Dennis Sun DATA

Overview A large number of data analytical procedures are used for the purposes of prediction. The general form of a prediction problem is as follows: Uusually, the prediction is to be made in a way that minimizes some objective function error: ˆ f = argminˆf ′ Error(f, ˆ f ′) The Error() can be computed differently depending on circumstances. The space of possible predictions { ˆ f ′ ()} may be limited in some ways as well. There are a number of special cases for the general prediction problem. We identify some of them below: 1. Regression problems. The range of f (¯ x) is the set of real numbers 1. 2. Classification problems. Also known as supervised learning problems. The range of f (¯ x) is a finite nominal or ordinal (categorical) set of values, known as classes or categories. 3. Clustering problems otherwise known as unsupervised learning problems. The range of f (¯ x) is an unknown finite nominal or ordinal set of values. The observed data consists only of the { ¯ x 1 ,. .. ¯ x n } set of data points, without 1 Or simply an infinite, or very large finite set of numbers.