COMP0024 Artificial Intelligence and Neural Computing Problem sheet 4
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COMP0024 Artificial Intelligence and Neural Computing
Problem sheet 4
[Question 1] Consider a simple robot that has the ability to carry a standard sized box to/from any location in a warehouse. Suppose it can also lift the box from the floor onto itself, and it can lower the boz onto the floor. How could the interval calculus formulae for the blocks world be adapted for the robot.
[Question 2] The following two basic probability assignments are defined for the frame of discernment = {α, β, γ}. Give the combined basic probability assignment, the resulting belief function, and the resulting plau-sibility function.
[Question 3] Let AC be the complement of A. Does Bel(A) + Bel(AC ) = 1 hold in general? If yes, give a proof. If no, give a counterexample.
[Question 4] Let m be a basic probability assignment. Does m 4 m = m? If so, give a proof. If not, give a counterexample.
[Question 5] Let Ω = {a, b}. For a proposition AΩ, let the interval [x, y] be such that x = Bel(A) and y = Pl(A). Consider the intervals [1, 1], [0, 1], and [0, 0]. For each of the intervals, give an example of a basic probability assignment (bpa) and the proposition (i.e. the subset of Ω) for which the interval would be obtained.
[Question 6] Give an example of a very simple database with 4 training examples and that with the ID3 algorithm will produce a classification tree with exactly 4 leaf nodes. Give the calculations to justify your answer.
[Question 7] For the ID3 algorithm, the expected information needed to classify a (training) example is given by I(p, n), where p (respectively n) is the number of positive (respectively negative) examples.
What are the maximum and minimum values that I(p, n) can give? Give a clear and precise explanation with your answer.
2023-05-18