Pathwise Coordinate Optimization for Sparse Learning: Algorithm and Theory

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it strong rule for coordinate preselection}. Such a complex algorithmic structure grants superior empirical performance, but also poses significant challenge to theoretical analysis. To tackle this long lasting problem, we develop a new theory showing that these three features play pivotal roles in guaranteeing the outstanding statistical and computational performance of the pathwise coordinate optimization framework. Particularly, we analyze the existing pathwise coordinate optimization algorithms and provide new theoretical insights into them. The obtained insights further motivate the development of several modifications to improve the pathwise coordinate optimization framework, which guarantees linear convergence to a unique sparse local optimum with optimal statistical properties in parameter estimation and support recovery. This is the first result on the computational and statistical guarantees of the pathwise coordinate optimization framework in high dimensions. Thorough numerical experiments are provided to support our theory.Comment: Accepted by the Annals of Statistics, 2016

Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery

We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tuning insensitiveness. Theoretically, we provide sufficient conditions under which CMR achieves the optimal rate of convergence in parameter estimation. Computationally, we propose an efficient smoothed proximal gradient algorithm with a worst-case numerical rate of convergence \cO(1/\epsilon), where $\epsilon$ is a pre-specified accuracy of the objective function value. We conduct thorough numerical simulations to illustrate that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR to solve a brain activity prediction problem and find that it is as competitive as a handcrafted model created by human experts. The R package \texttt{camel} implementing the proposed method is available on the Comprehensive R Archive Network \url{http://cran.r-project.org/web/packages/camel/}.Comment: Journal of Machine Learning Research, 201

Automatic higher order mesh generation and movement utilizing spring-field and vector-adding

In this research, an automatic, complex geometry applicable, unstructured curved 2D mesh generation method is developed. Based on this 2D method, an extension to 3D geometries is developed. The methodology of this mesh generation is to provide near-body and off-body meshes by an advancing-layer method to avoid mesh quality problems in transition areas, while using spring models to complement the advancing-layers by smoothing the mesh, especially in medial axis regions. After generating the linear mesh, a higher-order finite-element ready, curved mesh is obtained by deforming the linear mesh through “pipes” using a simple Vector-Adding approach. Different from most curved viscous mesh generation approaches, this method eschews a linear or nonlinear elasticity analogy while still providing positive-Jacobian mesh elements. In addition, the transformation from linear to curved meshes can be achieved by only deforming the necessary edges of the elements near domain boundaries while retaining the remaining non-curved edges to the benefit of numerical solvers. The CFD results of 30P30N airfoil on the curved mesh are given and are in good agreement with the experimental data. Further, a new method for moving boundary problems with viscous mesh layers is also presented. This method is an extension of the mesh generation approach above. It can be used not only for high-order mesh moving but also for high-order mesh generation. Also, based on the curved mesh deformation strategy, the method can handle high-order mesh movement or regeneration with minimal extra computational time compared with linear mesh movement. Several 2D boundary motion cases are tested including boundary translations, boundary rotations, and boundary morphing. The CFD results on the curved mesh after rotation are given and are in good agreement with the experimental data. This technique is also tested through the optimization of an airfoil to achieve a maximized lift and drag ratio. The results demonstrate that this approach can handle large boundary movements while preserving a good mesh quality

Analytical modeling of HSUPA-enabled UMTS networks for capacity planning

In recent years, mobile communication networks have experienced significant evolution. The 3G mobile communication system, UMTS, employs WCDMA as the air interface standard, which leads to quite different mobile network planning and dimensioning processes compared with 2G systems. The UMTS system capacity is limited by the received interference at NodeBs due to the unique features of WCDMA, which is denoted as `soft capacity'. Consequently, the key challenge in UMTS radio network planning has been shifted from channel allocation in the channelized 2G systems to blocking and outage probabilities computation under the `cell breathing' effects which are due to the relationship between network coverage and capacity. The interference characterization, especially for the other-cell interference, is one of the most important components in 3G mobile networks planning. This monograph firstly investigates the system behavior in the operation of UMTS uplink, and develops the analytic techniques to model interference and system load as fully-characterized random variables, which can be directly applicable to the performance modeling of such networks. When the analysis progresses from single-cell scenario to multi-cell scenario, as the target SIR oriented power control mechanism is employed for maximum capacity, more sophisticated system operation, `feedback behavior', has emerged, as the interference levels at different cells depend on each other. Such behaviors are also captured into the constructed interference model by iterative and approximation approaches. The models are then extended to cater for the features of the newly introduced HSUPA, which provides enhanced dedicated channels for the packet switched data services such that much higher bandwidth can be achieved for best-effort elastic traffic, which allows network operators to cope with the coexistence of both circuit-switched and packet-switched traffic and guarantee the QoS requirements. During the derivation, we consider various propagation models, traffic models, resource allocation schemes for many possible scenarios, each of which may lead to different analytical models. All the suggested models are validated with either Monte-Carlo simulations or discrete event simulations, where excellent matches between results are always achieved. Furthermore, this monograph studies the optimization-based resource allocation strategies in the UMTS uplink with integrated QoS/best-effort traffic. Optimization techniques, both linear-programming based and non-linear-programming based, are used to determine how much resource should be assigned to each enhanced uplink user in the multi-cell environment where each NodeB possesses full knowledge of the whole network. The system performance under such resource allocation schemes are analyzed and compared via Monte-Carlo simulations, which verifies that the proposed framework may serve as a good estimation and optimal reference to study how systems perform for network operators

Analysis of Toni Morrison’s A Mercy From the Perspective of Gender Performativity

Toni Morrison’s A Mercy capably combines the story of the black people in America with the gender relations, showing the author’s concerns for the gender issues in an ethnic context. Based on Judith Butler’s gender performativity theory, this paper regards the citation of the compulsory gender norms, discursive practices and performativity of the heroin Florens in Toni Morrison’s novel A Mercy from the ritual, language and theatrical dimensions, so as to arouse people’s attention to the gender relations in African American literature and broaden the research scope of the work