Bayesian Networks

1
Bayesian Networks

• Jay Gagnon
• Brian Keuling

2
Bayesian Networks

• Directed Acyclic Graph (DAG)
• Nodes variables
• Arcs dependence relationship
• Conditional probability associated with nodes
• Nodes with parents are called conditional
• Nodes without parents are called unconditional

3
Graph Example
4
Bayes Theorem

• Reverend Thomas Bayes (1702 - 1761)
• Uses inverse probability
• Probabilities of previous events affect the
  probability of a future event
• Bayes Rule P(AB) P(BA) x P(A) / P(B)
• The probability of A given B equals the
  probability of B given A times the probability of
  A, divided by the probability of B.
• posterior likelihood x prior / normalizing
  constant

5
Graph Example
Suppose that P(rain today) 0.20 and P(rain
tomorrow given that it rains today) 0.70 E1
rain today, E2 rain tomorrow P(E1,E2)
P(E1) P(E2E1)
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Joint Distributions
The joint distribution for the set of variables U
C,S1, S2, S3 from Figure 1 is specified as
p(U) p(C) p(S1C) p(S2C) p(S3C).
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Applications

• Google search engine
• Spam filter to remove unwanted pages from search
  results
• AI (decision making)
• Spam filters
• Breaks emails down into words and tokens
• Learns which tokens indicate spam and which
  indicate valid emails
• Harder to cheat, multi-lingual, incredibly
  effective when properly trained
• Microsoft Notification Platform
• E-mail and cell phone notifications
• Example on next Slide

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Applications (continued)

• Program observes user activity
• Email response time, keyboard activity, meetings
• Program creates Bayesian Network
• When emails arrive, program can use BN to
  determine appropriate action
• Email from The Boss vs from a middle manager

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Bibliography

• http//www.csse.monash.edu.au/bai/
• http//www.ia.uned.es/fjdiez/bayes/
• http//www.niedermayer.ca/papers/bayesian/bayes.ht
  ml
• http//en.wikipedia.org/wiki/Bayesian_networks
• http//site.ebrary.com.online.library.marist.edu/l
  ib/marist/Doc?id10047051
• http//www.cs.ubc.ca/murphyk/Bayes/Charniak_91.pd
  f
• http//www.gfi.com/whitepapers/why-bayesian-filter
  ing.pdf
• http//www.cs.ubc.ca/spider/poole/papers/canai94.p
  df
• http//www.cs.ualberta.ca/greiner/bn.html
• http//www.cs.ubc.ca/murphyk/Software/BNT/bnsoft.
  html
• http//www.cs.huji.ac.il/nir/Nips01-Tutorial/
• http//ite.gmu.edu/klaskey/papers/gecco99.pdf
• http//news.com.com/Old-schooltheoryisanewfor
  ce/2009-1001_3-984695.html