Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
cs-401r:assignment-2 [2014/09/18 04:34]
ringger [Exercises]
cs-401r:assignment-2 [2014/09/24 21:22] (current)
cs401rPML Updated labeling of sub-problems and/or problem options.
Line 12: Line 12:
 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 (option ​a) or (option ​b) (since they are equivalent),​ and apply the same [[Proofs|standard of proof]] as in assignment 1: 
-#* (a) $P(X | Y, Z) = P(X | Z)$ if and only if $P(Y | X, Z) = P(Y | Z)$ +#* (option ​a) $P(X | Y, Z) = P(X | Z)$ if and only if $P(Y | X, Z) = P(Y | Z)$ 
-#* (b) $P(X, Y | Z) = P(X | Z) \cdot P(Y|Z)$ if and only if $P(Y, X | Z) = P(Y | Z) \cdot P(X | Z)$+#* (option ​b) $P(X, Y | Z) = P(X | Z) \cdot P(Y|Z)$ if and only if $P(Y, X | Z) = P(Y | Z) \cdot P(X | Z)$
 #** (in other words, the "given $Z$" stays the same, while $X$ and $Y$ trade places). #** (in other words, the "given $Z$" stays the same, while $X$ and $Y$ trade places).
 # [20 points: 10 points each] (based on exercise 2.2 in Koller and Friedman) Independence:​ # [20 points: 10 points each] (based on exercise 2.2 in Koller and Friedman) Independence:​
-#* Prove that for binary random variables $X$ and $Y$, the event-level independence $(x^0 \bot y^0)$ implies random-variable independence $(X \bot Y)$.  Use the usual standard of proof. +#* (2.1) Prove that for binary random variables $X$ and $Y$, the event-level independence $(x^0 \bot y^0)$ implies random-variable independence $(X \bot Y)$.  Use the usual standard of proof. 
-#* Give a counterexample for nonbinary variables.+#* (2.2) 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.
 #* You may assume that you have access to a function that samples a uniform random variable with support [0,1]. #* You may assume that you have access to a function that samples a uniform random variable with support [0,1].
cs-401r/assignment-2.txt · Last modified: 2014/09/24 21:22 by cs401rPML
Back to top
CC Attribution-Share Alike 4.0 International
chimeric.de = chi`s home Valid CSS Driven by DokuWiki do yourself a favour and use a real browser - get firefox!! Recent changes RSS feed Valid XHTML 1.0