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EPGY Day 8


Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Cyber Stalking Assignments

  • AI Engineer - AI Scientist

Research Clusters - 20 minutes

Red and Black Review

Probability Range

  • 0 ≤ P(A) ≤ 1

Rule of Addition

  • P(A∪B) = P(A) + P(B) - P(A∩B)

Disjoint Events Events A and B are disjoint iff

  • P(A∩B) = 0

Conditional Probability

  • P(A | B) = P(A∩B) / P(B)
True Bayesians actually consider conditional probabilities as more basic than joint probabilities . It is easy to define P(A|B) without reference to the joint probability P(A,B). To see this note that we can rearrange the conditional probability formula to get:
P(A|B) P(B) = P(A,B)
but by symmetry we can also get:
P(B|A) P(A) = P(A,B)
It follows that:
which is the so-called Bayes Rule.

Bayes Problem/Solution

Remember: Finite State Machines? - Deterministic

Bayes Nets:

Building a k-D tree

Application: 3-D graphics

Algorithm BuildKDTree (S, depth) 

input: a set of points S, the current depth depth 
output: the root of a kD-tree storing S 

if S contains only one point 
    then return a leaf storing this point 
else if depth is even 
    then Split S into 2 subsets with a vertical line L through the median x-coord 
    else Split, 2 subsets with a horizontal line 

v_left <- BuildKDTree (S1, depth+1) 
v_right <- BuildKDTree (S2, depth+1) 
v <- L 
return v

Data Classification

Application: Separating Audio Tracks

Audio ML:


Application: Language

Language ML:

  • 20Q Wordnet Conceptnet
  • Argument Champion
  • Restaurant Game

Decision Trees


/soe/sherol/.html/teaching/data/pages/epgy/ai13/day_8.txt · Last modified: 2013/07/26 12:22 by ffpaladin