Download Reasoning Under Uncertainty in Expert System

Reasoning Under Uncertainty in
Expert System
Situations often arise wherein a decision
must be made when the results of each
possible choice are uncertain.
What is Uncertainty?
 Uncertainty is a situation which involves imperfect or unknown
information.
 Uncertainty is essentially lack of information to formulate a
decision.
 Uncertainty may result in making poor or bad decisions.
 As living creatures, we are accustomed to dealing with uncertainty –
that’s how we survive.
How to Expert Systems Deal with
Uncertainty?
 Expert systems provide an advantage when dealing with uncertainty
as compared to decision trees.
 With decision trees, all the facts must be known to arrive at an
outcome.
 Probability theory is devoted to dealing with theories of uncertainty.
 There are many theories of probability – each with advantages and
disadvantages.
Decision tree
Theories to Deal with Uncertainty
 Bayesian Probability
 Hartley Theory
 Shannon Theory
 Dempster-Shafer Theory
 Markov Models
 Zadeh’s Fuzzy Theory
Dealing with Uncertainty
What is Reasoning?
The action of thinking about something in a logical,
sensible way.
When we require any knowledge system to do something
it has not been explicitly told how to do it must reason.
Reasoning is the process of machining inferences from a
body of information.
Example:“zeno is a spider”
Given the information that ”zeno is a spider”, it is reasonable to conclude that
Zeno ha eight legs.
zeno is a spider
reasoning
Therefore,zeno has eight legs.
Type of Reasoning
Deductive Reasoning
Inductive Reasoning
Top down logic.
Bottom up logic.
Deals with exact facts and exact
conclusions.
Not as strong as deductive –
premises support the conclusion
but do not guarantee it.
“ uses patterns to arrive at a
conclusion ”
“ uses facts, rules, definition or
properties to arrive at a
conclusion”
Top down logic
Bottom up logic.
Errors Related to Hypothesis
Many types of errors contribute to uncertainty.
 Type I Error – accepting a hypothesis when it is not true
– False Positive.
 Type II Error – Rejecting a hypothesis when it is true
– False Negative
Errors Related to Measurement
Errors of precision – how well the truth is
known
Errors of accuracy – whether something is true
or not
Unreliability -(data)
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Types of Errors
Examples of Common Types of Errors
Classical Probability
 First proposed by Pascal and Fermat in 1654
 Also called a priori probability because it deals with ideal games or
systems:
-Assumes all possible events are known
-Each event is equally likely to happen
 Fundamental theorem for classical probability is P = W / N, where
W is the number of wins and N is the number of equally possible
events.
Deterministic vs. Nondeterministic
Systems
When repeated trials give the exact same results,
the system is deterministic.
Otherwise, the system is nondeterministic.
Nondeterministic does not necessarily mean
random – could just be more than one way to
meet one of the goals given the same input.
Sample Space of Intersecting Events
The sample space of an experiment is the set of all possible outcomes o
f that experiment.
the range of values of a random variable.
Experimental Probabilities
 Experimental probability is the ratio of the number of times an event
occurs to the total number of trials or times the activity is
performed.
Subjective probability
Subjective probability measure a person’s belief that an event will
occur.
 These probabilities vary from person to person.
 They also change as one learns new in formation.
OR
It is the probability assign to an event based on subjective judgment,
experience, information and belief.
Example:A doctor may feel a patient has a 90% chance of a full recovery.
Compound Probabilities
 Compound probabilities can be expressed by:
 S is the sample space and A and B are events.
 independent events are events that do not affect each other. For pairwise
independent events
Conditional Probabilities
 The probability of an event A occurring, given that event B has
already occurred is called conditional probability:
Example:Ali took two tests. The probability of her passing both tests is 0.6. The probability of
her passing the first test is 0.8. What is the probability of her passing the second test
given that she has passed the first test?
Passing both test A or B is=0.6
First test pass=0.8
Second test pass=?
formula:
P(A/B)=P(A/B)/P(B)
p(second test B)=P(Passing both test A or B )/P(First test pass)
=o.6/0.8
=0.75
So, second test pass =0.75
Baye’s Theorem
 Bayes Theorem is used heavily in statistics, analysis of data sets.
Bayes' theorem (also known as Baye's rule) is a useful tool for
calculating conditional probabilities.
 This is the inverse of conditional probability.
 Bayes’ Theorem is commonly used for decision tree analysis of
business and social sciences.
Temporal Reasoning
Reasoning about events that depend on time
Expert systems designed to do temporal
reasoning to explore multiple hypotheses in real
time are difficult to build.
One approach to temporal reasoning is with
probabilities – a system moving from one state to
another over time.
Markov Chain Characteristics
1. The process has a finite number of possible
states.
2. The process can be in one and only one state at
any one time.
3. The process moves or steps successively from
one state to another over time.
State Diagram
Interpretation of a Transition Matrix
Transition matrix – represents the probabilities that
the system in one state will move to another.