:**Simple Example of Bayesian Network.** Simple Bayesian Network for predicting rain (outcome variable, red) based on temperature and cloud cover (predictor variables, blue). The structure of the network indicates that the probabilities of the predictor variables are independently used to predict the outcome (“Naïve” Bayesian). Probabilities for each outcome given the state of the predictor are given in each predictor node, while the joint probability for each combination is given in the outcome box. The probability of a given outcome can then be calculated based on the joint probabilities given the state of the predictor variables and the prior probabilities of the outcomes. For example, assume cloudy skies and a hot temperature, and that the prior probabilities of rain/not rain are each .5, In this case, the prior probabilities cancel out and the conditional probability (P(rain)|Hot&Cloudy) equals (.15/(.15+.3)) = .33, and P(not rain|Hot&Cloudy) equals (.3/(.15+.3)) = .67. A Bayesian network classifier would therefore predict no rain. :**Simple Example of Support Vector Machine.** Simple Support Vector Machine for predicting rain given temperature and cloud cover, as in . Temperature is represented on the vertical axis, while cloud cover has been dichotomized (−1 = clear, 1 = cloudy). Clear instances are represented diamonds, while cloudy instances are represented by squares. The separating hyperplane is the dotted line, calculated as a combination of a subset of the training data points (support vectors). An instance to be classified that maps to the space above the hyperplane would be predicted to have no rain (e.g. high temperature, not cloudy), while those mapping below the hyperplane would be predicted to be rainy (e.g. low temperature, cloudy). In this ideal case, the hyperplane cleanly separates the classes; however, in a case where this would not be possible (e.g., a hot, clear, rainy day in the training data), the classifier attempts to construct a hyperplane that minimizes the error rate of the classifier.

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