Transcript Handling Uncertainties

Planning Chapter 7
article 7.4
Production Systems Chapter 5 article 5.3
RBS Chapter 7
article 7.2
RBS
Expert System:
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A SYSTEM that mimics a human expert
Human experts always have in most case
some vague (not very precise) ideas about
the associations
Handling uncertainties is a essential part of
an expert system
Expert systems are RBS with some level of
uncertainty incorporated in the system
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RBS
Choosing a Problem
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Costs:
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Technical Problems:
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Choose problems that justify the development cost
of the expert systems
Choose a problem that is highly technical in nature
problems with Well-formed knowledge are the best
choice.
Highly specialized expert requirements, solution time
for the problem is not short time.
Cooperation from an expert:
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Experts are willingly to participate in the activity.
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Choosing a Problem
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Problems that are not suitable
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Problems for which experts are not available
at all, or they are not willingly to participate
Problems in which high common sense
knowledge is involved
Problems which involve high physical skills
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RBS
ES Architecture
Explanation
system
interface
user
Inference
engine
Knowledge
Base
editor
Case
specific
Data
Knowledge
Base
Expert System Shell
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ES Architecture
Uses Menus, NLP, etc…
Which is used to interact
With the users
Explanation
system
interface
user
Inference
engine
Knowledge
Base
editor
Case
specific
Data
Knowledge
Base
Expert System Shell
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ES Architecture
Implements the
reasoning methods
Generally backward chaining
Explains why a decision
is taken, uses keywords
Such as HOW, WHY etc…
Explanation
system
interface
user
Updates the KB
Inference
engine
Knowledge
Base
editor
Case
specific
Data
Knowledge
Base
Expert System Shell
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ES Architecture
Pre-solved problems,
Frequently referred cases
Explanation
system
interface
user
Inference
engine
Knowledge
Base
editor
Expert System Shell
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Case
specific
Data
Knowledge
Base
Collection of facts
And rules
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Shells
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General purpose toolkit/shell is problem
independent
Shells commercially available
CLIPS is one such shell
Freely available
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Reasoning with Uncertainty
Case Studies:
 MYCIN
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Implements certainty factors approach
INTERNIST: Modeling Human Problem
Solving
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Implements Probability approach
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RBS
RBS: Handling Uncertainties
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How to handle vague concepts?
Why vagueness occurs?
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All rules are not 100% deterministic
Certain rules are often true but not always
Headache may be caused in flu, but may
not always occur
An expert may not always be sure about
certain relations and associations
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First Source of Uncertainty:
The Representation Language
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Possible States are large
Single representation may correspond to multiple
states, which the agent can’t represent
distinguishably
Languages are generally less expressive
on(A,B)  on(B,Table)  on(C,Table)  clear(A)  clear(C)
A
B
A
C
C
B
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A
B
C
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RBS
Second source of Uncertainty:
Imperfect Observation of the World
Observation of the world can be:
 Partial, e.g., a vision sensor can’t see
through obstacles (lack of percepts)
R1
R2
The robot may not know whether
there is dust in room R2
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RBS
Second source of Uncertainty:
Imperfect Observation of the World
Observation of the world can be:
 Partial, e.g., a vision sensor can’t see
through obstacles
 Ambiguous, e.g., percepts have multiple
possible interpretations
A
C
B
on(a,b)  on(a,c)
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RBS
Second source of Uncertainty:
Imperfect Observation of the World
Observation of the world can be:
 Partial, e.g., a vision sensor can’t see
through obstacles
 Ambiguous, e.g., percepts have multiple
possible interpretations
 Incorrect
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Third Source of Uncertainty:
Ignorance, Laziness, Efficiency
Laziness/Efficiency:
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An action may have a long list of preconditions, e.g.:
Drive-Car:
have(keys)  empty(gas-tank)  battery-Ok 
ignition-Ok  flat-Tires  stolen(Car) ...
