(24th-May-2020)
• If e is an example, a point estimate for target feature Y is a prediction of a particular value for Y on e. Let pval(e,Y) be the predicted value for target feature Y on example e. The error for this example on this feature is a measure of how close pval(e,Y) is to val(e,Y), where val(e,Y) is the actual value for feature Y in e.
• For regression, when the target feature Y is real valued, both pval(e,Y) and val(e,Y) are real numbers that can be compared arithmetically.
• For classification, when the target feature Y is a discrete variable, a number of alternatives exist:
• When Y is binary, one value can be associated with 0, the other value with 1, and a prediction can be some real number. The predicted and actual values can be compared numerically.
• When the domain of Y has more than two values, sometimes the values are totally ordered and can be scaled so a real number can be associated with each value of the domain of Y. In this case, the predicted and actual values can be compared on this scale. Often, this is not appropriate even when the values are totally ordered; for example, suppose the values are short, medium, and long. The prediction that the value is short ∨ long is very different from the prediction that the value is medium.
• When the domain of Y is {v1,...,vk}, where k>2, a separate prediction can be made for each vi. This can be modeled by having a binary indicator variable associated with each vi which, for each example, has value 1 when the example has value vi and the indicator variable has value 0 otherwise. For each training example, exactly one of the indicator variables associated with Y will be 1 and the others will be 0. A prediction gives k real numbers - one real number for each vi.
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