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Invatare automata

Universitatea Politehnica BucurestiAnul universitar 2008-2009

Adina Magda Floreahttp://turing.cs.pub.ro/inva_09 si

curs.cs.pub.ro

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Curs nr. 13

Invatare Bayesiana

Invatare PA

2

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Invatare Bayesiana

3

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Retele Bayesiene

4

Cutremur

Alarma

TelMihai TelDana

HotP!"

0.00!PC"

0.00"

! C PA"

# # 0.9$

# F 0.9%

F # 0."9

F F 0.00!

A P#"

# 0.9

F 0.0$

A P$"

# 0.&

F 0.0!

P# $ A! C " %

P#&A"' P$&A"'PA&

!

C "'P

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0.9 ' 0.( ' 0.001 ' 0.999 ' 0.998 % 0.000)2

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Invatarea in retele Bayesiene

Invatare *arametrii

Invatare structura

#o+ele +iscrete Modele continue

$ate com*lete

'ate inco(plete ) variabile ascunse *neobservabile+

5

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I*ote,a cea mai *roaila

MAP ,earning - (ai(u( aposteriori *curs !"+ e ac predictii pe ba1a ipote1ei celei (ai probabile

P*23++ )4 P*23hMAP+P*hMAP3++

Probabilitatea iecarei ipote1e:

P*hi3++ ) P*+3hi+ P*hi+

are ipote1a (ai(i1ea1a aceasta epresie5

6

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I*ote,a cea mai *roaila

Bo(boane de cirese si la(aie - o punga ontinuu de ipote1e asupra distributiei de bo(boane

Modela( cu o RB

P*F)cirese+ 6 7777 F - aro(a *var aleatoare+ 6 - para(etrul care se invata

7

Aroma - F

F P

cirese

lamaie 1-

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I*ote,a cea mai *roaila

8tragebo(boane ccirese si l)7cla(aie

P*+3h6+) ;

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I*ote,a cea mai *roaila

Bo(boane de cirese si la(aie - a(bala< verde sau rosu Modela( cu o RB

@ariabile aleatoare: - aro(a /7 a(bala