universiti tenaga nasional 1 ccsb354 artificial intelligence chapter 8.2 certainty factors chapter...

UNIVERSITI TENAGA NASIONAL 1

CCSB354ARTIFICIAL INTELLIGENCE

Chapter 8.2Certainty Factors

Instructor: Alicia Tang Y. C.


Uncertainty Handling Overview

In Expert Systems, we must often attempt to draw correct conclusions from poorly formed and uncertain evidence using unsound inference rules.

This is not an impossible task; we do it successfully in almost every aspect of our daily survival.

Doctors deliver correct medical treatment for ambiguous symptoms; we understand natural language statements that are incomplete or ambiguous and so on.

There are many approaches to representing uncertainty in AI.


AI methods to handle uncertainty

Abductive reasoningProperty inheritanceFuzzy logic Certainty factorProbabilistic inference (e.g.

Bayes theorem)Dempster-Shafer theoryNon monotonic reasoning

e.g. Suppose:If x is a bird then x flies

Abductive reasoning would say that“All fly things are birds”

By property inheritance “All birds can fly”

but, remember the case thatPenguin cannot fly?


Evaluation Criteria for uncertainty handling methods

Expressive powerLogical correctnessComputational efficiency of inference


Scheme used by expert system in Handling Uncertainty

MYCIN uses Certainty Factor The CF can be used to rank hypotheses in order

of importance. For example if a patient has certain symptoms that suggest several possible diseases, then the disease with the higher CF would be the one that is first investigated.

REVEAL Fuzzy logic was used

PROSPECTOR Bayes theorem


Bayesian Approach (I) Bayesian approach (or Bayes theorem) is based

on formal probability theory. It provides a way of computing the probability of a hypothesis (without sampling) following from a particular piece of evidence, given only the probabilities with which the evidence follows from actual cause.

Best defined technique for managing uncertainty

Important for quantitative analysis use


Bayesian approach (II)

p(E | Hi) * p(Hi)p(Hi | E) = ------------------------------ n p(E | Hk) * p(Hk) k= 1

Here, as you can see, a number of assumptions (i.e. independence of evidence) which cannot be made

for many applications (such as in medical cases).

evidence

assumption


Bayes theorem (III)

where: p(Hi | E) is the probability that Hi is true given evidence E. p(Hi) is the probability that Hi is true overall. p(E | Hi) is the probability of observing

evidence E when Hi is true.

n is the number of possible hypotheses.If there are not many cases of success of people who obtained an ‘A’ by studying hard then your chances of getting an ‘A’ caused by ‘hardworking’ is also lower!

Those who obtained an ‘A’ and they

indeed studied every night before exam

You will get an A if you study till late night for a week before exam


Bayes’s Rule and knowledge based systems

Advantages:

- Most significant is their sound theoretical foundation in probability theory.- Most mature uncertainty reasoning methods- Well defined semantics for decision making

Main disadvantage:

- They require a significant amount of probability data to construct a knowledge base.


Certainty Factor (CF)Certainty factors measure the confidence

that is placed on a conclusion based on the evidence known so far. A certainty factor is the difference between the following two components :

CF = MB[h:e] - MD[h:e]

A positive CF means the evidence supports the hypothesis since MB > MD.


CF[h:e] = MB[h:e] - MD[h:e] …………………… (I)

CF[h:e] is the certainty of a hypothesis h given the evidence e.

MB[h:e] is the measure of belief in h given e.

MD[h:e] is the measure of disbelief in h given e.

CFs can range from -1 (completely false) to +1 (completely true) with fractional values in between, and zero representing ignorance.

MDs and MBs can range between 0 to 1 only.

0 - 11 - 0


MB(P1 AND P2) = MIN(MB(p1), MB(p2)) ……. (II)

MB(P1 OR P2) = MAX(MB(P1), MB(P2)) ……… (III)

the MB in the negation of a fact can be derived as:

MB(NOT P1) = 1 - MB(P1) ………………………. (IV)


Each rule can have an credibility (attenuation)

A number from 0 to 1 which indicates its reliability. The credibility is then multiplied by the MB for the conclusion of the rule.

