arXiv subjects

Jie Lu

Publications and source records attributed to Jie Lu.

At least 181 records · Page 10Linked to original sources

arXiv2018

Deep Surface Light Fields

A surface light field represents the radiance of rays originating from any points on the surface in any directions. Traditional approaches require ultra-dense sampling to ensure the rendering quality. In this paper, we present a novel neural network based technique called deep surface light field or DSLF to use only moderate sampling for high fidelity rendering. DSLF automatically fills in the missing data by leveraging different sampling patterns across the vertices and at the same time eliminates redundancies due to the network's prediction capability. For real data, we address the image registration problem as well as conduct texture-aware remeshing for aligning texture edges with vertices to avoid blurring. Comprehensive experiments show that DSLF can further achieve high data compression ratio while facilitating real-time rendering on the GPU.

cs.CG↗

arXiv2018

Fenchel Dual Gradient Methods for Distributed Convex Optimization over Time-varying Networks

In the large collection of existing distributed algorithms for convex multi-agent optimization, only a handful of them provide convergence rate guarantees on agent networks with time-varying topologies, which, however, restrict the problem to be unconstrained. Motivated by this, we develop a family of distributed Fenchel dual gradient methods for solving constrained, strongly convex but not necessarily smooth multi-agent optimization problems over time-varying undirected networks. The proposed algorithms are constructed based on the application of weighted gradient methods to the Fenchel dual of the multi-agent optimization problem, and can be implemented in a fully decentralized fashion. We show that the proposed algorithms drive all the agents to both primal and dual optimality asymptotically under a minimal connectivity condition and at sublinear rates under a standard connectivity condition. Finally, the competent convergence performance of the distributed Fenchel dual gradient methods is demonstrated via simulations.

math.OC↗

arXiv2017

Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55

We introduce a large-scale 3D shape understanding benchmark using data and annotation from ShapeNet 3D object database. The benchmark consists of two tasks: part-level segmentation of 3D shapes and 3D reconstruction from single view images. Ten teams have participated in the challenge and the best performing teams have outperformed state-of-the-art approaches on both tasks. A few novel deep learning architectures have been proposed on various 3D representations on both tasks. We report the techniques used by each team and the corresponding performances. In addition, we summarize the major discoveries from the reported results and possible trends for the future work in the field.

cs.CV↗

arXiv2017

Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons

We consider Anderson transitions in two-dimensional spinful electron gases subject to random scalar potentials with time-reversal-symmetric spin-mixing tunneling (SMT) and spin-preserving tunneling (SPT) at potential saddle points (PSPs). A symplectic quantum network model, named as SMT-QNM, is constructed in which SMT and SPT have the same status and contribute independent tunneling channels rather than sharing a total-probability-fixed one. Two-dimensional continuous Dirac Hamiltonian is then extracted out from this discrete network model as the generator of certain unitary transformation. With the help of high-accuracy numerics based on transfer matrix technique, finite-size analysis on two-terminal conductance and normalized localization length provides a phase diagram drawn in the SMT-SPT plane. As a manifestation of symplectic ensembles, a normal-metal (NM) phase emerges between the quantum spin Hall (QSH) and normal-insulator (NI) phases when SMT appears. We systematically analyze the quantum phases on the boundary and in the interior of the phase space. Particularly, the phase diagram is closely related to that of disordered three-dimensional weak topological insulators by appropriate parameter mapping. At last, if time-reversal symmetry in electron trajectories between PSPs is destroyed, the system falls into unitary class with no more NM phase. A direct SMT-driven transition from QSH to NI phases exists and can be explained by spin-flip backscattering between the degenerate doublets at the same sample edge.

cond-mat.mes-hall↗

arXiv2017

Cooperative Hierarchical Dirichlet Processes: Superposition vs. Maximization

The cooperative hierarchical structure is a common and significant data structure observed in, or adopted by, many research areas, such as: text mining (author-paper-word) and multi-label classification (label-instance-feature). Renowned Bayesian approaches for cooperative hierarchical structure modeling are mostly based on topic models. However, these approaches suffer from a serious issue in that the number of hidden topics/factors needs to be fixed in advance and an inappropriate number may lead to overfitting or underfitting. One elegant way to resolve this issue is Bayesian nonparametric learning, but existing work in this area still cannot be applied to cooperative hierarchical structure modeling. In this paper, we propose a cooperative hierarchical Dirichlet process (CHDP) to fill this gap. Each node in a cooperative hierarchical structure is assigned a Dirichlet process to model its weights on the infinite hidden factors/topics. Together with measure inheritance from hierarchical Dirichlet process, two kinds of measure cooperation, i.e., superposition and maximization, are defined to capture the many-to-many relationships in the cooperative hierarchical structure. Furthermore, two constructive representations for CHDP, i.e., stick-breaking and international restaurant process, are designed to facilitate the model inference. Experiments on synthetic and real-world data with cooperative hierarchical structures demonstrate the properties and the ability of CHDP for cooperative hierarchical structure modeling and its potential for practical application scenarios.

