Chapter | 2 Statistical Machine Learning for HCI 9 where X is the random variable describing the example, represented by a d-dimensional vector, and Y is the class random variable. In that case, the objective is: given a new x, estimate the class poster- ior probabilities P(Y = 1|X = x) and P(Y = -1|X = x) and select the class yielding the highest estimate. In regression, the goal is to estimate a real valued scalar given some input vector. In this case, Z = (X, Y ) R d × R where now Y R . The objective becomes: given a new x, estimate E[Y |X = x], the expected value of Y given x. Finally, in density estimation, the problem is generally to esti- mate the probability that a given example is drawn from the same probability distribution as those of the training set. In that case, Z R d and the objective is: given a new z, estimate p(z).