arXiv subjects

Li Wang

Publications and source records attributed to Li Wang.

At least 397 records · Page 22Linked to original sources

arXiv2021

Simultaneous Confidence Corridors for Mean Functions in Functional Data Analysis of Imaging Data

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies we examine the finite-sample performance of the proposed method. Finally, the proposed method is applied to analyze brain Positron Emission Tomography (PET) data in two different studies. One dataset used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

stat.ME↗

arXiv2021

Efficient Estimation of Partially Linear Models for Spatial Data over Complex Domain

In this paper, we study the estimation of partially linear models for spatial data distributed over complex domains. We use bivariate splines over triangulations to represent the nonparametric component on an irregular two-dimensional domain. The proposed method is formulated as a constrained minimization problem which does not require constructing finite elements or locally supported basis functions. Thus, it allows an easier implementation of piecewise polynomial representations of various degrees and various smoothness over an arbitrary triangulation. Moreover, the constrained minimization problem is converted into an unconstrained minimization via a QR decomposition of the smoothness constraints, which allows for the development of a fast and efficient penalized least squares algorithm to fit the model. The estimators of the parameters are proved to be asymptotically normal under some regularity conditions. The estimator of the bivariate function is consistent, and its rate of convergence is also established. The proposed method enables us to construct confidence intervals and permits inference for the parameters. The performance of the estimators is evaluated by two simulation examples and by a real data analysis.

math.ST↗

arXiv2021

Multivariate Spline Estimation and Inference for Image-On-Scalar Regression

Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for imaging responses and scalar predictors. We propose using flexible multivariate splines over triangulations to handle the irregular domain of the objects of interest on the images, as well as other characteristics of images. The proposed estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. We also provide a consistent and computationally efficient estimator of the covariance function. Asymptotic pointwise confidence intervals and data-driven simultaneous confidence corridors for the coefficient functions are constructed. Our method can simultaneously estimate and make inferences on the coefficient functions while incorporating spatial heterogeneity and spatial correlation. A highly efficient and scalable estimation algorithm is developed. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed method, which is then applied to the spatially normalized positron emission tomography data of the Alzheimer's Disease Neuroimaging Initiative.

stat.ME↗

arXiv2021

When Homomorphic Encryption Marries Secret Sharing: Secure Large-Scale Sparse Logistic Regression and Applications in Risk Control

Logistic Regression (LR) is the most widely used machine learning model in industry for its efficiency, robustness, and interpretability. Due to the problem of data isolation and the requirement of high model performance, many applications in industry call for building a secure and efficient LR model for multiple parties. Most existing work uses either Homomorphic Encryption (HE) or Secret Sharing (SS) to build secure LR. HE based methods can deal with high-dimensional sparse features, but they incur potential security risks. SS based methods have provable security, but they have efficiency issue under high-dimensional sparse features. In this paper, we first present CAESAR, which combines HE and SS to build secure large-scale sparse logistic regression model and achieves both efficiency and security. We then present the distributed implementation of CAESAR for scalability requirement. We have deployed CAESAR in a risk control task and conducted comprehensive experiments. Our experimental results show that CAESAR improves the state-of-the-art model by around 130 times.

cs.CR↗

arXiv2021

Joint Training of the Superimposed Direct and Reflected Links in Reconfigurable Intelligent Surface Assisted Multiuser Communications

In Reconfigurable intelligent surface (RIS)-assisted systems the acquisition of CSI and the optimization of the reflecting coefficients constitute a pair of salient design issues. In this paper, a novel channel training protocol is proposed, which is capable of achieving a flexible performance vs. signalling and pilot overhead as well as implementation complexity trade-off. More specifically, first of all, we conceive a holistic channel estimation protocol, which integrates the existing channel estimation techniques and passive beamforming design. Secondly, we propose a new channel training framework. In contrast to the conventional channel estimation arrangements, our new framework divides the training phase into several periods, where the superimposed end-to-end channel is estimated instead of separately estimating the direct BS-user channel and cascaded reflected BS-RIS-user channels. As a result, the reflecting coefficients of the RIS are optimized by comparing the objective function values over multiple training periods. Moreover, the theoretical performance of our channel training protocol is analyzed and compared to that under the optimal reflecting coefficients. In addition, the potential benefits of our channel training protocol in reducing the complexity, pilot overhead as well as signalling overhead are also detailed. Thirdly, we derive the theoretical performance of channel estimation protocols and our channel training protocol in the presence of noise for a SISO scenario, which provides useful insights into the impact of the noise on the overall RIS performance. Finally, our numerical simulations characterize the performance of the proposed protocols and verify our theoretical analysis. In particular, the simulation results demonstrate that our channel training protocol is more competitive than the channel estimation protocol at low signal-to-noise ratios.

