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ex7 - CS221 Exercise Set 7 1 CS 221 Autumn 2007 Exercise...

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CS221 Exercise Set 7 1 CS 221, Autumn 2007 Exercise Set 7: Bayesian Networks 1. Bayesian Networks and Chocolate Suppose you’re watching chocolate being produced on a conveyor belt in a factory. There are two levers controlling production, one that controls whether the chocolate is plain or almond, and another that controls whether there is coconut or not. The levers stay in the position they’re in with probability .7 and switch to the other setting .3, the two levers operating independently. At the start of the day, the lever is in either setting with equal probability. From observing the conveyor belt, you can only tell what color the chocolate is, and have the following table of probabilities for the color given what’s inside. Inside P(Color=Light | Inside) P(Color=Dark | Inside) Plain 0.1 0.9 Almond 0.3 0.7 Coconut 0.8 0.2 Almond + Coconut 0.9 0.1 Let X i represent the state of the two levers at time step i , and let Y i represent the ob- servation at time step i . So, the domain of X i is { Plain, Almond, Coconut, Almond + Chocolate }
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