Hui Zou

Yanchen Zhu, Honghui Zou, Chufan Liu et al.

The success of vehicle electrification relies on efficient and adaptable charging infrastructure. Fixed-location charging stations often suffer from underutilization or congestion due to fluctuating demand, while mobile chargers offer flexibility by relocating as needed. This paper studies the optimal planning and operation of hybrid charging infrastructures that combine both fixed and mobile chargers within urban road networks. We formulate the Hybrid Charging Station Planning and Operation (HCSPO) problem, jointly optimizing the placement of fixed stations and the scheduling of mobile chargers. A charging demand prediction model based on Model Predictive Control (MPC) supports dynamic decision-making. To solve the HCSPO problem, we propose a deep reinforcement learning approach enhanced with heuristic scheduling. Experiments on real-world urban scenarios show that our method improves infrastructure availability - achieving up to 244.4% increase in coverage - and reduces user inconvenience with up to 79.8% shorter waiting times, compared to existing solutions.

Shixiang Chen, Shiqian Ma, Lingzhou Xue et al.

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Since non-smoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations or are heuristic and lack convergence guarantees. In this paper, we propose a new alternating manifold proximal gradient method to solve these two high-dimensional problems and provide a unified convergence analysis. Numerical experiment results are reported to demonstrate the advantages of our algorithm.

Boxiang Wang, Hui Zou

Distance weighted discrimination (DWD) is a margin-based classifier with an interesting geometric motivation. DWD was originally proposed as a superior alternative to the support vector machine (SVM), however DWD is yet to be popular compared with the SVM. The main reasons are twofold. First, the state-of-the-art algorithm for solving DWD is based on the second-order-cone programming (SOCP), while the SVM is a quadratic programming problem which is much more efficient to solve. Second, the current statistical theory of DWD mainly focuses on the linear DWD for the high-dimension-low-sample-size setting and data-piling, while the learning theory for the SVM mainly focuses on the Bayes risk consistency of the kernel SVM. In fact, the Bayes risk consistency of DWD is presented as an open problem in the original DWD paper. In this work, we advance the current understanding of DWD from both computational and theoretical perspectives. We propose a novel efficient algorithm for solving DWD, and our algorithm can be several hundred times faster than the existing state-of-the-art algorithm based on the SOCP. In addition, our algorithm can handle the generalized DWD, while the SOCP algorithm only works well for a special DWD but not the generalized DWD. Furthermore, we consider a natural kernel DWD in a reproducing kernel Hilbert space and then establish the Bayes risk consistency of the kernel DWD. We compare DWD and the SVM on several benchmark data sets and show that the two have comparable classification accuracy, but DWD equipped with our new algorithm can be much faster to compute than the SVM.

Boxiang Wang, Hui Zou

Distance weighted discrimination (DWD) was originally proposed to handle the data piling issue in the support vector machine. In this paper, we consider the sparse penalized DWD for high-dimensional classification. The state-of-the-art algorithm for solving the standard DWD is based on second-order cone programming, however such an algorithm does not work well for the sparse penalized DWD with high-dimensional data. In order to overcome the challenging computation difficulty, we develop a very efficient algorithm to compute the solution path of the sparse DWD at a given fine grid of regularization parameters. We implement the algorithm in a publicly available R package sdwd. We conduct extensive numerical experiments to demonstrate the computational efficiency and classification performance of our method.

Jianqing Fan, Han Liu, Yang Ning et al.

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed binary data are assumed to be obtained by dichotomizing a latent variable satisfying the Gaussian copula distribution or the nonparanormal distribution. The latent Gaussian model with the assumption that the latent variables are multivariate Gaussian is a special case of the proposed model. A novel rank-based approach is proposed for both latent graph estimation and latent principal component analysis. Theoretically, the proposed methods achieve the same rates of convergence for both precision matrix estimation and eigenvector estimation, as if the latent variables were observed. Under similar conditions, the consistency of graph structure recovery and feature selection for leading eigenvectors is established. The performance of the proposed methods is numerically assessed through simulation studies, and the usage of our methods is illustrated by a genetic dataset.

Jianqing Fan, Lingzhou Xue, Hui Zou

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

Shiqian Ma, Lingzhou Xue, Hui Zou

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this paper, we propose two alternating direction methods for solving this problem. The first method is to apply the classical alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient based alternating direction method of multipliers. Our methods exploit and take advantage of the special structure of the problem and thus can solve large problems very efficiently. Global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with one million variables in one to two minutes, and are usually five to thirty five times faster than a state-of-the-art Newton-CG proximal point algorithm.