cs.IT↗

arXiv2021

AGSFCOS: Based on attention mechanism and Scale-Equalizing pyramid network of object detection

Recently, the anchor-free object detection model has shown great potential for accuracy and speed to exceed anchor-based object detection. Therefore, two issues are mainly studied in this article: (1) How to let the backbone network in the anchor-free object detection model learn feature extraction? (2) How to make better use of the feature pyramid network? In order to solve the above problems, Experiments show that our model has a certain improvement in accuracy compared with the current popular detection models on the COCO dataset, the designed attention mechanism module can capture contextual information well, improve detection accuracy, and use sepc network to help balance abstract and detailed information, and reduce the problem of semantic gap in the feature pyramid network. Whether it is anchor-based network model YOLOv3, Faster RCNN, or anchor-free network model Foveabox, FSAF, FCOS. Our optimal model can get 39.5% COCO AP under the background of ResNet50.

cs.CV↗

arXiv2021

Towards a Model for LSH

As data volumes continue to grow, clustering and outlier detection algorithms are becoming increasingly time-consuming. Classical index structures for neighbor search are no longer sustainable due to the "curse of dimensionality". Instead, approximated index structures offer a good opportunity to significantly accelerate the neighbor search for clustering and outlier detection and to have the lowest possible error rate in the results of the algorithms. Locality-sensitive hashing is one of those. We indicate directions to model the properties of LSH.

cs.DB↗

arXiv2021

Privacy-Preserving Federated Learning on Partitioned Attributes

Real-world data is usually segmented by attributes and distributed across different parties. Federated learning empowers collaborative training without exposing local data or models. As we demonstrate through designed attacks, even with a small proportion of corrupted data, an adversary can accurately infer the input attributes. We introduce an adversarial learning based procedure which tunes a local model to release privacy-preserving intermediate representations. To alleviate the accuracy decline, we propose a defense method based on the forward-backward splitting algorithm, which respectively deals with the accuracy loss and privacy loss in the forward and backward gradient descent steps, achieving the two objectives simultaneously. Extensive experiments on a variety of datasets have shown that our defense significantly mitigates privacy leakage with negligible impact on the federated learning task.

cs.LG↗

arXiv2021

On Generalizing Trace Minimization

Ky Fan's trace minimization principle is extended along the line of the Brockett cost function $\mathrm{trace}(DX^H AX)$ in $X$ on the Stiefel manifold, where $D$ of an apt size is positive definite. Specifically, we investigate $\inf_X \mathrm{trace}(DX^H AX)$ subject to $X^H BX=I_k$ or $J_k=\mathrm{diag}(\pm 1)$. We establish conditions under which the infimum is finite and when it is finite, analytic solutions are obtained in terms of the eigenvalues and eigenvectors of the matrix pencil $A-λB$, where $B$ is possibly indefinite and singular, and $D$ is also possibly indefinite.

math.NA↗

arXiv2021

Depth-conditioned Dynamic Message Propagation for Monocular 3D Object Detection

The objective of this paper is to learn context- and depth-aware feature representation to solve the problem of monocular 3D object detection. We make following contributions: (i) rather than appealing to the complicated pseudo-LiDAR based approach, we propose a depth-conditioned dynamic message propagation (DDMP) network to effectively integrate the multi-scale depth information with the image context;(ii) this is achieved by first adaptively sampling context-aware nodes in the image context and then dynamically predicting hybrid depth-dependent filter weights and affinity matrices for propagating information; (iii) by augmenting a center-aware depth encoding (CDE) task, our method successfully alleviates the inaccurate depth prior; (iv) we thoroughly demonstrate the effectiveness of our proposed approach and show state-of-the-art results among the monocular-based approaches on the KITTI benchmark dataset. Particularly, we rank $1^{st}$ in the highly competitive KITTI monocular 3D object detection track on the submission day (November 16th, 2020). Code and models are released at \url{https://github.com/fudan-zvg/DDMP}

cs.CV↗

arXiv2021

An asymptotic preserving scheme for Lévy-Fokker-Planck equation with fractional diffusion limit

