Consider a regression problem of trying to estimate the function f x-> y where x is a vector of feature attributes and y is a continuous real valued output variable. you would like to use a bagging model where you first create m bootstrap samples and then use them to create m different models - hi, h2, hm. you can assume that all models are of the same type. the error for each of the models would be described as: e: (x) = f(x) - hi(x) where x is the input data and hi is the model created using i bootstrap sample the expected value of the squared error for any of the models will be defined as: e& (x)) = e[(f(x) - h; (x))"} the average value of the expected squared error for each of the models acting individually is defined as: eave = ž 6.(x)=) now, you decide to aggregate the models using a committee approach as follows: hagg(x) = ni (x) the error using the aggregated model is defined as: pagg(x) = el 4 = (x) = f(x)/ eagg which can be simplified as: ec=alex8.coli eagge where we used the value of is defined above. prove that eagg = favg provided you make the following assumptions: 1. each of the errors have a 0 mean e((x)) = 0 for all i 2. errors are uncorrelated e(€(x)=; (x)) = 0 for all i #j