nips nips2012 nips2012-52 knowledge-graph by maker-knowledge-mining

52 nips-2012-Bayesian Nonparametric Modeling of Suicide Attempts

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Author: Francisco Ruiz, Isabel Valera, Carlos Blanco, Fernando Pérez-Cruz

Abstract: The National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) database contains a large amount of information, regarding the way of life, medical conditions, etc., of a representative sample of the U.S. population. In this paper, we are interested in seeking the hidden causes behind the suicide attempts, for which we propose to model the subjects using a nonparametric latent model based on the Indian Buffet Process (IBP). Due to the nature of the data, we need to adapt the observation model for discrete random variables. We propose a generative model in which the observations are drawn from a multinomial-logit distribution given the IBP matrix. The implementation of an efﬁcient Gibbs sampler is accomplished using the Laplace approximation, which allows integrating out the weighting factors of the multinomial-logit likelihood model. Finally, the experiments over the NESARC database show that our model properly captures some of the hidden causes that model suicide attempts. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract The National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) database contains a large amount of information, regarding the way of life, medical conditions, etc. [sent-11, score-0.083]

2 In this paper, we are interested in seeking the hidden causes behind the suicide attempts, for which we propose to model the subjects using a nonparametric latent model based on the Indian Buffet Process (IBP). [sent-15, score-0.786]

3 Due to the nature of the data, we need to adapt the observation model for discrete random variables. [sent-16, score-0.075]

4 The implementation of an efﬁcient Gibbs sampler is accomplished using the Laplace approximation, which allows integrating out the weighting factors of the multinomial-logit likelihood model. [sent-18, score-0.074]

5 Finally, the experiments over the NESARC database show that our model properly captures some of the hidden causes that model suicide attempts. [sent-19, score-0.711]

6 , where suicide prevention is one of the top public health priorities [1]. [sent-22, score-0.755]

7 The current strategies for suicide prevention have focused mainly on both the detection and treatment of mental disorders [13], and on the treatment of the suicidal behaviors themselves [4]. [sent-23, score-0.888]

8 However, despite prevention efforts including improvements in the treatment of depression, the lifetime prevalence of suicide attempts in the U. [sent-24, score-0.855]

9 This suggests that there is a need to improve understanding of the risk factors for suicide attempts beyond psychiatric disorders, particularly in non-clinical populations. [sent-27, score-0.715]

10 According to the National Strategy for Suicide Prevention, an important ﬁrst step in a public health approach to suicide prevention is to identify those at increased risk for suicide attempts [1]. [sent-28, score-1.47]

11 Suicide attempts are, by far, the best predictor of completed suicide [12] and are also associated with major morbidity themselves [11]. [sent-29, score-0.656]

12 The estimation of suicide attempt risk is a challenging and complex task, with multiple risk factors linked to increased risk. [sent-30, score-0.78]

13 In the absence of reliable tools for identifying those at risk for suicide attempts, be they clinical or laboratory tests, risk detection still relays mainly on clinical variables. [sent-31, score-0.717]

14 The adequacy of the current predictive models and screening methods has been 1 questioned [12], and it has been suggested that the methods currently used for research on suicide risk factors and prediction models need revamping [9]. [sent-32, score-0.658]

15 Databases that model the behavior of human populations present typically many related questions and analyzing each one of them individually, or a small group of them, do not lead to conclusive results. [sent-33, score-0.14]

16 population with nearly 3,000 questions regarding, among others, their way of life, their medical conditions, depression and other mental disorders. [sent-36, score-0.288]

17 It contains yes-or-no questions, and some multiple-choice and questions with ordinal answers. [sent-37, score-0.14]

18 In this paper, we propose to model the subjects in this database using a nonparametric latent model that allows us to seek hidden causes and compact in a few features the immense redundant information. [sent-38, score-0.283]

19 Our starting point is the Indian Buffet Process (IBP) [5], because it allows us to infer which latent features inﬂuence the observations and how many features there are. [sent-39, score-0.229]

20 We need to adapt the observation model for discrete random variables, as the discrete nature of the database does not allow us to use the standard Gaussian observation model. [sent-40, score-0.193]

21 Furthermore, the multinomial-logit model, besides its versatility, allows the implementation of an efﬁcient Gibbs sampler where the Laplace approximation [10] is used to integrate out the weighting factors, which can be efﬁciently computed using the Matrix Inversion Lemma. [sent-42, score-0.101]

