Averaged one-dependence estimators

Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation. Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation. AODE seeks to estimate the probability of each class y given a specified set of features x1, ... xn, P(y | x1, ... xn). To do so it uses the formula where P ^ ( ⋅ ) {displaystyle {hat {P}}(cdot )} denotes an estimate of P ( ⋅ ) {displaystyle P(cdot )} , F ( ⋅ ) {displaystyle F(cdot )} is the frequency with which the argument appears in the sample data and m is a user specified minimum frequency with which a term must appear in order to be used in the outer summation. In recent practice m is usually set at 1. We seek to estimate P(y | x1, ... xn). By the definition of conditional probability For any 1 ≤ i ≤ n {displaystyle 1leq ileq n} , Under an assumption that x1, ... xn are independent given y and xi, it follows that This formula defines a special form of One Dependence Estimator (ODE), a variant of the naive Bayes classifier 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 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.