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502:{\displaystyle {\hat {P}}(y\mid x_{1},\ldots x_{n})={\frac {\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y,x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y,x_{i})}{\sum _{y^{\prime }\in Y}\sum _{i:1\leq i\leq n\wedge F(x_{i})\geq m}{\hat {P}}(y^{\prime },x_{i})\prod _{j=1}^{n}{\hat {P}}(x_{j}\mid y^{\prime },x_{i})}}}
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that makes the above independence assumption that is weaker (and hence potentially less harmful) than the naive Bayes' independence assumption. In consequence, each ODE should create a less biased estimator than naive Bayes. However, because the base probability estimates are each conditioned by two
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whereby the classifier can be updated efficiently with information from new examples as they become available. It predicts class probabilities rather than simply predicting a single class, allowing the user to determine the confidence with which each classification can be made. Its probabilistic
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is the number of classes. This makes it infeasible for application to high-dimensional data. However, within that limitation, it is linear with respect to the number of training examples and hence can efficiently process large numbers of training examples.
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variables rather than one, they are formed from less data (the training examples that satisfy both variables) and hence are likely to have more variance. AODE reduces this variance by averaging the estimates of all such ODEs.
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31:. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation.
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Like naive Bayes, AODE does not perform model selection and does not use tuneable parameters. As a result, it has low variance. It supports
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is a user specified minimum frequency with which a term must appear in order to be used in the outer summation. In recent practice
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786:{\displaystyle P(y\mid x_{1},\ldots x_{n})={\frac {P(y,x_{1},\ldots x_{n})}{P(x_{1},\ldots x_{n})}}.}
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technique. It was developed to address the attribute-independence problem of the popular
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This formula defines a special form of One
Dependence Estimator (ODE), a variant of the
1146:{\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})\prod _{j=1}^{n}P(x_{j}\mid y,x_{i}).}
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967:{\displaystyle P(y,x_{1},\ldots x_{n})=P(y,x_{i})P(x_{1},\ldots x_{n}\mid y,x_{i}).}
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is the frequency with which the argument appears in the sample data and
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model can directly handle situations where some data are missing.
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1412:"Not So Naive Bayes: Aggregating One-Dependence Estimators"
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machine learning suite includes an implementation of AODE.
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AODE seeks to estimate the probability of each class
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642:). By the definition of conditional probability
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543:{\displaystyle {\hat {P}}(\cdot )}
43:given a specified set of features
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620:Derivation of the AODE classifier
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1452:Statistical classification
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1290:Cluster-weighted modeling
1248:{\displaystyle O(kn^{2})}
1209:{\displaystyle O(ln^{2})}
977:Under an assumption that
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572:{\displaystyle P(\cdot )}
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29:naive Bayes classifier
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1447:Bayesian estimation
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1317:Please help
1312:verification
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1436:Categories
1398:References
1375:March 2011
1345:newspapers
1276:The free
1119:∣
1083:∏
1038:…
940:∣
927:…
864:…
813:≤
807:≤
762:…
725:…
678:…
662:∣
593:⋅
564:⋅
535:⋅
526:^
476:′
468:∣
449:^
423:∏
401:′
387:^
373:≥
351:∧
345:≤
339:≤
326:∑
317:∈
312:′
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278:∣
259:^
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204:^
190:≥
168:∧
162:≤
156:≤
143:∑
120:…
104:∣
92:^
1284:See also
796:For any
1359:scholar
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1340:
1332:
984:, ...
635:, ...
512:where
68:, ...
50:, ...
1366:JSTOR
1352:books
1338:news
1278:Weka
995:and
57:, P(
21:AODE
1420:doi
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