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Lecture 15 Overview This time... Bayesian Net Belief Propagation Algorithm LDPC/IRA Codes S. Cheng (OU-Tulsa) December 5, 2017 1 / 27 Lecture 15 Bayesian Net Bayesian Net Relationship of variables depicted by a directed graph with no

  1. Lecture 15 Overview This time... Bayesian Net Belief Propagation Algorithm LDPC/IRA Codes S. Cheng (OU-Tulsa) December 5, 2017 1 / 27

  2. Lecture 15 Bayesian Net Bayesian Net Relationship of variables depicted by a directed graph with no loop Given a variable’s parents, the variable is conditionally independent of any non-descendants Reduce model complexity B R Facilitate easier inference D T P S. Cheng (OU-Tulsa) December 5, 2017 2 / 27

  3. Lecture 15 Bayesian Net Burlgar and racoon Burlgar: B; Racoon: R; Dog barked: D; Police called: P; Trash can fell: T p ( p , d , b , t , r ) = p ( p | d , b , t , r ) p ( d | b , t , r ) p ( b | t , r ) p ( t | r ) p ( r ) B R D T P S. Cheng (OU-Tulsa) December 5, 2017 3 / 27

  4. Lecture 15 Bayesian Net Burlgar and racoon Burlgar: B; Racoon: R; Dog barked: D; Police called: P; Trash can fell: T p ( p , d , b , t , r ) = p ( p | d , b , t , r ) p ( d | b , t , r ) p ( b | t , r ) p ( t | r ) p ( r ) = p ( p | d , ✁ b , ✁ t , ✁ p ( d | b , ✁ t , ✁ t , r ) p ( b | ✁ r ) r ) p ( t | r ) p ( r ) � �� � 2 parameters B R D T P S. Cheng (OU-Tulsa) December 5, 2017 3 / 27

  5. Lecture 15 Bayesian Net Burlgar and racoon Burlgar: B; Racoon: R; Dog barked: D; Police called: P; Trash can fell: T p ( p , d , b , t , r ) = p ( p | d , b , t , r ) p ( d | b , t , r ) p ( b | t , r ) p ( t | r ) p ( r ) = p ( p | d , ✁ b , ✁ t , ✁ p ( d | b , ✁ t , ✁ t , r ) p ( b | ✁ r ) r ) p ( t | r ) p ( r ) � �� � 2 parameters P D p ( p | d ) B R p ¬ d 0.01 p d 0.4 ¬ p ¬ d 0.99 D T ¬ p 0.6 d T R p ( t | r ) P ¬ r 0.05 t 0.7 t r ¬ t ¬ r 0.95 ¬ t r 0.3 S. Cheng (OU-Tulsa) December 5, 2017 3 / 27

  6. Lecture 15 Bayesian Net Burlgar and racoon Burlgar: B; Racoon: R; Dog barked: D; Police called: P; Trash can fell: T p ( p , d , b , t , r ) = p ( p | d , b , t , r ) p ( d | b , t , r ) p ( b | t , r ) p ( t | r ) p ( r ) = p ( p | d , ✁ b , ✁ t , ✁ p ( d | b , ✁ t , ✁ t , r ) p ( b | ✁ r ) r ) p ( t | r ) p ( r ) � �� � 2 parameters P D p ( p | d ) p ( d | b , r ) D B R B R p ¬ d 0.01 ¬ b ¬ r 0.1 d p d 0.4 d ¬ b r 0.5 ¬ p ¬ d 0.99 D T ¬ r 1 d b ¬ p 0.6 d d b r 1 T R p ( t | r ) ¬ d ¬ b ¬ r 0.9 P ¬ r 0.05 t ¬ d ¬ b 0.5 r 0.7 t r ¬ d b ¬ r 0 ¬ t ¬ r 0.95 ¬ d 0 b r ¬ t r 0.3 S. Cheng (OU-Tulsa) December 5, 2017 3 / 27

  7. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 B R D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  8. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: B R D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  9. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: p ( p | d ): 2 B R D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  10. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: p ( p | d ): 2 p ( d | b , r ): 4 B R D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  11. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: p ( p | d ): 2 p ( d | b , r ): 4 B R p ( b ): 1 D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  12. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: p ( p | d ): 2 p ( d | b , r ): 4 B R p ( b ): 1 p ( t | r ): 2 D T P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  13. Lecture 15 Bayesian Net Comparison of # parameters # parameters of complete model: 2 5 − 1 = 31 # parameters of Bayesian net: p ( p | d ): 2 p ( d | b , r ): 4 B R p ( b ): 1 p ( t | r ): 2 p ( r ): 1 D T Total: 2 + 4 + 1 + 2 + 1 = 10 The model size reduces to less than 1 3 ! P S. Cheng (OU-Tulsa) December 5, 2017 4 / 27

  14. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? Let p ( r ) = 0 . 2 and p ( b ) = 0 . 01 p ( d | b , r ) D B R ¬ b ¬ r 0.1 d d ¬ b r 0.5 ¬ r 1 d b d b r 1 ¬ d ¬ b ¬ r 0.9 ¬ d ¬ b 0.5 r ¬ d b ¬ r 0 ¬ d 0 b r S. Cheng (OU-Tulsa) December 5, 2017 5 / 27

