesian networks N"F^k with n variables. For non-fully connected k-valued Bayesian networks N^k without V-structure, we prove that the two dimensional values are (k-1)@?"i"="1^nk^m^"^i+1, where m"i denotes the number of parents for the i^t^h variable. We also derive the upper and lower bounds on the minimum dimension of the inner product space induced by non-fully connected Bayesian networks.