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Yapay Zeka 802600715151

Doç. Dr. Mehmet Serdar GÜZEL

Slides are mainly adapted from the following course page:

at http://ai.berkeley.edu created by Dan Klein and Pieter Abbeel for CS188

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Lecturer

Instructor: Assoc. Prof Dr. Mehmet S Güzel

Office hours: Tuesday, 1:30-2:30pm

Open door policy – don’t hesitate to stop by!

Watch the course website

Assignments, lab tutorials, lecture notes

slid e 2

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e

Markov Models

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e

Markov Models

In probability theory, a Markov model is a stochastic model used to model randomly changing systems. It is assumed that future states

depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property)

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Independence

Two variables are independent in a joint distribution if:

Says the joint distribution factors into a product of two simple ones

Usually variables aren’t independent!

Can use independence as a modeling assumption

Independence can be a simplifying assumption

Empirical joint distributions: at best “close” to independent

What could we assume for {Weather, Traffic, Cavity}?

Independence is like something from CSPs: what?

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Example: Independence?

T W P

hot sun 0.4

hot rain 0.1 cold sun 0.2 cold rain 0.3

T W P

hot sun 0.3

hot rain 0.2 cold sun 0.3 cold rain 0.2

T P

hot 0.5 cold 0.5

W P

sun 0.6

rain 0.4

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Example: Independence

N fair, independent coin flips:

H 0.5

T 0.5

H 0.5

T 0.5

H 0.5

T 0.5

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Conditional Independence

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Conditional Independence

P(Toothache, Cavity, Catch)

If I have a cavity, the probability that the probe catches in it doesn't depend on whether I have a toothache:

P(+catch | +toothache, +cavity) = P(+catch | +cavity)

The same independence holds if I don’t have a cavity:

P(+catch | +toothache, -cavity) = P(+catch| -cavity)

Catch is conditionally independent of Toothache given Cavity:

P(Catch | Toothache, Cavity) = P(Catch | Cavity)

 Equivalent statements:

 P(Toothache | Catch , Cavity) = P(Toothache | Cavity)

 P(Toothache, Catch | Cavity) = P(Toothache | Cavity) P(Catch | Cavity)

 One can be derived from the other easily

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Conditional Independence

 Unconditional (absolute) independence very rare (why?)

Conditional independence is our most basic and robust form of knowledge about uncertain environments.

 X is conditionally independent of Y given Z if and only if:

or, equivalently, if and only if

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Conditional Independence

 What about this domain:

Traffic

Umbrella

Raining

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Conditional Independence

 What about this domain:

Fire

Smoke

Alarm

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Probability Recap

 Conditional probability

 Product rule

 Chain rule

 X, Y independent if and only if:

 X and Y are conditionally independent given Z if and only if:

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