Medical Treatment
symptoms(p,toothache)  disease(p, cavity)
The writer may not list all the condition
Results in incorrect representation or several
interpretations
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Third Source of Uncertainty:
Ignorance, Laziness, Efficiency
Ignorance:
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Theoretical: The domain knowledge in itself may not
be complete. The domain knowledge may not have a
complete theory
e.g. many instances in Medical science are
unexplainable
Practical Ignorance: The domain knowledge is
complete but the implementing it in an real/artificial
environment may be difficult.
e.g., some tests may yield poor results due to low
instrument precision
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Modelling Uncertainty
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Non-deterministic model:
Uncertainty is represented by a set of possible
values, e.g., a set of possible worlds, a set of
possible effects,
Probabilistic model:
Uncertainty is represented by a probabilistic
distribution over a set of possible values
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Case specific models: Certainty factors used in
MYCIN
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Fuzzy models
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Example:
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Non-deterministic: list all possible states,
belief state represents all the states of the
world that are possible at a given time or at a
given stage of reasoning
Probabilistic: probability is attached to each
state to measure its likelihood to be the actual
state
0.2
0.3
0.4
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0.1
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Probabilities ?
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Probabilities: frequency interpretation
Relative occurrence of a particular state defined by
the probabilistic distribution
0.2
0.3
0.4
0.1
This state would occur
20% of the times
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Example
We have a Dentist D who meets a new patient
D is interested in only one thing: whether Patient has a
cavity, which D models using the proposition Cavity
Before making any observation, D’s belief state is:
Cavity
p
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 Cavity
1-p
This means that if D believes that a fraction p of
patients have cavities
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Example
Now an observation is made ‘toothache’
D’s belief state wrt toothache is:
toothache
p
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 toothache
1-p
Can the observation and the effect be related
i.e. cavity and toothache (YES), How?
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Example
Lets relate the two:
The patient has a cavity if he / she has toothache
This sentence suffers from laziness and/or ignorance.
 Why? It may not be necessary that every patient that
suffers from toothache may also have cavity. Then in
order to capture real situation we may keep on
increasing the reasons of toothache I.e,
The patient has cavity or gum problem or … if he /she
suffers from toothache.
 Is there a simple way to solve this problem. YES
 Attach probability to initial rule and that would
summarize the uncertainty caused because of laziness
and ignorance
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RBS
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Example
Lets relate the two:
The patient has a cavity if he / she has toothache
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Probability of 0.7 (70% chance)
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70% summarizes:
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Cases in which all the factors needed for cavity to cause
toothache are present
And cases in which the patient has both cavity and toothache
but the two are unconnected
30% summarizes
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all the other possible causes of toothache that we are too
lazy/ignorant to confirm or deny
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RBS
Making decisions under uncertainty
P(A1 gets me to goal | …)
P(A2 gets me to goal | …)
P(A3 gets me to goal | …)
P(A4 gets me to goal | …)
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= 0.04
= 0.70
= 0.95
= 0.99
Which action to choose?
Depends on my preferences for missing flight vs. time
spent waiting, etc.
 Probability theory: summarizes uncertainties
 Utility theory: represents and infers preferences
Decision theory = probability theory + utility theory
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RBS
Probability
Degree of believe in a fact ‘x’, P(x)
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P(H): degree of believe in H, when supporting evidence
is NOT given, H is the hypothesis
Joint Probabilities
P(H|E): degree of believe in H, when supporting
evidence is given, E is the evidence supporting
hypothesis
P(H|E): conditional probability
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Prior probability
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Prior or unconditional probabilities of propositions
e.g., P(Cavity = true) = 0.1 and P(Weather = sunny) = 0.72
Probability distribution gives values for all possible
assignments:
P(Weather) = <0.72,0.1,0.08,0.1> (normalized, i.e., sums to 1)
Joint probability distribution for a set of random variables
gives the probability of every atomic event on those random
variables
P(Weather,Cavity) = 4 × 2 matrix of values:
Weather =
Cavity = true
Cavity = false
sunny rainy cloudy snow
0.144 0.02 0.016 0.02
0.576 0.08 0.064 0.08
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Conditional Probability
P(H|E): conditional probability is given
through a LAW (RULE)
P(H|E)=P(H^E)/P(E)
where P(H^E) is the probability of H and E
occurring together (both are TRUE): joint
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Inference: Joint Prob.
