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 D={(x1,x12),(x2,x22)}. 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 (E[Eout]) of our learning system with respect to the squared error measure, the bias and the var. (Week5 slides Page27 to Page29) (a) Give the analytic expression for the average function g(x). You are not required to compute ED[x1] and ED[x2] inside the formula of g(x). Hint: Use g(x)=ax+b,g(x1)=x12,g(x2)=x22 to obtain g(x)=ED[g(D)(x)]. (b) Compute analytically what E[Eout], bias and var should be. Hint: ED[x]=0,ED[x2]=31,ED[x3]=0,ED[x4]=51. 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 D={(x1,x12),(x2,x22)}. 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 (E[Eout]) of our learning system with respect to the squared error measure, the bias and the var. (Week5 slides Page27 to Page29) (a) Give the analytic expression for the average function g(x). You are not required to compute ED[x1] and ED[x2] inside the formula of g(x). Hint: Use g(x)=ax+b,g(x1)=x12,g(x2)=x22 to obtain g(x)=ED[g(D)(x)]. (b) Compute analytically what E[Eout], bias and var should be. Hint: ED[x]=0,ED[x2]=31,ED[x3]=0,ED[x4]=51