22 The IBP model combined with discrete observations has already been tackled in several related works. [sent-43, score-0.074]

23 They apply the ICD to focused topic modeling, where the instances are documents and the observations are words from a ﬁnite vocabulary, and focus on decoupling the prevalence of a topic in a document and its prevalence in all documents. [sent-45, score-0.176]

24 Despite the discrete nature of the observations under this model, these assumptions are not appropriate for categorical observations such as the set of possible responses to the questions in the NESARC database. [sent-46, score-0.254]

25 In this model, each (discrete) component in the observation vector of an instance depends only on one of the active latent features of that object, randomly drawn from a multinomial distribution. [sent-48, score-0.208]

26 Our model is more ﬂexible in the sense that it allows different probability distributions for every component in the observation vector, which is accomplished by weighting differently the latent variables. [sent-50, score-0.149]

27 2 The Indian Buffet Process In latent feature modeling, each object can be represented by a vector of latent features, and the observations are generated from a distribution determined by those latent feature values. [sent-51, score-0.379]

28 Typically, we have access to the set of observations and the main goal of these models is to ﬁnd out the latent variables that represent the data. [sent-52, score-0.123]

29 The most common nonparametric tool for latent feature modeling is the Indian Buffet Process (IBP). [sent-53, score-0.128]

30 The nth row of Z, denoted by zn· , represents the vector of latent features of the nth data point, and every entry nk is denoted by znk . [sent-61, score-0.449]

31 Note that each element znk ∈ {0, 1} indicates whether the k th feature contributes to the nth data point. [sent-62, score-0.275]

32 Given a binary latent feature matrix Z, we assume that the N × D observation matrix X, where the nth row contains a D-dimensional observation vector xn· , is distributed according to a probability distribution p(X|Z). [sent-63, score-0.312]

33 Additionally, x·d stands for the dth column of X, and each element of the 2 matrix is denoted by xnd . [sent-64, score-0.206]

34 MCMC (Markov Chain Monte Carlo) methods have been broadly applied to infer the latent structure Z from a given observation matrix X (see, e. [sent-66, score-0.155]

35 In particular, we focus on the use of Gibbs sampling for posterior inference over the latent variables. [sent-69, score-0.116]

36 The algorithm iteratively samples the value of each element znk given the remaining variables, i. [sent-70, score-0.19]

37 , it samples from p(znk = 1|X, Z¬nk ) ∝ p(X|Z)p(znk = 1|Z¬nk ), (1) where Z¬nk denotes all the entries of Z other than znk . [sent-72, score-0.19]

38 The distribution p(znk = 1|Z¬nk ) can be readily derived from the exchangeable IBP and can be written as p(znk = 1|Z¬nk ) = m−n,k /N, where m−n,k is the number of data points with feature k, not including n, i. [sent-73, score-0.08]

39 , Rd }, where this ﬁnite set contains the indexes to all the possible values of xnd . [sent-81, score-0.146]

40 We introduce matrices Bd of size K × R to model the probability distribution over X, such that Bd links the hidden latent variables with the dth column of the observation matrix X. [sent-83, score-0.226]

41 We assume r that the probability of xnd taking value r (r = 1, . [sent-84, score-0.146]

42 , r πnd = p(xnd = r|zn· , Bd ) = exp (zn· bd ) ·r , R exp (zn· bd ·r (2) ) r =1 where bd denotes the rth column of Bd . [sent-89, score-1.497]

43 Note that the matrices Bd are used to weight differently ·r the contribution of every latent feature for every component d, similarly as in the standard Gaussian observation model in [5]. [sent-90, score-0.169]

44 We assume that the mixing vectors bd are Gaussian distributed with zero ·r 2 mean and covariance matrix Σb = σB I. [sent-91, score-0.53]

45 We consider that elements xnd are independent given the latent feature matrix Z and the D matrices Bd . [sent-97, score-0.305]

46 p(xnd |zn· , Bd ) = (3) n=1 d=1 Laplace approximation for inference In Section 2, the (heuristic) Gibbs sampling algorithm for the posterior inference over the latent variables of the IBP has been reviewed and it is detailed in [5]. [sent-103, score-0.116]

47 Recall that our model assumes independence among the observations given the hidden latent variables. [sent-108, score-0.165]

48 By deﬁning (ρd )kr = N r n=1 znk πnd , the gradient of ψ(Bd ) can be derived as ψ = Md − ρd − 1 d 2 B . [sent-124, score-0.19]

