Unsupervised Learning

Abstract

The previous chapters have been concerned with predicting the values of one or more outputs or response variables Y = (Y ₁,..., Y _m ) for a given set of input or predictor variables X = (X ₁,..., X _P ). Denote by x _i = (x _i1,..., x _ip ) the inputs for the ith training case, and let y _i be a response measurement. The predictions are based on the training sample (x ₁, y ₁),..., (x _N , y _N ) of previously solved cases, where the joint values of all of the variables are known. This is called supervised learning or “learning with a teacher.” Under this metaphor the “student” presents an answer ŷ _i for each x _i in the training sample, and the supervisor or “teacher” provides either the correct answer and/or an error associated with the student’s answer. This is usually characterized by some loss function L(y, ŷ), for example, L(y, ŷ) = (y − ŷ)².