Planning Chapter 7 article 7.4 Production Systems Chapter 5 article 5.3 RBSChapter 7 article 7.2.
-
date post
19-Dec-2015 -
Category
Documents
-
view
226 -
download
1
Transcript of Planning Chapter 7 article 7.4 Production Systems Chapter 5 article 5.3 RBSChapter 7 article 7.2.
Planning Chapter 7 article 7.4Production Systems Chapter 5 article 5.3RBS Chapter 7 article 7.2
CS 331/531 Dr M M Awais 2
RBS
RBS: Handling Uncertainties
How to handle vague concepts? Why vagueness occurs?
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
CS 331/531 Dr M M Awais 3
RBS
First Source of Uncertainty:The Representation Language
There are many more states of the real world than can be expressed in the representation language
So, any state represented in the language may correspond to many different states of the real world, which the agent can’t represent distinguishably
A
B C
A
BC
A
B C
On(A,B) On(B,Table) On(C,Table) Clear(A) Clear(C)
CS 331/531 Dr M M Awais 4
RBS First Source of Uncertainty:The Representation Language
6 propositions On(x,y), where x, y = A, B, C and x y
3 propositions On(x,Table), where x = A, B, C 3 propositions Clear(x), where x = A, B, C At most 212 states can be distinguished in the
language [in fact much fewer, because of state constraints such as On(x,y) On(y,x)]
But there are infinitely many states of the real world
A
B C
A
BC
A
B C
On(A,B) On(B,Table) On(C,Table) Clear(A) Clear(C)
CS 331/531 Dr M M Awais 5
RBSSecond 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
CS 331/531 Dr M M Awais 6
RBSSecond 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
BCOn(A,B) On(A,C)
CS 331/531 Dr M M Awais 7
RBSSecond 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
CS 331/531 Dr M M Awais 8
RBS
Third Source of Uncertainty:Ignorance, Laziness, Efficiency
An action may have a long list of preconditions, e.g.:
Drive-Car:P = Have(Keys) Empty(Gas-Tank) Battery-Ok Ignition-Ok Flat-Tires Stolen(Car) ...
The agent’s designer may ignore some preconditions... or by laziness or for efficiency, may not want to include all of them in the action representation
The result is a representation that is either incorrect – executing the action may not have the described effects – or that describes several alternative effects
CS 331/531 Dr M M Awais 9
RBS
Representation of Uncertainty Many models of uncertainty We will consider two important models:
• 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
CS 331/531 Dr M M Awais 10
RBS
Example: Belief State In the presence of non-deterministic sensory
uncertainty, an agent belief state represents all the states of the world that it thinks are possible at a given time or at a given stage of reasoning
In the probabilistic model of uncertainty, a probability is associated with each state to measure its likelihood to be the actual state
0.2 0.3 0.4 0.1
CS 331/531 Dr M M Awais 11
RBS
What do probabilities mean?
Probabilities have a natural frequency interpretation
The agent believes that if it was able to return many times to a situation where it has the same belief state, then the actual states in this situation would occur at a relative frequency defined by the probabilistic distribution
0.2 0.3 0.4 0.1
This state would occur 20% of the times
CS 331/531 Dr M M Awais 12
RBS
Example Consider a world where a dentist agent D meets a
new patient P
D is interested in only one thing: whether P has a cavity, which D models using the proposition Cavity
Before making any observation, D’s belief state is:
This means that if D believes that a fraction p of patients have cavities
Cavity Cavityp 1-p
CS 331/531 Dr M M Awais 13
RBS
Where do probabilities come from?
Frequencies observed in the past, e.g., by the agent, its designer, or others
Symmetries, e.g.:• If I roll a dice, each of the 6 outcomes has probability 1/6
Subjectivism, e.g.:• If I drive on Highway 280 at 120mph, I will get a speeding
ticket with probability 0.6• Principle of indifference: If there is no knowledge to
consider one possibility more probable than another, give them the same probability
CS 331/531 Dr M M Awais 14
RBS
Expert System: 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
CS 331/531 Dr M M Awais 15
RBS
Choosing a Problem Costs:
Choose problems that justify the development cost of the expert systems
Technical Problems: 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:
Experts are willingly to participate in the activity.