MB(Conclusion) = MB(conditions) * credibility ….. (V)

MB[h:e1,e2] = MB[h:e1] + MB[h:e2] * (1-MB[h:e1]) …….. (VI)

For each ruleThe hypotheses


CERTAINTY FACTORThis scheme does not permit the distinction

between conflict of interest (MB and MD are both high) as oppose to lack of evidence (MB and MD both low), which could sometimes be important.


CERTAINTY FACTORWhen experts put together the rule base

they must agree on a CF to go with each rule. This CF reflects their confidence in the rule’s reliability. Certainty measures may be adjusted to tune the system’s overall performance, although slight variations in this confidence measure tend to have little effect on the overall running of the system.


CERTAINTY FACTORThe conditions of each rule are formed of

the and and or of a number of facts. When a production rule is used, the

certainty factors that are associated with each condition are combined to produce the overall premise in the following manner.


A Worked Example Rule 1 IF X drives a Gen2 AND X reads the Berita Harian THEN X will vote Barisan Nasional Rule 2 IF X loves the setia song OR X supports Vision 2020 THEN X will vote Barisan Nasional Rule 3 IF X uses unleaded petrol OR X does not support Vision 2020 THEN X will not vote Barisan Nasional


Let assume that the individual MBs for theConditions are as follows:

X drives a Gen2 0.9X reads the Berita Harian 0.7X loves the Setia song 0.8X supports Vision 2020 0.6X uses unleaded petrol 0.7


The credibility of the rules are as follows:

Rule 1 0.7Rule 2 0.8Rule 3 0.6


To determine: CF[ X votes BN: Rule 1, Rule 2, Rule 3 ]

Rule1 and Rule2 give the MB in the proposition “X votes BN” :

MB[X votes BN: Rule 1] = MIN (0.9, 0.7) * 0.7 = 0.49-- using II and V

MB[X votes BN: Rule 2] = MAX (0.8, 0.6) * 0.8 = 0.64-- using III and V

MB[X votes BN: Rule 3] = MAX (0.7), (1-0.6)) * 0.6 = 0.42

-- using II, IV and V

Hypotheses, assumed goal


Combining the Rule 1 and Rule 2:

MB[X votes BN: Rule1, Rule2] = MB[X votes BN: Rule1] + MB[X votes BN: Rule2] * ( 1 - MB[X votes BN: Rule 1] )

---- using (VI) = 0.49 + 0.64 * (1 - 0.49) = 0.82

Combining the three rules:CF[ X votes BN: Rule 1, Rule 2, Rule 3 ] = MB[X votes BN: Rule 1, Rule 2] - MD[X votes BN: Rule 3] = 0.82 - 0.42 = 0.4

So, what do you think is the answer for the question:“Will someone in KL vote for BN party”?

Disbelieve you will note

I believe you wont vote


In an expert system that implements “uncertainty handling”

The answer is

“May be”(and not a “yes” or a “no”)

Isn’t it exactly the way you and I say it!

Certainty Factor has been criticised to be excessively ad-hoc.The semantic of the certainty value can be subjective and relative.

But the human expert’s confidence in his reasoning is also approximate, heuristic and informal


Advantages:

- a simple computational model that permits experts to estimate their confidence in conclusion

- it permits the expressions of belief and disbelief in each hypothesis (expression of multiple sources of evidence is thus allowed)

- gathering the value of CF is easier than those in other methods


Dempster-Shafer theory(1967, Arthur Shafer) This theory was designed as a mathematical

theory of evidence where a value between 0 and 1 is assigned to some fact as its degree of support.

Similar to Bayesian method but is more general. As the belief in a fact and its negation need not sum

to one ‘1’. Both values can be zero (reflecting that no

information is available to make a judgment)

Read text if you want to find out more about this scheme

universiti tenaga nasional 1 ccsb354 artificial intelligence chapter 8.2 certainty factors chapter...

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