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cs-401r:assignment-2 [2014/09/12 08:51]
ringger [Exercises]
cs-401r:assignment-2 [2014/09/17 22:34]
ringger [Exercises]
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-Bayes Nets =+Probability Theory ​=
  
 == Objectives == == Objectives ==
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 == Exercises == == Exercises ==
  
-Show your work. Be clear and concise. ​ '''​This assignment must be typed.'''​+Show your work.  Be clear and concise. ​ '''​This assignment must be typed.'''​
  
 # [10 points] Prove that the relationship we call ''​conditional independence''​ is symmetric. ​ In other words, Prove either (a) or (b) (since they are equivalent),​ and apply the same [[Proofs|standard of proof]] as in assignment 1: # [10 points] Prove that the relationship we call ''​conditional independence''​ is symmetric. ​ In other words, Prove either (a) or (b) (since they are equivalent),​ and apply the same [[Proofs|standard of proof]] as in assignment 1:
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 #* Give a counterexample for nonbinary variables. #* Give a counterexample for nonbinary variables.
 # [20 points] Consider how to sample from a categorical distribution over four colors. ​ Think of a spinner with four regions having probabilities $p_{red}$, $p_{green}$,​ $p_{yellow}$,​ and $p_{blue}$. ​ Write pseudo-code for choosing a sample from this distribution. # [20 points] Consider how to sample from a categorical distribution over four colors. ​ Think of a spinner with four regions having probabilities $p_{red}$, $p_{green}$,​ $p_{yellow}$,​ and $p_{blue}$. ​ Write pseudo-code for choosing a sample from this distribution.
-# [10 points] Does your pseudo-code scale to a distribution over ten thousand values? ​ If not, rewrite it.  If so, say why. +#* You may assume that you have access to a function that samples a uniform random variable with support [0,1]. 
-# [20 points] Implement your pseudo-code,​ run it 100 times, ​and give the results as a vector of counts over the four colors.+# [10 points] Does your pseudo-code scale to run efficiently on a distribution over ten thousand values? ​ If not, rewrite it.  If so, say why. 
 +# [20 points] Implement your pseudo-code, ​choose values for the four probabilities on the spinner as parameters to your procedure, and run it 100 times, ​keeping track of how many times each color shows up.  Give the results as a vector of counts over the four colors.
 # [10 points] Normalize your count vector by 100.  How does the result compare with your chosen parameters? # [10 points] Normalize your count vector by 100.  How does the result compare with your chosen parameters?
-# [10 points] Compute the mean and variance of the estimated multinomial distribution you just discovered. 
  
  
cs-401r/assignment-2.txt · Last modified: 2014/09/24 15:22 by cs401rPML
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