In this paper, we develop a numerical method for the Lévy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the fractional Laplacian operator to a power law decay distribution. The other arises from long-time/small mean-free-path scaling, which introduces stiffness to the equation. To resolve the first difficulty, we use a change of variable to convert the unbounded domain into a bounded one and then apply the Chebyshev polynomial based pseudo-spectral method. To treat the multiple scales, we propose an asymptotic preserving scheme based on a novel micro-macro decomposition that uses the structure of the test function in proving the fractional diffusion limit analytically. Finally, the efficiency and accuracy of our scheme are illustrated by a suite of numerical examples.

math.NA↗

arXiv2021

S-AT GCN: Spatial-Attention Graph Convolution Network based Feature Enhancement for 3D Object Detection

3D object detection plays a crucial role in environmental perception for autonomous vehicles, which is the prerequisite of decision and control. This paper analyses partition-based methods' inherent drawbacks. In the partition operation, a single instance such as a pedestrian is sliced into several pieces, which we call it the partition effect. We propose the Spatial-Attention Graph Convolution (S-AT GCN), forming the Feature Enhancement (FE) layers to overcome this drawback. The S-AT GCN utilizes the graph convolution and the spatial attention mechanism to extract local geometrical structure features. This allows the network to have more meaningful features for the foreground. Our experiments on the KITTI 3D object and bird's eye view detection show that S-AT Conv and FE layers are effective, especially for small objects. FE layers boost the pedestrian class performance by 3.62\% and cyclist class by 4.21\% 3D mAP. The time cost of these extra FE layers are limited. PointPillars with FE layers can achieve 48 PFS, satisfying the real-time requirement.

cs.CV↗

arXiv2021

Show, Recall, and Tell: Image Captioning with Recall Mechanism

Generating natural and accurate descriptions in image cap-tioning has always been a challenge. In this paper, we pro-pose a novel recall mechanism to imitate the way human con-duct captioning. There are three parts in our recall mecha-nism : recall unit, semantic guide (SG) and recalled-wordslot (RWS). Recall unit is a text-retrieval module designedto retrieve recalled words for images. SG and RWS are de-signed for the best use of recalled words. SG branch cangenerate a recalled context, which can guide the process ofgenerating caption. RWS branch is responsible for copyingrecalled words to the caption. Inspired by pointing mecha-nism in text summarization, we adopt a soft switch to balancethe generated-word probabilities between SG and RWS. Inthe CIDEr optimization step, we also introduce an individualrecalled-word reward (WR) to boost training. Our proposedmethods (SG+RWS+WR) achieve BLEU-4 / CIDEr / SPICEscores of 36.6 / 116.9 / 21.3 with cross-entropy loss and 38.7 /129.1 / 22.4 with CIDEr optimization on MSCOCO Karpathytest split, which surpass the results of other state-of-the-artmethods.

cs.CV↗

arXiv2021

DM algorithms in health industry

This survey reviews several approaches of data mining (DM) in healthindustry from many research groups world wide. The focus is on modern multi-core processors built into today's commodity computers, which are typically found at university institutes both as small server and workstation computers. So they are deliberately not high-performance computers. Modern multi-core processors consist of several (2 to over 100) computer cores, which work independently of each other according to the principle of "multiple instruction multiple data" (MIMD). They have a common main memory (shared memory). Each of these computer cores has several (2-16) arithmetic-logic units, which can simultaneously carry out the same arithmetic operation on several data in a vector-like manner (single instruction multiple data, SIMD). DM algorithms must use both types of parallelism (SIMD and MIMD), with access to the main memory (centralized component) being the main barrier to increased efficiency. This is important for DM in healthindustry applications like ECG, EEG, CT, SPECT, fMRI, DTI, ultrasound, microscopy, dermascopy, etc.

