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Unformatted text preview: CSCI 5512: Artificial Intelligence II (Spring10) Homework 3 (Due April 12 at 4pm) 1. (15 points) Describe all the assumptions that a Kalman filter model makes. Describe one concrete scenario in which one/more of the assumptions are inappropriate. Do you think extended Kalman filtering will be more appropriate in this scenario? 2. (35 points) [Programming Assignment] Consider the umbrella network shown in Figure 1. Let u 1: T = ( U 1 ,U 2 ,...,U T ) denote the sequence of evidence variables for the first T time steps, where i, U i = t (true) or f (false). Let R i be the random variable corresponding to the hidden state at step i . Consider the following three evidence sequences: (i) u 1:10 = ( t,t,t,t,f,f,f,f,f,f ) (ii) u 1:10 = ( f,f,f,f,f,f,f,f,t,t ) (iii) u 1:10 = ( t,f,t,f,t,f,t,f,t,f ) t Rain t Umbrella Rain t-1 Umbrella t-1 Rain t +1 Umbrella t +1 R t-1 t P(R ) 0.3 f 0.7 t t R t P(U ) 0.9 t 0.2 f Figure 1: The Umbrella Network For each of the three choices of u 1:10 , (a) (15 points) Estimate P ( R 10 | u 1:10 ) using likelihood weighting using 100 and 1000 samples. You have to submit code for lwUmbrella which takes 3 arguments: an integer numSamples , denoting the number of samples (set to 100 and 1000), an integer numSteps , denoting the number of steps (set to 10), and a vector evidence , denoting the evidence u 1: numSteps as a binary vector (with t = 1 ,f = 0) of length numSteps . The output should be the estimate P ( R numSteps | u 1: numSteps ) and the variance of the estimate. Note that lwUmbrella script will be different from the likelihood weighting code for Homework 2, since all samples have to be run in parallel for the umbrella network....
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- Spring '08