Introduction to Artificial Intelligence by Wolfgang Ertel

Author:Wolfgang Ertel
Language: eng
Format: epub, pdf
ISBN: 9783319584874
Publisher: Springer International Publishing

Exercise 7.5

Using the Lagrange multiplier method, show that, without explicit constraints, the uniform distribution p 1 = p 2 = … = p n = 1/n represents maximum entropy. Do not forget the implicitly ever-present constraint p 1 + p 2 + ··· + p n = 1. How can we show this same result using indifference?

Exercise 7.6

Use the PIT system (http://​www.​pit-systems.​de) or SPIRIT (http://​www.​xspirit.​de) to calculate the MaxEnt solution for P (B) under the constraint P (A) = α and P (B|A) = β. Which disadvantage of PIT, compared with calculation by hand, do you notice here?

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