presentacionBayes.ppt

!"#$ &' (')*+*",'+ -+$,&" .,/"0-'+ 12"3$3*4*+5$+ Dr. Dr. Pedro Aarón Hernández Her nández Ávalos Áv alos

C.A.T.I.A.

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C.A.T.I.A.

Cuerpo Académico en Tecnologías Tecnologías de la Información Aplicada

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!"#$%&'((!)"

C.A.T.I.A.

Cuerpo Académico en Tecnologías Tecnologías de la Información Aplicada

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"+,-.+/01+ 2-.345+ 60/ 7489.0

C.A.T.I.A.

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6278','+ &' 4$ 92"3$3*4*&$& •

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¿Cómo ganar? C.A.T.I.A.

Cuerpo Académico en Tecnologías de la Información Aplicada

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¿Cómo osamos hablar de leyes del azar? ¿No es, acaso, el azar la antítesis de cualquier ley? Bertrand Rusell

C.A.T.I.A.

5

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>?+ @.49+93/36+6 A45 +B-6+ + ,48+. 6023534A05C La probabilidad de tener un accidente de tráfico aumenta con el tiempo que pasas en la calle. Por tanto, cuanto mas rápido circules, menor es la probabilidad de que tengas un accidente.

C.A.T.I.A.

7

>?+ @.49+93/36+6 A45 +B-6+ + ,48+. 6023534A05C El 33 % de los accidentes mortales involucran a alguien que ha bebido. Por tanto, el 67 % restante ha sido causado por alguien que no había bebido.

A la vista de esto y de lo anterior, esta claro que la forma más segura de conducir es ir borracho y a gran velocidad. C.A.T.I.A.

8

BC-D ,')'+*5" 9$2$ 5"#$2 -,$ 602353DA ', #* E*&$F •

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C.A.T.I.A.


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I$ J,/"2#$)*K, )"#" 'G' E*5$4 9$2$ 5"#$2 &')*+*",'+ •

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C.A.T.I.A.


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("+ /-',5'+ &' *,/"2#$)*K, ', ,-'+52" )'2'32" • •

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C.A.T.I.A.


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:'92'+',5$)*K, &' 4$ J,/"2#$)*K, • •

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C.A.T.I.A.


12

P (A|B )

=

P A ∩ B) P (B )

G$%H;H!?!&;& (%"&!(!%";?

C.A.T.I.A.


13

635',*',&" 92"3$3*4*&$&'+ E7$ >"-9/+64C >?/-F3+C '+5$&7+H)$ I I J I I J I I J J I

J J I J J I I J J

P (A|B )

P( Nub | Lluvia)

P( Nub | Lluvia)

6

P(Nublado)

=

P( Nublado) P(Lluvia) P( Lluvia ) C.A.T.I.A.

=

10 4 10

4 =

=

10 6 10

=

=

=

=

0.6 0.4

P( Nub | Lluvia)

P( Nub | Lluvia)

=

P (A ∩ B ) P (B )

P( Nub ! Lluvia) =

0.3 =

P( Lluvia)

0.4

P( Nub ! Lluvia) =

0.1 =

P( Lluvia)

0.3 =

P( Lluvia)

=

0.6

P( Nub ! Lluvia) =

0.3 =

P( Lluvia)

0.25

=

0.4

P( Nub ! Lluvia) =

0.75

=

=

0.6

0.50 0.50

0.4 0.6

14

P (A|B )

=

P (A ∩ B ) P ( A | B )

P (A ∩ B ) P (B )

= P (A|B ) × P (B ) =

P ( B | A ) ! P ( A ) P ( B )

#<%$<:; &< H;K<= C.A.T.I.A.


15

W #U0-*,$+> 92"&-)5"+ &'/')5-"+"+ 0.05

0.6

A

0.95

0.10 0.2

B

0.90

0.7

0.3

C

0.93

D no D D

¿ P (A|D) ?

no D D no D

P. Condicional

P (A|B ) C.A.T.I.A.


16

W #U0-*,$+> 92"&-)5"+ &'/')5-"+"+ A

B

D

P ( A | D )

P ( D ! A ) =

P ( D )

Intersección

P (A ∩ B )

C

C.A.T.I.A.

= P (A|B ) × P (B )

P (D ∩ A)


= 0.05 × 0.6 = 0.03

17

";!L< H;K<=

C.A.T.I.A.


18

C.A.T.I.A.

Outlook

Temp

Humidity

Windy

Class

sunny

hot

high

false

Don't Play

sunny

hot

high

true

Don't Play

overcast

hot

high

false

Play

rainy

mild

high

false

Play

rainy

cool

normal

false

Play

rainy

cool

normal

true

Don’t Play

overcast

cool

normal

true

Play

sunny

mild

high

false

Don’t Play

sunny

cool

normal

false

Play

rainy

mild

normal

false

Play

sunny

mild

normal

true

Play

overcast

mild

high

true

Play

overcast

hot

normal

false

Play

rainy

mild

high

true

Don’t Play


( $ 5 $ A ' 5

19

= 4 $ + * L ) $ ) * K ,

C.A.T.I.A.

Outlook

Temp

Humidity

Windy

Class

sunny

cool

high

true

?


