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## Maximum a Posteriori Tree Augmented Naive Bayes Classifiers (2003)

### Citations

3469 |
UCI repository of machine learning databases
- Blake, Merz
- 1998
(Show Context)
Citation Context ... of some types of prior information such as “if edge (u, v) exists then edge (w, z) is very likely to exist”. 6 Empirical results We tested four algorithms over 17 datasets from the Irvine repository =-=[1]-=-. To discretize continuous attributes we used equal frequency discretization with 5 intervals. For each dataset and algorithm we tested both error rate and LogScore. LogScore is calculated by adding t... |

1157 | Learning Bayesian networks: The combination of knowledge and statistical data. - Heckerman, Geiger, et al. - 1995 |

818 | On the optimality of the simple Bayesian classifier under zero-one loss.
- Domingos, Pazzani
- 1997
(Show Context)
Citation Context ...classifiers. We end up with some conclusions and future work in section 7. 2s2 Tree Augmented Naive Bayes Tree Augmented Naive Bayes (TAN) appears as a natural extension to the Naive Bayes classifier =-=[10, 11, 6]-=-. TAN models are a restricted family of Bayesian networks in which the class variable has no parents and each attribute has as parents the class variable and at most one other attribute. An example of... |

796 | Bayesian network classifiers.
- Friedman, Geiger, et al.
- 1997
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Citation Context ...etworks, Bayesian network classifiers, Naive Bayes, decomposable distributions, Bayesian model averaging. 1s1 Introduction Bayesian classifiers as Naive Bayes [11] or Tree Augmented Naive Bayes (TAN) =-=[7]-=- have shown excellent performance in spite of their simplicity and heavy underlying independence assumptions. In our opinion, the TAN classifier, as presented in [7], has two weak points: not taking i... |

439 | An analysis of Bayesian classifier
- Langley, Iba, et al.
- 1992
(Show Context)
Citation Context ...uivalent complexity. Keywords: Bayesian networks, Bayesian network classifiers, Naive Bayes, decomposable distributions, Bayesian model averaging. 1s1 Introduction Bayesian classifiers as Naive Bayes =-=[11]-=- or Tree Augmented Naive Bayes (TAN) [7] have shown excellent performance in spite of their simplicity and heavy underlying independence assumptions. In our opinion, the TAN classifier, as presented i... |

145 | Learning with mixtures of trees
- Meilă, Jordan
(Show Context)
Citation Context ...u|C(su, sC) = θC(sC) = ′ N u,v,C (su,sv,sC ) N ′ v,C (sv,sC) ′ N u,C (su,sC) N ′ C (sC ) ′ N C (sC ) N ′ (24) A similar result in the case of decomposable distribution over trees can also be found in =-=[14]-=-. Given a decomposable prior we can calculate the decomposable posterior using the result in section 3.3 and then apply the result we have just enunciated to the posterior. The posterior probability d... |

58 | An Optimal Minimum Spanning Tree Algorithm,
- Pettie, Ramachandran
- 2002
(Show Context)
Citation Context ...e undirected tree by calculating the logarithm of every element in the matrix and then running any algorithm for finding the MWST. The complexity of the MWST algorithm for a complete graph is O(n 2 ) =-=[15]-=-. 4.2 Calculating the MAP TAN structure given a prior decomposable distribution over TANs In section 3.3 we enunciated that if we assume a decomposable prior distribution over TANs with hyperparameter... |

44 | Tractable Bayesian learning of tree belief networks.
- Meila, Jaakkola
- 2006
(Show Context)
Citation Context ... edges of the tree is much more (equiv. much less) likely than the others it is very easy to incorporate this knowledge when fixing the prior hyperparameter matrix β. Evidently, as was pointed out in =-=[12]-=-, decomposable distributions do not allow the expression of some types of prior information such as “if edge (u, v) exists then edge (w, z) is very likely to exist”. 6 Empirical results We tested four... |

22 |
An algorithm for finding k minimum spanning trees,”
- Katoh, Ibaraki, et al.
- 1981
(Show Context)
Citation Context ...bability weights given a prior decomposable distribution over TANs The problem of computing the k MWST in order is well known and can be solved in O((log(β(n 2 , n)) + k) · n 2 ) for a complete graph =-=[9]-=-. It is easy to see 9sprocedure MAPTANStructure (Dataset D,Matrix β,CountingSet N ′ ) var CountingSet N ′ ; Matrix lβ ∗ ; begin N ′∗ = CalcN’PosteriorTAN(D,N ′ ); lβ ∗ = CalcLogBetaPosteriorTAN(β,N ′ ... |

9 | Bayes Optimal Instance-Based Learning.
- Kontkanen, Myllymaki, et al.
- 1998
(Show Context)
Citation Context ...classifiers. We end up with some conclusions and future work in section 7. 2s2 Tree Augmented Naive Bayes Tree Augmented Naive Bayes (TAN) appears as a natural extension to the Naive Bayes classifier =-=[10, 11, 6]-=-. TAN models are a restricted family of Bayesian networks in which the class variable has no parents and each attribute has as parents the class variable and at most one other attribute. An example of... |

5 | Applying General Bayesian Techniques to Improve TAN Induction
- Cerquides
- 1999
(Show Context)
Citation Context ...[7], has two weak points: not taking into account model uncertainty and lacking a theoretically well founded explanation for the use of softening of the induced model parameters (see section 2.2). In =-=[3]-=- an alternative classifier based on empirical local Bayesian model averaging was proposed as a possible improvement for the first weak point. Furthermore, in [4] the fact that decomposable distributio... |

4 |
Some thoughts on the current state of data mining software applications
- Thearling
- 1998
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Citation Context ...hm for learning k TAN models proposed in [3]. maptan+bma has a classification time complexity, O(nrk) reasonably higher than that of stan. Furthermore, we can use k as an effort knob, in the sense of =-=[16]-=-, hence providing a useful feature for data mining users that allows them to decide how much computational power they want to spend in the task. In our opinion, maptan+bma provides a good complexity t... |

1 |
Improving bayesian network classifiers. PhD thesis draft, downloadable at http://www.maia.ub.es/∼cerquide/papers/PhD.pdf
- Cerquides
(Show Context)
Citation Context ...ution with hyperparameters β, N ′ . Then, P (C = sC|V = S, E, ξ), the probability of a class sC given an unclassified instance S and an undirected TAN structure E, fulfills where The proof appears in =-=[2]-=-. P (C = sC|V = S, E, ξ) ∝ h S,sC 0 h S,sC 0 h S,sC u,v = = 1 1 Zβ N ′ � Au∈V � u,v∈E h S,sC u,v (18) N ′ u,C(su, sC) (19) N ′ v,u,C (sv, su, sC) N ′ u,C (su, sC)N ′ v,C (sv, sC) (20) 4 Maximum a Post... |