Section A (Use a separate answer book for this Section) la Given the target function output representation what is the Least Mean Squares (LMS) training rule used for and how is it defined? Derive the gradient descent training rule assuming that the target function representation is: 1b Define explicitly the cost/error function E, assuming that a set of training examples D is provided, where each training example d e D is associated with the target output td. lc Prove that the LMS training rule performs a gradient descent to minimize the cost/error function E defined in 1b. Consider the instance space consisting of integer points in the x, y plane, where 0sx, ys 10, and the set of hypothesis consisting of rectangles (i.e., being of the form (a sxsb, cSy Sd), where 0sa, b, c, d10 What is the smallest number of training examples one needs to provide so that the CANDIDATE-ELIMINATION algorithm perfectly learns a particular target concept (e.g., (23xs4,6 3ys9)? Explain your answer in a clear manner (i.e., explain when can we say that the target concept is exactly learned in the case of the CANDIDATE-ELIMINATION algorithm and what is the optimal query strategy). ld Section A (Use a separate answer book for this Section) la Given the target function output representation what is the Least Mean Squares (LMS) training rule used for and how is it defined? Derive the gradient descent training rule assuming that the target function representation is: 1b Define explicitly the cost/error function E, assuming that a set of training examples D is provided, where each training example d e D is associated with the target output td. lc Prove that the LMS training rule performs a gradient descent to minimize the cost/error function E defined in 1b. Consider the instance space consisting of integer points in the x, y plane, where 0sx, ys 10, and the set of hypothesis consisting of rectangles (i.e., being of the form (a sxsb, cSy Sd), where 0sa, b, c, d10 What is the smallest number of training examples one needs to provide so that the CANDIDATE-ELIMINATION algorithm perfectly learns a particular target concept (e.g., (23xs4,6 3ys9)? Explain your answer in a clear manner (i.e., explain when can we say that the target concept is exactly learned in the case of the CANDIDATE-ELIMINATION algorithm and what is the optimal query strategy). ld