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Bayesian Nonparametric Modeling of Suicide Attempts Francisco J. R. Ruiz, Isabel Valera, Carlos Blanco, Fernando Perez-Cruz I
Indian Bu↵et process: Z ⇠ IBP(↵).
I
Discrete observations: xnd 2 {1, . . . , R}.
p(xnd
p(xnd = ‘red’|zn· , Bd ) / exp (zn· bd·red ), p(xnd = ‘blue’|zn· , Bd ) / exp (zn· bd·blue ), .. . exp (zn· bd·r ) = r |zn· , Bd ) = R , r = 1, . . . , R, X d exp (zn· b·r 0 ) r 0 =1
where bd·r ⇠ N (0, ⌃b = Bayesian Nonparametric Modeling of Suicide Attempts
2 B I). F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
Inference I
Gibbs sampling algorithm (requires p(X|Z)).
I
The posterior of B1 , . . . , BD factorizes as Non Gauss
Gauss
z }| { z }| { D D z }| { Y d Y p(x |B , Z) p(Bd ) ·d p(B1 , . . . , BD |X, Z) = p(Bd |x·d , Z) = . p(x·d |Z) Non Gauss
d=1
I I
d=1
We define (Bd ) = log p(x·d |Bd , Z) + log p(Bd ). We want to compute Z p(x·d |Z) = exp (Bd ) dBd .
Laplace approximation: Approximate (Bd ) by its second-order Taylor series expansion. Assume p(Bd |X, Z) is a Gaussian distribution. Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
Results I
NESARC database (National Epidemiologic Survey on Alcohol and Related Conditions): I I I
Samples the U.S. population. Multiple-choice questions (‘Blank’, ‘Unknown’, ‘Yes’ and ‘No’). We select the 20 questions with the highest mutual information with the question about having attempted suicide.
Figure: Probability of each response to the 20 selected questions. Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
NESARC database I
Suicide attempt probability in the whole database: ⇠ 8%. Latent features
1 -
1 -
1 0 0 1 1
1 0 1 0 1
1 -
1 -
1 -
Suicide attempt probability Train Hold-out 6.74% 5.55% 10.56% 11.16% 3.72% 4.60% 25.23% 22.25% 8.64% 9.69% 6.90% 7.18% 14.29% 14.18% 30.77% 28.55% 82.35% 61.95% 0.83% 0.87% 14.89% 16.52%
Number of cases Train Hold-out 430 8072 322 6083 457 8632 111 2355 301 5782 464 8928 91 1664 26 571 17 297 363 6574 94 2058
Visit us on Thursday 2:00 - 6:00pm, Poster Th41 Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
Indian Bu↵et process: Z ⇠ IBP(↵).
I
Discrete observations: xnd 2 {1, . . . , R}.
p(xnd
p(xnd = ‘red’|zn· , Bd ) / exp (zn· bd·red ), p(xnd = ‘blue’|zn· , Bd ) / exp (zn· bd·blue ), .. . exp (zn· bd·r ) = r |zn· , Bd ) = R , r = 1, . . . , R, X d exp (zn· b·r 0 ) r 0 =1
where bd·r ⇠ N (0, ⌃b = Bayesian Nonparametric Modeling of Suicide Attempts
2 B I). F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
Inference I
Gibbs sampling algorithm (requires p(X|Z)).
I
The posterior of B1 , . . . , BD factorizes as Non Gauss
Gauss
z }| { z }| { D D z }| { Y d Y p(x |B , Z) p(Bd ) ·d p(B1 , . . . , BD |X, Z) = p(Bd |x·d , Z) = . p(x·d |Z) Non Gauss
d=1
I I
d=1
We define (Bd ) = log p(x·d |Bd , Z) + log p(Bd ). We want to compute Z p(x·d |Z) = exp (Bd ) dBd .
Laplace approximation: Approximate (Bd ) by its second-order Taylor series expansion. Assume p(Bd |X, Z) is a Gaussian distribution. Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
Results I
NESARC database (National Epidemiologic Survey on Alcohol and Related Conditions): I I I
Samples the U.S. population. Multiple-choice questions (‘Blank’, ‘Unknown’, ‘Yes’ and ‘No’). We select the 20 questions with the highest mutual information with the question about having attempted suicide.
Figure: Probability of each response to the 20 selected questions. Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
NESARC database I
Suicide attempt probability in the whole database: ⇠ 8%. Latent features
1 -
1 -
1 0 0 1 1
1 0 1 0 1
1 -
1 -
1 -
Suicide attempt probability Train Hold-out 6.74% 5.55% 10.56% 11.16% 3.72% 4.60% 25.23% 22.25% 8.64% 9.69% 6.90% 7.18% 14.29% 14.18% 30.77% 28.55% 82.35% 61.95% 0.83% 0.87% 14.89% 16.52%
Number of cases Train Hold-out 430 8072 322 6083 457 8632 111 2355 301 5782 464 8928 91 1664 26 571 17 297 363 6574 94 2058
Visit us on Thursday 2:00 - 6:00pm, Poster Th41 Bayesian Nonparametric Modeling of Suicide Attempts
F. J. R. Ruiz, I. Valera, C. Blanco, F. Perez-Cruz
