A Cyclic Coordinate Descent Method for Convex Optimization on Polytopes

Coordinate descent algorithms are popular for huge-scale optimization problems due to their low cost per-iteration. Coordinate descent methods apply to problems where the constraint set is separable across coordinates. In this paper, we propose a new variant of the cyclic coordinate descent method that can handle polyhedral constraints provided that the polyhedral set does not have too many extreme points such as L1-ball and the standard simplex. Loosely speaking, our proposed algorithm PolyCD, can be viewed as a hybrid of cyclic coordinate descent and the Frank-Wolfe algorithms. We prove that PolyCD has a O(1/k) convergence rate for smooth convex objectives. Inspired by the away-step variant of Frank-Wolfe, we propose PolyCDwA, a variant of PolyCD with away steps which has a linear convergence rate when the loss function is smooth and strongly convex. Empirical studies demonstrate that PolyCDwA achieves strong computational performance for large-scale benchmark problems including L1-constrained linear regression, L1-constrained logistic regression and kernel density estimation

On the Convergence of CART under Sufficient Impurity Decrease Condition

The decision tree is a flexible machine learning model that finds its success in numerous applications. It is usually fitted in a recursively greedy manner using CART. In this paper, we investigate the convergence rate of CART under a regression setting. First, we establish an upper bound on the prediction error of CART under a sufficient impurity decrease (SID) condition \cite{chi2022asymptotic} -- our result improves upon the known result by \cite{chi2022asymptotic} under a similar assumption. Furthermore, we provide examples that demonstrate the error bound cannot be further improved by more than a constant or a logarithmic factor. Second, we introduce a set of easily verifiable sufficient conditions for the SID condition. Specifically, we demonstrate that the SID condition can be satisfied in the case of an additive model, provided that the component functions adhere to a ``locally reverse Poincar{\'e} inequality". We discuss several well-known function classes in non-parametric estimation to illustrate the practical utility of this concept

Mobile O2O Commerce Platform Quality: Scale Development and Validation

The Drainage effect of mobile O2O commerce is closely related to the platform quality. However, to date there has been no measure specifically designed to measure mobile O2O commerce platform quality (MCPQ). The purpose of this study is to develop a scale for measuring MCPQ based on the IS success model. Exploratory factor analysis (study 1) and confirmatory factor analysis (study 2) were performed on 613 samples. Results showed that the scale of MCPQ is a reliable and valid instrument, and that mobile O2O commerce platform quality is a multi-dimensional construct composed of five dimensions, i.e., interface design, operational efficiency, content quality, demand responsiveness, and privacy protection

A Dynamic Credit Evaluation Approach Using Sensitivity-Optimized Weights for Supply Chain Finance

Supply chain financing provides important funding channels for micro and small enterprises (MSEs), but effectively evaluating their creditworthiness remains challenging. Past methods overly rely on static financial indicators and subjective judgment in determining credit evaluation weights. This study proposes a dynamic credit evaluation approach that uses sensitivity analysis to optimize the weighting scheme. An indicator system is constructed based on the unique characteristics of e-commerce MSEs. The weight optimization integrates subjective, objective, and sensitivity-based methods to reflect specific financing scenarios. A system dynamics model simulates the credit evaluation mechanism and identifies the sensitivity of each influencing factor. The resultant comprehensive weights are applied in a TOPSIS-GRA dynamic evaluation model to assess MSE credit levels over time. An empirical analysis of 20 online stores demonstrates the proposed model\u27s advantages in accurately revealing credit rankings relative to conventional static models. This research provides an effective data-driven weighting technique and dynamic evaluation framework for supply chain finance credit assessment