Data have just y and x as output and input variables.
We are interested in constructing a step function learner as follows:
First draw a random number U uniformly on the interval spanned by the
minimum and maximum values of the inputs (x1, ... , xn) and then use it to construct the following function whose purpose is to give the prediction of
Y given X = x: f(x)= alpha1 I(U <= x) + Alpha2 I(U >x),
where alpha1 and alpha2 are just unknown constants to be learned.
It goes without saying that I(some statement) is the indicator function that equals 1 when the statement is true and 0 otherwise.
a. Use two different methods to compute the estimate f(x)= alpha1 I(U<=
x)+ alpha2 I(U > x). Is f^ a strong learner?
b. Use one of the previous two methods to write an R function that takes as input x and the data (x1, ..., xn, y1; ..., yn) and gives as output f^(x). Make sure the function is capable of dealing with the case where x conatains more than one number.
c. Using three different runs of the previous function, create three different plots where, on each, f^ is shown together with the scatter plot of the data.