CS 331/531 Dr M M Awais 16
RBS
Choosing a Problem
Problems that are not suitable 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
CS 331/531 Dr M M Awais 17
RBS
ES Architecture
interface
user
Explanationsystem
Inferenceengine
KnowledgeBaseeditor
Case specific
Data
KnowledgeBase
Expert System Shell
CS 331/531 Dr M M Awais 18
RBS
ES Architecture
interface
user
Explanationsystem
Inferenceengine
KnowledgeBaseeditor
Case specific
Data
KnowledgeBase
Expert System Shell
Uses Menus, NLP, etc… Which is used to interact With the users
CS 331/531 Dr M M Awais 19
RBS
ES Architecture
interface
user
Explanationsystem
Inferenceengine
KnowledgeBaseeditor
Case specific
Data
KnowledgeBase
Expert System Shell
Explains why a decision is taken, uses keywordsSuch as HOW, WHY etc… Implements the
reasoning methodsGenerally backward chaining
Updates the KB
CS 331/531 Dr M M Awais 20
RBS
ES Architecture
interface
user
Explanationsystem
Inferenceengine
KnowledgeBaseeditor
Case specific
Data
KnowledgeBase
Expert System Shell
Pre-solved problems, Frequently referred cases
Collection of factsAnd rules
CS 331/531 Dr M M Awais 21
RBS
Shells General purpose toolkit/shell is
problem independent Shells commercially available CLIPS is one such shell Freely available
CS 331/531 Dr M M Awais 22
RBS Reasoning with Uncertainty
Case Studies: MYCIN
Implements certainty factors approach INTERNIST: Modeling Human Problem
Solving Implements Probability approach
CS 331/531 Dr M M Awais 23
RBS
Probability based ES Probability:
Degree of believe in a fact ‘x’, P(x) P(H): degree of believe in H, when
supporting evidence is NOT given, H is the hypothesis
P(H|E): degree of believe in H, when supporting evidence is given, E is the evidence supporting hypothesis
P(H|E): conditional probability
CS 331/531 Dr M M Awais 24
RBS
Conditional Probability P(H|E): conditional probability is
given through a LAW (RULE)
P(H|E)=P(H^E)/P(E)P(H|E)=P(H^E)/P(E)
where P(H^E) is the probability of H where P(H^E) is the probability of H and E occurring together (and E occurring together (both are both are TRUETRUE))
CS 331/531 Dr M M Awais 25
RBSEvaluating: Conditional Probability
P(H|E): P(Heart Attack|shooting arm pain) Two approaches can be adopted:
Asking an expert about the frequency of it happening
Finding the probability from the given data
Second Approach Collect the data for all the patients
complaining about the shooting arm pain. Find the proportion of the patients that
had an heart attack from the data collected in step 1
CS 331/531 Dr M M Awais 26
RBSEvaluating: 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
CS 331/531 Dr M M Awais 27
RBSEvaluating: 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.
CS 331/531 Dr M M Awais 28
RBSEvaluating: 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
CS 331/531 Dr M M Awais 29
RBSEvaluating: 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)P(H|E)=[P(E|H)*P(H)]/P(E)
CS 331/531 Dr M M Awais 30
RBSEvaluating: Conditional Probability
More than one evidence Independence of eventsP(H|E1^E2)=P(H^E1^E2)/P(E1^E2)
P(H|E1^E2)=[P(E1|H)* P(E2|H)* P(H)]/P(E1)*P(E2)P(H|E1^E2)=[P(E1|H)* P(E2|H)* P(H)]/P(E1)*P(E2)
CS 331/531 Dr M M Awais 31
RBS
Inference through Joint Prob. Start with the joint probability distribution:
CS 331/531 Dr M M Awais 32
RBS
Inference by enumeration Start with the joint probability distribution:
P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2
CS 331/531 Dr M M Awais 33
RBS
Inference by enumeration Start with the joint probability distribution:
P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2
CS 331/531 Dr M M Awais 34
RBS
Inference by enumeration Start with the joint probability distribution:
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
CS 331/531 Dr M M Awais 35
RBS
Certainty Factors (CF) CF for rules CF(R)
From the experts CF for Pre-conditions CF(PC)
From the end user CF for conclusions CF(cl) CF(cl)=CF(R)*CF(PC)
CS 331/531 Dr M M Awais 36
RBS
Certainty Factors (CF) CF for rules CF(R)
IF A then B CF(R) = 0.6 CF for Pre-conditions CF(PC)
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
CS 331/531 Dr M M Awais 37
RBS
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
CS 331/531 Dr M M Awais 38
RBS Combining Certainty factors
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) |]
CS 331/531 Dr M M Awais 39
RBS
Example Please see the class handouts
CS 331/531 Dr M M Awais 40
RBS