Uncertainty and Reasoning

Arya MirΤεχνίτη Νοημοσύνη και Ρομποτική

26 Νοε 2011 (πριν από 5 χρόνια και 8 μήνες)

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Uncertainty and Reasoning
A first look
March 9, 2006
In case you missed it


Coping with uncertainty is essential

Modern AI has turned
probabilistic

Russell and
Norvig
has good coverage

Chapter 13 covers basics;
it is essential
that you
read all of it (the
Wumpus
World in Ch. 13.7 is
optional)

Chapter 14 talks about reasoning; please read this
along with and the
D

Ambrosio
and
Charniak
;
skip all discussions of continuous distributions
;
skip 14.5, 14.6 as well
Probability Theory Basics

Basic notions today

Get used to manipulating probabilities and
conditional probabilities

Basics of Bayesian Networks
Probability Basics:
Conditional Probability
Probability Basics:
Joint Probability and Marginal Probability
Variables, Events and Distributions
An Exercise in Stereotyping
Difficulties with Probabilistic Reasoning
Worked Example: Malignancy
Bayes

Theorem
P(A|B) =
P(B|A) P(A)
P(B)
Basics of Bayesian Reasoning:
Bayes

Rule: Combining Diagnostic and
Causal Reasoning
Prior = .01%
P(S)=P(S | M)P(M)+P(S | not M)P(not M)
Normalisation of posteriors
80% of people with

Meningitis have a stiff neck

Normalisation of Posteriors
Numbers not percentages
Aiding Bayesian Reasoning with Frequencies
Formal Result indicating why Probabilities
are
not
Rules of Varying Strength
Why?
Exploiting Conditional Independence 1:
Joint Distributions in terms of Conditionals
Storage: Exponential in

number of random variables
Bayesian Network Semantics
Network structure to encode (conditional)

independencies

Between variables and this

makes representation compact.
Bayesian Network Semantics - 2
Conditional Independence in a Bayesian Network
P(A,B|C)=P(A|C)P(B|C)
A is conditionally
i
ndependent of B given C
Or, P(A|B,C)=P(A|C)
No edge ~
Independence!
Basics of Bayesian Networks

Nodes are random variables.

Informally, edges represent

causation

(no directed cycles
allowed - graph is a DAG).

Formally, local Markov property
says: node is conditionally
independent of its non-descendants
{Z} given its parents {U}.

Notation:
X

{Z
1j

Z
nj
} | {U
1

U
m
}