Robust Likelihood Ratio Test Using α−Divergence

Learning Robust and Sparse Principal Components With the α-Divergence

In this paper, novel robust principal component analysis (RPCA) methods are proposed to exploit the local structure of datasets. The proposed methods are derived by minimizing the α -divergence between the sample distribution and the Gaussian density model. The α- divergence is used in different frameworks to represent variants of RPCA approaches including orthogonal, non-orthogonal, and sparse methods. We show that the classical PCA is a special case of our proposed methods where the α- divergence is reduced to the Kullback-Leibler (KL) divergence. It is shown in simulations that the proposed approaches recover the underlying principal components (PCs) by down-weighting the importance of structured and unstructured outliers. Furthermore, using simulated data, it is shown that the proposed methods can be applied to fMRI signal recovery and Foreground-Background (FB) separation in video analysis. Results on real world problems of FB separation as well as image reconstruction are also provided.

Analysis and evaluation of explainable artificial intelligence on suicide risk assessment

This study explores the effectiveness of Explainable Artificial Intelligence (XAI) for predicting suicide risk from medical tabular data. Given the common challenge of limited datasets in health-related Machine Learning (ML) applications, we use data augmentation in tandem with ML to enhance the identification of individuals at high risk of suicide. We use SHapley Additive exPlanations (SHAP) for XAI and traditional correlation analysis to rank feature importance, pinpointing primary factors influencing suicide risk and preventive measures. Experimental results show the Random Forest (RF) model is excelling in accuracy, F1 score, and AUC (>97% across metrics). According to SHAP, anger issues, depression, and social isolation emerge as top predictors of suicide risk, while individuals with high incomes, esteemed professions, and higher education present the lowest risk. Our findings underscore the effectiveness of ML and XAI in suicide risk assessment, offering valuable insights for psychiatrists and facilitating informed clinical decisions.

Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging

Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the α- divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter α . It is shown that when α→ 1 , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of . Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.