Journal Press India^®

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This study presents a mathematical comparison of Generative Adversarial Networks (GANs) and traditional machine learning models for predicting suicidal behavior. The dataset D={(x_i,y_i ) }_(i=)^N consists of feature vectors x_i∈R^d, representing psychosocial, behavioral, and demographic factor and binary labels y_i∈{0,1}, denoting suicidal risk (1: at risk, 0: not at risk). The task is to estimate the conditional probability P(y_i∣x_i ) for each instance.In GANs, the generator G(z;θ_g ) and discriminator D(x;θ_d ) are trained adversarially. The loss function for the discriminator and generator is given by:L_GAN=E_(x∼p_"datat "  (x)) [log⁡D(x;θ_d ) ]+E_(z∼p_z (z)) [log⁡(1-D(G(z;θ_g );θ_d ) ) ], Wherez is the latent vector and p_"data "  (x) is the true data distribution.
For traditional models, SVM minimizes the hinge loss:L_SVM=∑_(i=1)^N▒  max(0,1-y_i w^T x_i ). Logistic Regression (LR) minimizes the log-loss (cross-entropy):L_LR=-∑_(i=1)^N▒  [y_i log⁡(σ(w^T x_i ) )+(1-y_i )log⁡(1-σ(w^T x_i ) ) ]. Random Forest (RF) optimizes the Gini impurity:L_RF=∑_(j=1)^K▒  [N_j/N (1-∑_(c=1)^C▒  p_jc^2 ) ]. Evaluation metrics, such as accuracy A_r precision P, recall R, F1-score F_1, and AUC, are calculated to assess predictive performance. Results indicate that GANs outperform traditional methods, offering superior generalization and enhanced performance in terms of F1-score and AUC due to their ability to generate synthetic, informative data.
 

Keywords

Generative adversarial networks; Suicidal behavior prediction; Support vector machine; Logistic regression; Random forest; Adversarial training

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