1. Lecture 05 Rule-based Uncertain Reasoning
Topics
Information Uncertainty
Bayesian Inference Model
Certainty Factor Model
Discussion

2. Information uncertainty
Information can be incomplete, inconsistent, uncertain, or imprecise.
Incomplete: missing knowledge
Inconsistent: conflicting Knowledge, such as from different experts
Uncertainty: lack of exact knowledge
Imprecise: ambiguous knowledge, such as terms of often, sometimes, frequently and hardly ever

3. Information uncertainty

4. Bayesian inference model
Representation (Cause-effect rule)
IF H is true
THEN E is true {with probability p}
Semantics
IF event H occurs, THEN the probability that event E will occur is p, or p(E|H) = p.
p(H), p(E): prior probability
p(EH), p(HE): conditional probability
Inference
Given p(H) and p(E|H)
Find p(H|E).

5. Bayesian inference model
Bayesian rule

6. Bayesian inference model
Single evidence and single hypothesis
Single evidence and multiple hypotheses

7. Bayesian inference model
Multiple evidence and multiple hypotheses
Multiple evidence and multiple hypotheses under conditional independence

8. Bayesian inference model
Example: Naïve Bayesian Classifier
P(Hi) H1 H2 H3 Hm
P(Ej|Hi) E1 E2 E3 En

9. Characteristics of Bayesian inference
Humans are hard eliciting probability values consistent with the Bayesian rules.
Humans tend to make different assumptions when assessing the conditional and prior probabilities.
Bayesian Inference is most appropriate in the domains where reliable statistical data exist, for instance, forecasting.
Bayesian inference is of exponential complexity, and thus is impractical for large knowledge bases.

10. Certainty factor model
Representation (diagnostic rule)
IF evidence E
THEN hypothesis H {cf}
Semantics
Given that evidence E has occurred, we have cf degree of belief that hypothesis H will happen.
{ –1 <= cf <= +1}
Inference
Given cf(E) and cf
Find cf(H, E)

11. Certainty factor model
Meaning of certainty factors

12. Certainty factor model
Single evidence and single hypothesis
IF evidence E
THEN hypothesis H {cf }
cf (H, E) = cf (E)  cf
Conjunctive rules
cf (H, E1E2...En) = min [cf (E1), cf (E2),..., cf (En)]  cf

13. Certainty factor model
Disjunctive rules
cf (H, E1E2...En) = max [cf (E1), cf (E2),..., cf (En)]  cf

14. Certainty factor model
Multiple rules conclude with the same hypothesis
cfi is the confidence in hypothesis H established by Rule i

15. Characteristics of Certain factors
Certainty factors are used in domains where the probabilities are not known or are too difficult or expensive to obtain, for instance in medicine.
The evidential reasoning mechanism can manage incrementally acquired evidence, the conjunction and disjunction of hypotheses, as well as evidence with different degrees of belief.

16. Discussion More inexact reasoning models Likelihood inference
Dempster-Shafer evidential reasoning
Fuzzy inference