Consider a simplified learning scenario. Assume that the input dimension is one. Assume that the input variable x is uniformly distributed in the interval [-1, 1] . The data set consists of 2 points {x1, x2} and assume that the target function is f (x) = x2.
Thus, the full data set is The learning algorithm returns the line fitting these two points as g (H consists of functions of the form h(x) = ax + b). We are interested in the test performance (Bout) of our learning system with respect to the squared error measure, the bias and the var.
(a) Give the analytic expression for the average function g(x).
(b) Describe an experiment that you could run to determine (numerically) g(x) , Bout , bias, and var.
(c) Run your experiment and report the results. Compare Bout with bias+var. Provide a plot of your g(x) and f(x) (on the same plot).
(d) Compute analytically what Bout. bias and var should be.