20

Naive Bayes Outlook

temperature

yes

no

yes

no

sunny

2

3

hot

2

2

overcast

4

0

mild

4

2

rainy

3

2

cool

3

1

sunny

2/9

3/5

hot

2/9

overcast 4/9

0/5

mild

2/5

cool

rainy

3/9

humidity

windy

yes

no

yes

no

High

3

4

False

6

2

normal

6

1

true

3

3

2/5

high

3/9

4/5

false

6/9

2/5

4/9

2/5

normal

6/9

5/5

true

3/9

3/5

3/9

1/5

play

yes

no

9

5

9/14

5/14

C.A.T.I.A.


21

Naive Bayes (Test) Outlook

Temp

Humidity

Windy

Class

sunny

cool

high

true

?

• P(Class = yes | Outlook = sunny ! Temp = cool ! Humidity = high ! Windy = true) • P(Class = no | Outlook = sunny ! Temp = cool ! Humidity = high ! Windy = true)

Teorema de Bayes C.A.T.I.A.

P ( A | B )

=

P ( B | A ) ! P ( A )


P ( B ) 22

Naive Bayes (Test) P(Class

=

yes | Outlook

P(Outlook

=

sunny

!

=

sunny

Temp

=

!

Temp

cool

!

=

cool

!

Humidity

=

Humidity high

!

=

high

Windy

=

!

Windy

true)

=

true|Class

=

=

yes) " P(Class

=

yes)

=

=

P(Outlook P(Outlook P(Windy

"

=

=

=

sunny | Class

true|Class

=

sunny

=

!

Temp

yes) " P(Temp

yes) " P(Class

=

=

cool

=

!

Humidity

cool | Class

=

=

high

!

Windy

yes) " P(Humidity

=

=

true)

high|Class

=

yes) "

yes)

=

=

P(Outlook

=

sunny

!

Temp

=

cool

!

Humidity

=

high

!

Windy

2 3 3 3 9 9 " 9 " 9 " 9 " 14

=

P(Outlook

=

sunny

!

Temp

=

cool

!

Humidity

=

true)

= =

high

!

Windy

high

!

Windy

=

true)

0,0053 =

P(Outlook

C.A.T.I.A.

=

sunny

!

Temp

=

cool

!

Humidity

=

=

true)


23

Naive Bayes (Test) P(Class

=

no | Outlook

P(Outlook

=

=

sunny ! Temp

"

P(Windy

=

=

=

=

cool ! Humidity

sunny ! Temp cool ! Humidity =

P(Outlook P(Outlook

=

=

=

sunny | Class

true | Class P(Outlook

=

=

sunny ! Temp

=

no) " P(Temp

no) " P(Class

=

=

=

=

=

high ! Windy

high ! Windy

cool ! Humidity cool | Class

=

=

=

=

true)

true | Class

high ! Windy

no) " P(Humidity

=

=

=

=

no) " P(Class

=

no) =

true)

high | Class

=

no ) "

n o)


=

high ! Windy

3 1 4 3 5 " " " " 5 5 5 5 14

P(Outlook

=


=

high ! Windy true)

=

true)

=

=

=

0,0206 =

C.A.T.I.A.

P(Outlook

=


=

high ! Windy

=

true)


24

Naive Bayes (Test)

P(Class yes | Outlook sunny ! Temp cool ! Humidity =

=

=

=

high ! Windy true) =

=

0,0053 =

P(Outlook sunny ! Temp cool ! Humidity =

=

=

high ! Windy true)

P(Class no | Outlook sunny ! Temp cool ! Humidity =

=

=

=

=


=

0,0206 =

P(Outlook sunny ! Temp cool ! Humidity =

C.A.T.I.A.

=

=



25

Naive Bayes (Test)

P yes

=

0,0053

0,0053

P(E) 0,0053 0,0206

P(E) 0,0053 + 0,0206

P(E)

+

=

P ( E )

=

0,0053 0,0259

=

20.5%

P ( E )

0,0206 P no

=

P(E) 0,0053 0,0206 P(E)

C.A.T.I.A.

+

P ( E )

=

79,5%

NO se juega


26

;G?!(;(!%"<=

C.A.T.I.A.


27

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C.A.T.I.A.

29

17S'4@ Pi + x + el: Picture element. R 2

f (r , c)

=

p

p : tono de color. =

r row, (renglón). =

c

=

column (columna).

Vo + x + el: Volume element. R 3

C.A.T.I.A.

30

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;,$4*[$2 -,$ J#$8', •

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C.A.T.I.A.

W_ 1-,5"+ 34$,)"+ )", `a 97S'4'+ &' +-9'2L)*' ', 92"#'&*" P 1-,5"+ )", +-9'2L)*' #$b"2 0-' Maa 97S'4'+

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.,5',&*#*',5" &' -,$ J#$8', •

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.,5',&*#*',5" &' -,$ J#$8', Scale Invariant Features Transform (SIFT) Detección de Objetos.

C.A.T.I.A.

37

;94*)$)*",'+ &' 4$ :')-9'2$)*K, T*+-$4 •

J,/"2#UH)$ eD&*)$ –

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C.A.T.I.A.

6/'25$+ b 1-34*)*&$& 38

presentacionBayes.ppt

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