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Reasoning
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P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2
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Reasoning
Can also compute conditional probabilities:
P(cavity | toothache) = P(cavity  toothache)
P(toothache)
=
0.016+0.064
0.108 + 0.012 + 0.016 + 0.064
= 0.4
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RBS
Without Joint distributions
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Conditional Probabilities are found,
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Single evidence: Simple
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If multiple evidences are available then
BAYESIAN Updating is done through the use of
conditional independence
Find the conditional probabilities directly through
the chain rule
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RBS
Evaluating: Conditional Probability
P(H|E): P(Heart Attack|shooting arm pain)
Two approaches can be adopted:
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Asking an expert about the frequency of it
happening
Finding the probability from the given data
Second Approach
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Collect the data for all the patients
complaining about the shooting arm pain.
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Find the proportion of the patients that had
an heart attack from the data collected in
step 1
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Evaluating: Conditional Probability
P(H|E): P(Heart Attack|shooting arm pain)
Probability of Disease given symptoms
VS
P(E|H): P(shooting arm pain|Heart Attack)
Probability of symptoms given Disease
Which is easier to find of the two?
Perhaps P(E|H) is easier
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RBS
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Evaluating: Conditional Probability
P(H|E): P(Heart Attack|shooting arm pain)
Probability of Disease given symptoms
Headache is mostly experienced when a
patient suffers from flu, fever, tumor, etc…
Find out whether a patient suffers from
tumor, given headache
Collect the data for all the headache
patients, and then find the proportion of
patients that have tumor.
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RBS
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Evaluating: Conditional Probability
P(E|H): P(shooting arm pain|Heart Attack)
Probability of symptoms given Disease
Headache is mostly experienced when a
patient suffers from flu, fever, tumor, etc…
Find out whether a tumor patient suffers
from headache
Collect the data for all the tumor patients,
and then find the proportion of patients that
have headache
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RBS
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Evaluating: Conditional Probability
Generally speaking P(E|H): P(shooting
arm pain|Heart Attack) is easier to
find.
Therefore the we need to convert
P(H|E) in terms of P(E|H)
P(H|E)=P(H^E)/P(E)
P(H|E)=[P(E|H)*P(H)]/P(E)
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RBS
Evaluating: Conditional Probability
More than one evidence
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Independence of events
P(H|E1^E2)=P(H^E1^E2)/P(E1^E2)
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P(H|E1^E2)=[P(E1|H)* P(E2|H)*
P(H)]/(P(E1)*P(E2))
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Other Approaches
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Certainty Factors (CF)-MYCIN
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CF for rules CF(R)
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CF for Pre-conditions CF(PC)
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From the experts
From the end user
CF for conclusions CF(cl)
CF(cl)=CF(R)*CF(PC)
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Certainty Factors (CF)
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CF for rules CF(R)
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CF(R) = 0.6
CF for Pre-conditions CF(PC)
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IF A then B
IF A (0.4) then B
CF(A)= 0.4
CF for conclusions CF(cl)
CF(B)=CF(R)*CF(A)= 0.6*0.4=0.24
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Finding Overall CF for PC
If A(0.1) and B(0.4) and C(0.5) Then D
Overall CF(PC)=min(CF(A),CF(B),CF(C))
CF(PC)=0.1
 If A(0.1) or B(0.4) or C(0.5) Then D
Overall CF(PC)=max(CF(A),CF(B),CF(C))
CF(PC)=0.5

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CFs for same conclusion rules
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When the conclusions are same and certainty
factors are positive:
CF(R1)+CF(R2) – CF(R1)*CF(R2)
When the conclusions are same and the
certainty factors are both negative
CF(R1)+CF(R2) + CF(R1)*CF(R2)
Otherwise: both conclusions are same but have
different signs
[CF(R1)+CF(R2)] / [1 – min ( | CF(R1) | , | CF(R1) |]
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Example
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Please see the class handouts
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