Uncertainty

1. Uncertainty
Dr L.Srinivasan
Associate Professor/CSE
Dr N.G.P IT
CS3491 –AI & ML
UNIT-2
01

2. Uncertainty -Introduction
 What is Uncertain information?
 Doubtful Information
 Most intelligent systems have some degree of uncertainty associated
with them
 (i.e) including human
2

3. Uncertainty -Causes
 Uncertainty may occur in Knowledge Base(KB) because of the problems
with the data
 Data might be missing or unavailable
 Data might be present but unreliable or confusing due to
measurement errors
 The representation of data may be inaccurate
 Data may just be experts best guess
 Data may be based on defaults
3

4. Uncertainty –How to solve this?
 To solve this uncertain information we must be concerned with three
issues
 How to represent uncertain data?
 How to combine two or more pieces of uncertain data?
 How to draw inference(knowledge) using certain data?
● Finally we need to manage uncertain information
4

5. Uncertainty –How to solve this?
 Methods for managing uncertain information
 Probability
 Bayesian belief network
 Temporal nodes
 Hidden Markov models
5

6. Uncertainty –Introduction
 Example for uncertainty –Wumpus world
6
1.Agent A moves right to sensor BREEZE
B ->Y
2.If BREEZE is available in the square the
neighboring squares may/may not contain PIT
3.If u take expert guess and move right to PIT game is
over
4.Instead of moving right from BREEZE If u guess and
move up the game exists –But still it is not
correct(Bcoz Poss of PIT)
5.So the Agent Moves back and moves above which is
sensor STENCH
S -> Y

7. Uncertainty –Introduction
 Example for uncertainty –Wumpus world
7
6.If Stench is present in Square,its neighbor might be
Wumpus
Now,we have PIT,WUMPUS P,W near Stench Right
7.Now Lets combine Conditions
B ->Y and S -> Y
8. B ->Y then S -> N and
S -> Y then B -> N this means there is no P,W so lets
move right
So after combining 2 conditions we get a new move

8. Uncertainty –Introduction
 Real time example for uncertainty
 The agent wants to drive someone to the airport to catch a flight
 This involves leaving home 90 minutes before the flight departs and
driving at a reasonable speed
 Even though the airport is only 15 miles away ,the agent will not be
able to conclude with certainty that “plan will get us to the airport in
time”
8

9. Uncertainty –Introduction
 Real time example for uncertainty
 As long as
 My car doesn’t break down
 Run out of petrol/gas
 Don’t get into an accident
 No accidents on the bridge
 Plane doesn’t leave early
9

10. Uncertainty –Introduction
 Handling uncertain knowledge
 Uncertainty and rational decisions
10

11. Handling uncertain knowledge
 Example :Dental diagnosis
 Consider the following rule (FOL-First order logic expression)
∀p Symptom(p, Toothache) ⇒ Disease(p, Cavity)
(∀ -for all)
Toothache -pain in a tooth or teeth
Cavity -hole in your tooth
 This rule is wrong .Not all patients with toothaches have cavities
 Some of them have gum disease, an abscess(swelling), or one of other
several problems
11

12. Handling uncertain knowledge
 ∀p Symptom(p, Toothache) ⇒ Disease(p, Cavity) ∨
Disease(p, GumDisease) ∨ Disease(p, Abscess)…
 We could turn the rule into causal rule
∀p Disease (p, Cavity) ⇒ Symptom(p, Toothache)
 But this rule is not right either;not all cavities cause pain
12

13. Handling uncertain knowledge
Degree of Belief
 The agent’s knowledge can at best provide only a degree of belief in the
relevant sentences(Based on knowledge u r believing someone)
 The main tool for dealing with degrees of belief will be probability theory,
which assigns to each sentence a numerical degree of belief between 0
to 1
 Ex: The probability that the patient has a cavity is 0.8 is about the agent’s
belief ,not directly about the world
13

14. Handling uncertain knowledge
Evidence
 Beliefs depends on the percepts(a general rule intended to regulate
behavior or thought) that EVIDENCE the agent has received to date
 These percepts constitute the evidence on which probability assertions
are based
 As the agent receives new percept’s, its probability assessments are
updated to reflect the new evidence
 Before the evidence is obtained, it is termed as prior or unconditional
probability
 After the evidence is obtained, it is termed as posterior or conditional
probability
14

15. Uncertainty and Rational decisions
 Decision theory= probability theory + utility theory
 The fundamental idea of decision theory is that an agent is
rational(correct) if and only if it chooses the action that yields the highest
expected utility, averaged over all the possible outcomes of the action
 This is called principle of Maximum expected utility(MEU)
 Ex:if there are 5 outcomes 1 1 1 1 1(probability theory) and in that I select 1
best(utility theory)
15