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# Probabilistic reasoning

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Artificial intelligence- Probabilistic Reasoning.

Artificial intelligence- Probabilistic Reasoning.

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• 1. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 1
• 2. The Conditional Independence relationship among the Variables can greatly reduce the number of Probabilities we specified in order to define the Full Joint distribution. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 2
• 3. It introduces the Data Structure called a Bayesian Network to represent the dependencies among variables and to concise specification of any Full Joint distribution. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 3
• 4. A Bayesian Network is a Directed Graph in which each node is annotated with Quantitative Probability information October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 4
• 5. The Full Specification is as follows: A set of Random Variables makes up the nodes of the network. Variable may be Discrete or Continuous. A set of directed links or arrows connects pairs of nodes. if there is an arrow from node X to node Y, X is said to be parent of Y. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 5
• 6. Each node Xi has a conditional probability distribution p(Xi |Parents(Xi)) than Quantifies the effect of the parents on the node. The graph has no directed cycles (directed, DAG, or acyclic graph). October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 6
• 7. The Set of Nodes and Links specifies the Conditional independences relationships that hold in the domain. The intuitive meaning of an arrow in a properly constructed network is usually that X has a direct influence on Y. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 7
• 8. Once the Topology of the Bayesian Network is laid out, we need only specify a conditional probability distribution for each variable given it’s parents. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 8
• 9. Consisting the Variables, i)Toothache ii)Cavity iii)Catch and iv)Weather. Here, Draw the Bayesian Network for the above Variable October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 9
• 10. 1) Weather is independent of the other variables. 2) Toothache and Catch are conditionally independent, given Cavity. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 10
• 11. This relationships are represents in Bayesian Network Weather Cavity CatchToothache October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 11
• 12. Weather Cavity CatchToothache Conditionally independence October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 12
• 13. Probabilistic Reasoning - K.Iniya CSE Weather Cavity CatchToothache Absence of a link October 9, 2013 13
• 14. Probabilistic Reasoning - K.Iniya CSEOctober 9, 2013 14 Weather Cavity CatchToothache No direct causal relationship
• 15. Weather Cavity CatchToothache Independent with other variables October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 15
• 16. Consider the variables i)Dog ii)Venus iii)Pet iv)Human v)Planet vi)Mercury vii) Cat BAYESIAN NETWORK? October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 16
• 17. Dog Pet Cat Human Mercury Planet Venus October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 17
• 18. A Burglar Alarm is installed at Home. It’s fairly reliable at detecting a burglary and It also responds for minor Earthquakes. You have two neighbors John and Mary who have promised to call you at work when they hear the alarm Draw the Bayesian Network October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 18
• 19. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 19 Burglary Alarm John calls Mary calls Earthquake
• 20. John always calls when hears the alarm, but sometimes confuses the telephone ringing with the alarm and calls. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 20
• 21. Mary likes rather loud Music and sometimes misses the alarm. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 21
• 22. The Burglary and Earthquake directly affect the probability of the alarm going’s off. But John and Mary call depends only on the alarm. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 22
• 23. The degree of approximation can be improved if we introduce the additional relevant information. CPT Stands for Conditional Probability Table. Each row in a CPT contains the conditional probability of each node for a conditioning case. A Conditioning Case is just possible combination of values for the parent nodes(a miniature atomic event) . October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 23
• 24. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 24 Burglary Earthquake Alarm John calls Mary calls
• 25. Probabilistic Reasoning - K.Iniya CSEOctober 9, 2013 25 Burglary Earthquake Alarm John calls Mary calls P(Burglary) 0.001 P(Earthquake) 0.002 Alarm t f P(John) 0.90 0.05 Alarm t f P(Mary) 0.70 0.01 B E P(Alarm) t t t f f t f f 0.95 0.94 0.29 0.001
• 26. For Boolean Variables, once you know the probability of a true value is p. the probability of a false value is 1-p. A Table for a Boolean variable with k Boolean parents contains 2 independently specifiable probabilities. A node with no parents has only one row representing prior probabilities. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 26 k
• 27. October 9, 2013 Probabilistic Reasoning - K.Iniya CSE 27