Hong Seng Sim

Modeling bivariate count data with complex dispersion and dependence structures remains a significant challenge in statistical data analysis. This article introduces two new bivariate count distributions derived from the generalized shifted inverse trinomial distribution. The proposed models, denoted by BGIT-I and BGIT-II, are constructed using convolution and trivariate reduction methods. They provide flexible joint frameworks for modeling correlated count data while accommodating different marginal dispersion patterns. BGIT-I allows negative, near-zero, and positive dependence, whereas BGIT-II induces non-negative dependence through a common component. The proposed models have simple, tractable probability generating functions, which facilitate the derivation of probabilistic properties and motivate a probability-generating-function-based estimation approach alongside maximum-likelihood estimation. The finite-sample performance of the estimators is further examined through a Monte Carlo simulation study. The practical utility of the proposed models is illustrated using two real bivariate count data sets involving shunter accidents and patient counts in critical care and emergency room settings. The results show that the proposed BGIT models provide competitive alternatives for modeling bivariate count data with different dispersion and dependence characteristics.

In this paper, we introduce a new gradient method called the Diagonal Variable Matrix method. Our proposed method is aimed to minimize H_k+1 over the log-determinant norm subject to weak secant relation. The derived diagonal matrix H_k+1 is the approximation of the inverse Hessian matrix, which enables the calculation of the search direction, d_k = −H_k+1g_k, where g_k denotes the gradient of the objective function. The proposed method is coupled with the backtracking Armijo line search. The proposed method is specifically designed to reduce the number of iterations and training duration, particularly in the context of solving large-dimensional problems. Finally, as a practical illustration, the proposed method is applied to solve the image deblurring problem, and its performance is analyzed using image quality metrics. The results demonstrate that the proposed method outperforms various conjugate gradient (CG) methods and multiple damping gradient method.

This paper presents a new training optimizer for deep learning models, called the Spectral Proximal (SP) method with saliency matrix, that aims to improve their ability to generalize to new data. Generalization is the measure of how well a model can perform on data that it has not seen during training. The SP method addresses a pair of hurdles affecting generalization: the problem of gradient confusion within complex model architectures and the limited availability of training data. The key innovation of the SP method is the use of a proximal operator with a saliency matrix, which adjusts the descent direction based on the importance of each parameter and avoids overfit issues. This leads to improved performance on image classification (MNIST and CIFAR-10) and object detection (YOLOv7) tasks and better ability to generalize to new data. We conducted a comprehensive inquiry by performing experiments on various configurations while controlling for potential confounding factors. The SP method consistently outperformed the baseline method based on the results.

In this paper, we propose a modified mean-variance portfolio selection procedure using the proximal gradient method. This novel selection procedure has the advantage of encouraging sparsity in the entire portfolio usingl₀−norm while requiring only O(n) storage. The proximal gradient method (PSG) introduces a multiple damping gradient (MDG) method to reduce the computation time, with Lipschitz constant serving as the step size, and iterative thresholding (IHT) as the proximal method to induce the sparsity of the portfolio. To find the optimal portfolio, an efficient algorithm is developed. The performance of the proposed selection procedure is illustrated by its application to real-life data set. It is shown that the proposed portfolio performs consistently better in comparison with other methods.

Model generalization refers to a model’s ability to perform well on unseen data. In this paper, we present the Spectral Proximal (SP) method with saliency matrix as a training technique for deep learning models that aims to improve their generalization ability. The SP method addresses two challenges that can hinder generalization: the gradient confusion issue in deep model structures and the scarcity of training data. The method uses a damping matrix and a proximal operator with a saliency matrix to correct for errors in the descent direction and prevent over-fitting, respectively. This results in improved performance on image classification (MNIST and CIFAR-10) and detection (YOLOv7) tasks, as well as better generalization on unseen data. We conducted a thorough investigation through experiments on a diverse range of setups, controlling for potential confounding variables. The results consistently showed that the SP method outperformed the baseline method in the majority of cases.

This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under the measure defined as a ratio of the determinant of updating matrix over its largest eigenvalue. Coupled with a nonmonotone line search strategy where backtracking-type line search is applied selectively, the spectral parameter acts as a stepsize during iterations when no line search is performed and as a milder form of quasi-Newton update when backtracking line search is employed. Convergence properties of the proposed method are established for uniformly convex functions. Extensive numerical experiments are conducted and the results indicate that our proposed spectral gradient method outperforms some standard conjugate-gradient methods.