《人工智能(智能系统指南,第二版)》读书笔记——4、第三章
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1. introduction to knowledge-based intelligent systems(summary / questions for review / references)
2. rule-based expert systems
3. uncertainty management in rule-based expert systems
4. fuzzy expert systems
5. frame-based expert systems
6. artificial neural networks
7. evolutionary computation
8. hybrid intelligent systems
9. knowledge engineering and data mining
3. uncertainty management in rule-based expert systems: (Bayesian reasoning and Certainty factors)
The main sources of uncertain knowledge in expert systems are: weak implications, imprecise language, missing data and combining the views of different experts.
Probability theory provides an exact, mathematically correct, approach to uncertainty management in expert systems.
(p62-p64)Bayesian reasoning:
P(H|E) =
P(Hi|E) =
P(Hi|E1E2...En) = { p(E1E2...En|Hi)*p(Hi) } / { k:1-m, add, p(E1E2...En|Hk)*p(Hk) }
P(Hi|E1E2...En) = { p(E1|Hi)*p(E2|Hi)*...*p(En|Hi)*p(Hi) } / { k:1-m, add, p(E1|Hk)*p(E2|Hk)*...*p(En|Hk)*p(Hk) }
In the Bayesian approach, an expert is required to provide the prior probability of hypothesis H and values for the likelihood of sufficiency(充分性的似然值), LS, to measure belief in the hypothesis if evidence E is present, and the likelihood of necessity(必要性的似然值), LN, to measure disbelief in hypothesis H if the same evidence is missing. The Bayesian method uses rules of the following form:
IF E is true {LS,LN}
THEN H is true {prior probability}
(p62-p64)Bayesian accumulation of evidence:
LS = P( E | H ) / P( E | /H )
LN = P( /E | H ) / P( /E | /H )
Note that LN cannot be derived from LS. The domain expert must provide both values independently.
In the rule-based expert system, the overall probability of something is drivened through the following steps:
1) the prior probability of the consequent, p(H), is converted into the prior odds (先验概率 -> 先验几率):
O(H) = p(H) / { 1 - p(H) };
2) p(H) is only used for 1). In order to obtain the posterior odds(后验几率), the prior odds are updated by LS if the antecedent of the rule (or evidence) is true and by LN if the antecedent is false:
O( H | E ) = LS * O(H) AND O( H | /E ) = LN * O(H)
3) The posterior odds are then used to recover the posterior probabilitises:
p( H | E) = O( H | E ) / { 1 + O( H | E ) } AND p( H | /E ) = O( H | /E ) / { 1 + O( H | /E ) }
Certainty factors theory is a popular alternative to Bayesian reasoning. An expert is required to provide a certainty factor, cf, to represent the level of belief in hypothesis H given that evidence E has been observed. The certainty factors method uses rules of the following form:
IF E is true
THEN H is true {cf}
..............
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