[Designing the optimal predictor for continuous output spaces] We studied in class that the "Bayes Classifier" (f := arg maxy PYX)) is optimal in the sense that it minimizes generalization error over the underlying distribution that is, it maximizes z.y 1 g(z) = y But what can we say when the output space is continuous? Consider predictors of the kind g : X R that predict a real-valued output for a given input E . One intuitive way to define the quality of of such a predictor g is as Observe that one would want a predictor g with the lowest Q(g). Show that if one defines the predictor as f(x) := E[YX = x], then Q(f) Q(g) for any g, thereby showing that f is the optimal predictor with respect to Q for continuous output spaces. [Designing the optimal predictor for continuous output spaces] We studied in class that the "Bayes Classifier" (f := arg maxy PYX)) is optimal in the sense that it minimizes generalization error over the underlying distribution that is, it maximizes z.y 1 g(z) = y But what can we say when the output space is continuous? Consider predictors of the kind g : X R that predict a real-valued output for a given input E . One intuitive way to define the quality of of such a predictor g is as Observe that one would want a predictor g with the lowest Q(g). Show that if one defines the predictor as f(x) := E[YX = x], then Q(f) Q(g) for any g, thereby showing that f is the optimal predictor with respect to Q for continuous output spaces