The point of optimal scoring is to turn the categorical class labels into quantitative variables. Let θ(g) = [θ(g1), . . ., θ(gn)]T be the n × 1 vector of quantitative scores assigned to g for the kth class. The optimal scoring problem involves finding the vector of coefficients η ≡ (η1, η2, . . ., ηp) and the scoring map θ : {0, 1} → R that minimize the following average squared residual: ASR=n−1∑i=1n{θ(gi)−XiTη}2.(1)
