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# Homework-6 - Homework-6 Question 1 As discussed in class...

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Homework-6 Question 1 As discussed in class the concept of a medium built man can be expressed as an axis parallel rectangle. Therefore, it can be defined in terms of 4 real numbers: a, b, c, d such that: a height b, c weight d We assume that a consistent algorithm is available. Part I In this part we take as hypotheses 4 floating point numbers, each represented in terms of 4 bytes (32 bits). a How many hypotheses are in the hypotheses class? b How many rendomly obtained examples are needed for PAC learning with accuracy parameter = 0 . 1 and confidence parameter δ = 0 . 05? c What is the confidence level (what is δ ) if it is known that 1000 randomly chosen examples were used, and the desired accuracy is level is = 0 . 1? d What is the accuracy level (what is ) if it is known that 1000 randomly chosen examples were used, and the desired confidence level is δ = 0 . 05? Part II In this part we assume that we are able to represent arbitrarily accurate axis parallel rectangles. a Prove that the VC dimension of the concept class of all axis parallel rectangles is d = 4. b How many rendomly obtained examples are needed for PAC learning with accuracy parameter = 0 . 1 and confidence parameter δ = 0 . 05? c What is the confidence level (what is δ ) if it is known that 1000 randomly chosen examples were used, and the desired accuracy is level is = 0 . 1?

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