49 The Hessian matrix can now be readily computed taking the derivatives of the gradient, yielding ψ=− 1 2 IRK + σB log p(x·d |β d , Z) N =− 1 diag(π nd ) − (π nd ) π nd ⊗ (zn· zn· ), 2 IRK − σB n=1 (7) R 2 1 where π nd = πnd , πnd , . [sent-128, score-0.166]

50 , πnd , and diag(π nd ) is a diagonal matrix with the values of the vector π nd as its diagonal elements. [sent-131, score-0.081]

51 9 by replacing K by K+ , Z by the submatrix containing only the non-zero columns of Z, and Bd MAP by the submatrix containing the K+ corresponding rows. [sent-141, score-0.095]

52 Since vn vn is a rank-one matrix, we can apply the Woodbury ·d identity [18] N times to invert the matrix − ψ, similar to the RLS (Recursive Least Squares) updates [7]. [sent-148, score-0.225]

53 , N , we compute (D(n) )−1 = D(n−1) − vn vn −1 = (D(n−1) )−1 + (D(n−1) )−1 vn vn (D(n−1) )−1 . [sent-152, score-0.388]

54 1 − vn (D(n−1) )−1 vn (12) For the ﬁrst iteration, we deﬁne D(0) as the block-diagonal matrix D, whose inverse matrix involves computing the R matrix inversions of size K+ × K+ of the matrices in (11), which can be efﬁciently solved applying the Matrix Inversion Lemma. [sent-153, score-0.287]

55 We also multiply each pixel independently with equiprobable binary noise, hence each white pixel in the composite image can be turned black 50% of the times, while black pixels always remain black. [sent-161, score-0.162]

56 The Gibbs sampler has been initialized with K+ = 2, setting each znk = 1 2 with probability 1/2, and the hyperparameters have been set to α = 0. [sent-164, score-0.239]

57 After 200 iterations, the Gibbs sampler returns four latent features. [sent-166, score-0.132]

58 As expected, the black pixels are known to be black (almost zero probability of being white) and the white pixels have about a 50/50 chance of being black or white, due to the multiplicative noise. [sent-169, score-0.128]

59 The Gibbs sampler has used as many as nine hidden features, but after iteration 60, the ﬁrst four features represent the base images and the others just lock on a noise pattern, which eventually fades away. [sent-170, score-0.144]

60 2 National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) The NESARC was designed to determine the magnitude of alcohol use disorders and their associated disabilities. [sent-172, score-0.154]

61 Two waves of interviews have been ﬁelded for this survey (ﬁrst wave in 2001-2002 and second wave in 2004-2005). [sent-173, score-0.151]

62 (b) Probability of each pixel being white, when a single feature is active (ordered to match the images on the left), computed using Bd . [sent-180, score-0.106]

63 (d) Probabilities of each pixel being white after 200 iterations of the Gibbs sampler inferred for the four data points on (c). [sent-183, score-0.129]

64 (e) The number of latent features K+ and (f) the approximate log of p(X|Z) over the 200 iterations of the Gibbs sampler. [sent-185, score-0.136]

65 The survey includes a question about having attempted suicide as well as other related questions such as ‘felt like wanted to die’ and ‘thought a lot about own death’. [sent-187, score-0.827]

66 In the present paper, we use the IBP with discrete observations for a preliminary study in seeking the latent causes which lead to committing suicide. [sent-188, score-0.211]

67 Most of the questions in the survey (over 2,500) are yes-or-no questions, which have four possible outcomes: ‘blank’ (B), ‘unknown’ (U), ‘yes’ (Y) and ‘no’ (N). [sent-189, score-0.175]

68 If a question is left blank the question was not asked1 . [sent-190, score-0.13]

69 If a question is said to be unknown either it was not answered or was unknown to the respondent. [sent-191, score-0.087]

70 In our ongoing study, we want to ﬁnd a latent model that describes this database and can be used to infer patterns of behavior and, speciﬁcally, be able to predict suicide. [sent-192, score-0.126]

71 In this paper, we build an unsupervised model with the 20 variables that present the highest mutual information with the suicide attempt question, which are shown in Table 1 together with their code in the questionnaire. [sent-193, score-0.662]

72 We run the Gibbs sampler over 500 randomly chosen subjects out of the 13,670 that have answered afﬁrmatively to having had a period of low mood. [sent-194, score-0.142]

