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6 / 1 6 / 1 6 / 1 1 6 / 1 0 6 / 2 1 3 0 2 x 1 x 2 (X 1 ,X 2 ) ) x , (x F 2 1 X , X 2 1 ) x X , x P(X 2 2 1 1 ]) x , ( X ], x , ( P(X 2 2 1 1 ]) x , ( ] x , ( ) X , P((X 2 1 2 1 BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial- NoDerivs 2.5 License.

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Page 1: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

x1

x2

(X1,X2)

)x,(xF 21X,X 21)xX,xP(X 2211

])x,(X],x,(P(X 2211

])x,(]x,()X,P((X 2121

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 2: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

x1

x2

x1

(X1,X2)

)x,(xF 21X,X 21)xX,xP(X 2211

])x,(X],x,(P(X 2211

])x,(]x,()X,P((X 2121

1-1

3

-2

x2

x2

1-1

3

-2

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 3: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(x 21

)x,(xF 21X,X 21

0

x1

x2

x1

x2

2 xó 1x 21

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 4: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(x 21

(-1,-2)

)x,(xF 21X,X 21

0

2/6

x1

x2

x1

x2

2 xó 1x 21

3x2- 1,x1- 21

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 5: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(x 21

(-1,-2)

(-1,3)

)x,(xF 21X,X 21

0

2/6

3/6

x1

x2

x1

x2

2 xó 1x 21

3x2- 1,x1- 21

3 x1,x1- 21

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 6: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(x 21

(-1,-2) (1,-2)

)x,(xF 21X,X 21

0

2/6

3/6

x1

x2

x1

x2

3/6

2 xó 1x 21

3x2- 1,x1- 21

0x2- 1,x 21

3 x1,x1- 21

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 7: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(x 21

(-1,-2) (1,-2)

(1,0)

)x,(xF 21X,X 21

0

4/6

x1

x2

x1

x2

3/6

2/6

3/6

2 xó 1x 21

3x2- 1,x1- 21

3x0 1,x 21

0x2- 1,x 21

3 x1,x1- 21

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

http://creativecommons.org/licenses/by-nc-nd/2.5/es/
http://www.ugr.es/local/cdpye
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Page 8: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(xF 21X,X 21

2 xó 1x 21 0

)x,(x 21

(-1,-2)2/6 3x2- 1,x1- 21

(-1,3)

(1,-2)

(1,0)

(1,3)

3 x1,x 21 1

x1

x2

x1

x2

3x0 1,x 21 4/6

0x2- 1,x 21 3/6

3 x1,x1- 21 3/6

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.

Page 9: x1x1 x2x2 (X 1,X 2 ) BY: Grupo CDPYE-UGR This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License

6/16/16/11

6/106/21

302

1-1

3

-2

)x,(xF 21X,X 21

2 xó 1x 21 0

2/6 3x2- 1,x1- 21

3 x1,x 21 1

x1

x2

x1

x2

3x0 1,x 21 4/6

0x2- 1,x 21 3/6

3 x1,x1- 21 3/6

BY: Grupo CDPYE-UGR

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 2.5 License.


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Recap: Reasoning Over Time Stationary Markov models Hidden Markov models X2X2 X1X1 X3X3 X4X4 rainsun 0.7 0.3 X5X5 X2X2 E1E1 X1X1 X3X3 X4X4 E2E2 E3E3

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