l11usesofbayesiannetworks-展示頁(yè)
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【正文】 mize the parameters using EM. ? .. ? Easy to pute ? Can be good estimation of “true” distribution ? Might be plex to use (cardinality of latent variable might be very large) Page 22 BN Methods for Density Estimation ? LT model for density estimation ? Pearl 1988: As model over manifest variables, LTMs ? Are putationally very simple to work with. ? Can represent plex relationships among manifest variables. Page 23 BN Methods for Density Estimation ? New approximate inference algorithm for Bayesian works (Wang, Zhang and Chen, AAAI 08, JAIR 32: 879900, 08 ) Sample Learn sparse sparse dense dense Page 24 Outline ? Traditional Uses ? Structure Discovery ? Density Estimation ? Classification ? Clustering ? An HKUST Project Page 25 Bayesian Networks for Classification ? The problem: ? Given data: ? Find mapping ? (A1, A2, …, An) | C ? Possible solutions ? ANN ? Decision tree (Quinlan) ? … ? (SVM: Continuous data) A1 A2 … An C 0 1 … 0 T 1 0 … 1 F .. .. .. .. .. Page 26 Bayesian Networks for Classification ? Na239。 Technology Page 2 Outline ? Traditional Uses ? Structure Discovery ? Density Estimation ? Classification ? Clustering ? An HKUST Project Page 3 Traditional Uses ? Probabilistic Expert Systems ? Diagnostic ? Prediction ? Example: BN for diagnosing “blue baby” over phone in a London Hospital Comparable to specialist, Better than others Page 4 Traditional Uses ? Language for describing probabilistic models in Science amp。L11: Uses of Bayesian Networks Nevin L. Zhang Department of Computer Science amp。 Engineering The Hong Kong University of Science amp。 Engineering ? Example: BN for turbo code Page 5 Traditional Uses ? Language for describing probabilistic models in Science amp。ve Bayes model ? From data, learn ? P(C), P(Ai|C) ? Classification ? arg max_c P(C=c|A1=a1, …, An=an) ? Very good in practice Page 27 ? Drawback of NB: ? Attributes mutually independent given class variable ? Often violated, leading to double counting. ? Fixes: ? General BN classifiers ? Tree augmented Na239。ve Bayes models ? N. L. Zhang, T. D. Nielsen, and F. V. Jensen (2022). Latent variable discovery in classification models. Artificial Intelligence in Medicine, to appear. ? Capture dependence among attributes using latent variables ? Detect interesting latent structures besides classification ? Algorithm in the step of DHC.. ? … Page 31 Bayesian Networks for Classification ? Bayes Rule ? . ? ChowLiu ? LC model ? LT Model ? Wang Yi: Bayes rule + LT model is for superior Page 32 Outline ? Traditional Uses ? Structure Discovery ? Density Estimation ? Classification ? Clustering ? An HKUST Project Page 33 BN for Clustering ? Latent class (LC) model ? One latent variable ? A set of manifest variables ? Conditional Independence Assumption: ? Xi?s mutually independent given Y. ? Also known as Local Independence Assumption ? Used for cluster analysis of categorical data ? Determine cardinality of Y: number of clusters ? Determine P(Xi|Y): characteristics of clusters Page 34 BN for Clustering Clustering Criteria ? Distance based clustering: ? Minimizes intra
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