  15. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? Let p ( r ) = 0 . 2 and p ( b ) = 0 . 01 p ( d | b , r ) p ( d , b , r ) D B R D B R ¬ b ¬ r 0.1 ¬ b ¬ r 0.0792 d d d ¬ b r 0.5 d ¬ b r 0.099 ¬ r 1 ¬ r 0.008 d b d b d b r 1 ⇒ d b r 0.002 ¬ d ¬ b ¬ r 0.9 ¬ d ¬ b ¬ r 0.7128 ¬ d ¬ b 0.5 ¬ d ¬ b 0.099 r r ¬ d b ¬ r 0 ¬ d b ¬ r 0 ¬ d 0 ¬ d 0 b r b r S. Cheng (OU-Tulsa) December 5, 2017 5 / 27

  16. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p ) P D B R ¬ b ¬ r 0.0792 p d p d ¬ b r 0.099 p ( p | d ) P D ¬ r 0.008 p d b ¬ d 0.01 p p d b r 0.002 p d 0.4 p ¬ d ¬ b ¬ r 0.7128 ¬ p ¬ d 0.99 ¬ d ¬ b 0.099 p r ¬ p 0.6 d p ¬ d b ¬ r 0 ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 6 / 27

  17. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p ) P D B R ¬ b ¬ r 0.0792 p d p d ¬ b r 0.099 p ( p | d ) P D ¬ r 0.008 p d b ¬ d 0.01 p p d b r 0.002 p d 0.4 p ¬ d ¬ b ¬ r 0.007128 ¬ p ¬ d 0.99 ¬ d ¬ b 0.00099 p r ¬ p 0.6 d p ¬ d b ¬ r 0 ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 6 / 27

  18. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p ) P D B R ¬ b ¬ r 0.03168 p d p d ¬ b r 0.0396 p ( p | d ) P D ¬ r 0.0032 p d b ¬ d 0.01 p p d b r 0.0008 p d 0.4 p ¬ d ¬ b ¬ r 0.007128 ¬ p ¬ d 0.99 ¬ d ¬ b 0.00099 p r ¬ p 0.6 d p ¬ d b ¬ r 0 ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 6 / 27

  19. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p , t ) T P D B R ¬ t ¬ b ¬ r 0.03168 p d ¬ t p d ¬ b r 0.0396 p ( t | r ) T R ¬ t ¬ r 0.0032 p d b ¬ r 0.05 t ¬ t p d b r 0.0008 t r 0.7 ¬ t p ¬ d ¬ b ¬ r 0.007128 ¬ t ¬ r 0.95 ¬ t ¬ d ¬ b 0.00099 p r ¬ t 0.3 r ¬ t p ¬ d b ¬ r 0 ¬ t ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 7 / 27

  20. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p , t ) T P D B R ¬ t ¬ b ¬ r 0.030096 p d ¬ t p d ¬ b r 0.0396 p ( t | r ) T R ¬ t ¬ r 0.00304 p d b ¬ r 0.05 t ¬ t p d b r 0.0008 t r 0.7 ¬ t p ¬ d ¬ b ¬ r 0.0067716 ¬ t ¬ r 0.95 ¬ t ¬ d ¬ b 0.00099 p r ¬ t 0.3 r ¬ t p ¬ d b ¬ r 0 ¬ t ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 7 / 27

  21. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? p ( d , b , r , p , t ) T P D B R ¬ t ¬ b ¬ r 0.030096 p d ¬ t p d ¬ b r 0.01188 p ( t | r ) T R ¬ t ¬ r 0.00304 p d b ¬ r 0.05 t ¬ t p d b r 0.00024 t r 0.7 ¬ t p ¬ d ¬ b ¬ r 0.0067716 ¬ t ¬ r 0.95 ¬ t ¬ d ¬ b 0.000297 p r ¬ t 0.3 r ¬ t p ¬ d b ¬ r 0 ¬ t ¬ d 0 p b r · · · S. Cheng (OU-Tulsa) December 5, 2017 7 / 27

  22. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? T P D B R p ( d , b , r , p ) ¬ t p d ¬ b ¬ r 0.030096 ¬ t ¬ b 0.01188 p d r ¬ t p d b ¬ r 0.00304 ¬ t 0.00024 p d b r Normalize... ¬ t ¬ d ¬ b ¬ r 0.0067716 p ¬ t p ¬ d ¬ b r 0.000297 ¬ t ¬ d ¬ r 0 p b ¬ t p ¬ d b r 0 · · · S. Cheng (OU-Tulsa) December 5, 2017 8 / 27

  23. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? T P D B R p ( d , b , r , p ) ¬ t p d ¬ b ¬ r 0.57518 ¬ t ¬ b 0.22704 p d r ¬ t p d b ¬ r 0.058099 ¬ t 0.0045868 p d b r Normalize... ¬ t ¬ d ¬ b ¬ r 0.12942 p ¬ t p ¬ d ¬ b r 0.0056761 ¬ t ¬ d ¬ r 0 p b ¬ t p ¬ d b r 0 · · · S. Cheng (OU-Tulsa) December 5, 2017 8 / 27

  24. Lecture 15 Bayesian Net Burglar and racoon Question: What is the probability of a burglar visit if police was called but trash can stayed untouched? T P D B R p ( d , b , r , p ) ¬ t p d ¬ b ¬ r 0.57518 ¬ t ¬ b 0.22704 p d r ¬ t p d b ¬ r 0.058099 p ( b |¬ t , p ) ¬ t 0.0045868 p d b r ¬ t ¬ d ¬ b ¬ r 0.12942 =0 . 058099 + 0 . 0045868 p ¬ t p ¬ d ¬ b r 0.0056761 ≈ 0 . 0626 ¬ t ¬ d ¬ r 0 p b ¬ t p ¬ d b r 0 · · · S. Cheng (OU-Tulsa) December 5, 2017 8 / 27

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