cs.LG↗

arXiv2021

Primal dual methods for Wasserstein gradient flows

Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science, and biological swarming. Our method proceeds as follows: First, we discretize in time, either via the classical JKO scheme or via a novel Crank-Nicolson type method we introduce. Next, we use the Benamou-Brenier dynamical characterization of the Wasserstein distance to reduce computing the solution of the discrete time equations to solving fully discrete minimization problems, with strictly convex objective functions and linear constraints. Third, we compute the minimizers by applying a recently introduced, provably convergent primal dual splitting scheme for three operators [Yan 2018]. By leveraging the PDEs' underlying variational structure, our method overcomes stability issues present in previous numerical work built on explicit time discretizations, which suffer due to the equations' strong nonlinearities and degeneracies. Our method is also naturally positivity and mass preserving and, in the case of the JKO scheme, energy decreasing. We prove that minimizers of the fully discrete problem converge to minimizers of the spatially continuous, discrete time problem as the spatial discretization is refined. We conclude with simulations of nonlinear PDEs and Wasserstein geodesics in one and two dimensions that illustrate the key properties of our approach, including higher order convergence our novel Crank-Nicolson type method, when compared to the classical JKO method.

math.NA↗

arXiv2021

Spectrum Sharing for 6G Integrated Satellite-Terrestrial Communication Networks Based on NOMA and Cognitive Radio

The explosive growth of bandwidth hungry Internet applications has led to the rapid development of new generation mobile network technologies that are expected to provide broadband access to the Internet in a pervasive manner. For example, 6G networks are capable of providing high-speed network access by exploiting higher frequency spectrum; high-throughout satellite communication services are also adopted to achieve pervasive coverage in remote and isolated areas. In order to enable seamless access, Integrated Satellite-Terrestrial Communication Networks (ISTCN) has emerged as an important research area. ISTCN aims to provide high speed and pervasive network services by integrating broadband terrestrial mobile networks with satellite communication networks. As terrestrial mobile networks began to use higher frequency spectrum (between 3GHz to 40GHz) which overlaps with that of satellite communication (4GHz to 8GHz for C band and 26GHz to 40GHz for Ka band), there are opportunities and challenges. On one hand, satellite terminals can potentially access terrestrial networks in an integrated manner; on the other hand, there will be more congestion and interference in this spectrum, hence more efficient spectrum management techniques are required. In this paper, we propose a new technique to improve spectrum sharing performance by introducing Non-orthogonal Frequency Division Multiplexing (NOMA) and Cognitive Radio (CR) in the spectrum sharing of ISTCN. In essence, NOMA technology improves spectrum efficiency by allowing different users to transmit on the same carrier and distinguishing users by user power levels while CR technology improves spectrum efficiency through dynamic spectrum sharing. Furthermore, some open researches and challenges in ISTCN will be discussed.

eess.SP↗

arXiv2021

Further results on generalized Holmgren's principle to the Lamé operator and applications

In our earlier paper [9], it is proved that a homogeneous rigid, traction or impedance condition on one or two intersecting line segments together with a certain zero point-value condition implies that the solution to the Lamé system must be identically zero, which is referred to as the generalized Holmgren principle (GHP). The GHP enables us to solve a longstanding inverse scattering problem of determining a polygonal elastic obstacle of general impedance type by at most a few far-field measurements. In this paper, we include all the possible physical boundary conditions from linear elasticity into the GHP study with additionally the soft-clamped, simply-supported as well as the associated impedance-type conditions. We derive a comprehensive and complete characterisation of the GHP associated with all of the aforementioned physical conditions. As significant applications, we establish novel unique identifiability results by at most a few scattering measurements not only for the inverse elastic obstacle problem but also for the inverse elastic diffraction grating problem within polygonal geometry in the most general physical scenario. We follow the general strategy from [9] in establishing the results. However, we develop technically new ingredients to tackle the more general and challenging physical and mathematical setups. It is particularly worth noting that in [9], the impedance parameters were assumed to be constant whereas in this work they can be variable functions.

math.AP↗

arXiv2021

Trace Ratio Optimization with an Application to Multi-view Learning

A trace ratio optimization problem over the Stiefel manifold is investigated from the perspectives of both theory and numerical computations. At least three special cases of the problem have arisen from Fisher linear discriminant analysis, canonical correlation analysis, and unbalanced Procrustes problem, respectively. Necessary conditions in the form of nonlinear eigenvalue problem with eigenvector dependency are established and a numerical method based on the self-consistent field (SCF) iteration is designed and proved to be always convergent. As an application to multi-view subspace learning, a new framework and its instantiated concrete models are proposed and demonstrated on real world data sets. Numerical results show that the efficiency of the proposed numerical methods and effectiveness of the new multi-view subspace learning models.

math.OC↗