73 We have initialized the sampler with an active feature, i. [sent-196, score-0.08]

74 , K+ = 1, and have set znk = 1 randomly with probability 0. [sent-198, score-0.19]

75 In Figure 2, we have plotted the posterior probability for each question when a single feature is active. [sent-201, score-0.107]

76 In these plots, white means 0 and black 1, and each row sums up to one. [sent-202, score-0.076]

77 Feature 1 is active for modeling the ‘blank’ and ‘no’ answers and, fundamentally, those who were not asked Questions 8 and 10. [sent-203, score-0.08]

78 Feature 3 models blank answers for most of the questions and negative responses to 1, 2, 5, 8 and 10, which are questions related to suicide. [sent-205, score-0.401]

79 Feature 5 models the ‘yes’ answer to Questions 3, 4, 6, 7, 8, 1 In a questionnaire of this size some questions are not asked when a previous question was answered in a predetermined way to reduce the burden of taking the survey. [sent-207, score-0.227]

80 For example, if a person has never had a period of low mood, the attempt suicide question is not asked. [sent-208, score-0.691]

81 Feature 7 models answering afﬁrmatively to Questions 15, 16, 19 and 20, which are related to alcohol abuse. [sent-211, score-0.133]

82 We show the percentage of respondents that answered positively to the suicide attempt questions in Table 2, independently for the 500 samples that were used to learn the IBP and the 9,500 hold-out samples, together with the total number of respondents. [sent-212, score-0.86]

83 A dash indicates that the feature can be active or inactive. [sent-213, score-0.076]

84 Throughout the database, the prevalence of suicide attempt is 7. [sent-216, score-0.706]

85 As expected, Features 2, 4, 5 and 7 favor suicide attempt risk, although Feature 5 only mildly, and Features 1, 3 and 6 decrease the probability of attempting suicide. [sent-218, score-0.7]

86 From the above description of each feature, it is clear that having Features 4 or 7 active should increase the risk of attempting suicide, while having Features 3 and 1 active should cause the opposite effect. [sent-219, score-0.159]

87 The other combinations favor an increased rate of suicide attempts that goes from doubling (‘11’) to quadrupling (‘00’), to a ten-fold increase (‘01’), and the percentages of population with these features are, respectively, 21%, 6% and 3%. [sent-221, score-0.742]

88 In the ﬁnal part of Table 2, we show combinations of features that signiﬁcantly increase the suicide attempt rate for a reduced percentage of the population, as well as combinations of features that signiﬁcantly decrease the suicide attempt rate for a large chunk of the population. [sent-222, score-1.43]

89 These results are interesting as they can be used to discard signiﬁcant portions of the population in suicide attempt studies and focus on the groups that present much higher risk. [sent-223, score-0.695]

90 Hence, our IBP with discrete observations is being able to obtain features that describe the hidden structure of the NESARC database and makes it possible to pin-point the people that have a higher risk of attempting suicide. [sent-224, score-0.335]

91 We have applied our model to the NESARC database to ﬁnd out the hidden features that characterize the suicide attempt risk. [sent-229, score-0.8]

92 We 7 Hidden features 1 0 1 1 1 - 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 - 1 1 - 1 1 0 0 - Suicide attempt probability Train Hold-out 6. [sent-230, score-0.116]

93 The ‘train ensemble’ columns contain the results for the 500 data points used to obtain the model, whereas the ‘hold-out ensemble’ columns contain the results for the remaining subjects. [sent-264, score-0.078]

94 These probabilities have been obtained with the posterior mean weights Bd MAP , when only one of the seven latent features (sorted from left to right to match the order in Table 2) is active. [sent-266, score-0.195]

95 have analyzed how each of the seven inferred features contributes to the suicide attempt probability. [sent-267, score-0.741]

96 8 References [1] Summary of national strategy for suicide prevention: Goals and objectives for action, 2007. [sent-273, score-0.599]

97 Cognitive therapy for the prevention of suicide attempts: a randomized controlled trial. [sent-302, score-0.726]

98 Trends in suicide ideation, plans, gestures, and attempts in the united states, 1990-1992 to 2001-2003. [sent-327, score-0.656]

99 The struggle to prevent and evaluate: application of population attributable risk and preventive fraction to suicide prevention research. [sent-332, score-0.818]

100 A suicide prevention program in a region with a very high suicide rate. [sent-384, score-1.325]

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