Pattern Recognition, 4th Edition

3.5. Mean Square Estimation Revisited

3.5.1. Mean Square Error Regression

In this subsection, we will approach the MSE task from a slightly different perspective and in a more general framework.

Let y, x be two random vector variables of dimensions M × 1 and l × 1, respectively, and assume that they are described by the joint pdf p(y, x). The task of interest is to estimate the value of y, given the value of x that is obtained from an experiment. No doubt the classification task falls under this more general formulation. For example, when we are given a feature vector x, our goal is to estimate the value of the class label y, which is ±1 in the two-class case. In a more general setting, the values of y may not be discrete. Take, as an example, ...