cs.LG↗

arXiv2017

Relaxed Connected Dominating Set Problem with Application to Secure Power Network Design

This paper investigates a combinatorial optimization problem motived from a secure power network design application in [Dán and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a relaxed version of the connected dominating set problem, and hence the considered problem is referred to as relaxed connected dominating set (RCDS) problem. The RCDS problem is shown to be NP-hard, even for planar graphs. A mixed integer linear programming formulation is presented. In addition, for planar graphs a fixed parameter polynomial time solution methodology based on sphere-cut decomposition and dynamic programming is presented. The computation cost of the sphere-cut decomposition based approach grows linearly with problem instance size, provided that the branchwidth of the underlying graph is fixed and small. A case study with IEEE benchmark power networks verifies that small branchwidth are not uncommon in practice. The case study also indicates that the proposed methods show promise in computation efficiency.

math.OC↗

arXiv2017

Scalable Inference for Nested Chinese Restaurant Process Topic Models

Nested Chinese Restaurant Process (nCRP) topic models are powerful nonparametric Bayesian methods to extract a topic hierarchy from a given text corpus, where the hierarchical structure is automatically determined by the data. Hierarchical Latent Dirichlet Allocation (hLDA) is a popular instance of nCRP topic models. However, hLDA has only been evaluated at small scale, because the existing collapsed Gibbs sampling and instantiated weight variational inference algorithms either are not scalable or sacrifice inference quality with mean-field assumptions. Moreover, an efficient distributed implementation of the data structures, such as dynamically growing count matrices and trees, is challenging. In this paper, we propose a novel partially collapsed Gibbs sampling (PCGS) algorithm, which combines the advantages of collapsed and instantiated weight algorithms to achieve good scalability as well as high model quality. An initialization strategy is presented to further improve the model quality. Finally, we propose an efficient distributed implementation of PCGS through vectorization, pre-processing, and a careful design of the concurrent data structures and communication strategy. Empirical studies show that our algorithm is 111 times more efficient than the previous open-source implementation for hLDA, with comparable or even better model quality. Our distributed implementation can extract 1,722 topics from a 131-million-document corpus with 28 billion tokens, which is 4-5 orders of magnitude larger than the previous largest corpus, with 50 machines in 7 hours.

stat.ML↗

arXiv2016

A Distributed Algorithm for Solving Positive Definite Linear Equations over Networks with Membership Dynamics

This paper considers the problem of solving a symmetric positive definite system of linear equations over a network of agents with arbitrary asynchronous interactions and membership dynamics. The latter implies that each agent is allowed to join and leave the network at any time, for infinitely many times, and lose all its memory upon leaving. We develop Subset Equalizing (SE), a distributed asynchronous algorithm for solving such a problem. To design and analyze SE, we introduce a novel time-varying Lyapunov-like function, defined on a state space with changing dimension, and a generalized concept of network connectivity, capable of handling such interactions and membership dynamics. Based on them, we establish the boundedness, asymptotic convergence, and exponential convergence of SE, along with a bound on its convergence rate. Finally, through extensive simulation, we show that SE is effective in a volatile agent network and that a special case of SE, termed Groupwise Equalizing, is significantly more bandwidth/energy efficient than two existing algorithms in multi-hop wireless networks.

eess.SY↗

arXiv2016

General planar transverse domain walls realized by optimized transverse magnetic field pulses in magnetic biaxial nanowires

We report the realization of a planar transverse domain wall (TDW) with arbitrary tilting angle in a magnetic biaxial nanowire under a transverse magnetic field (TMF) pulse with fixed strength and optimized orientation profile. We smooth any twisting in azimuthal angle plane of a TDW and thus completely decouple the polar and azimuthal degrees of freedom. The analytical differential equation that describes the polar angle distribution is then derived and the resulting solution is not a Walker-ansatz form. With this optimized TMF pulse comoving, the field-driven dynamics of the planar TDW is investigated. It turns out the comoving TMF pulse increases the wall velocity under the same axial driving field. These results will help to design a series of modern logic and memory nanodevices based on general planar TDWs.

cond-mat.mes-hall↗

arXiv2016

Statics and field-driven dynamics of transverse domain walls in biaxial nanowires under uniform transverse magnetic fields

In this work, we report analytical results on transverse domain wall (TDW) statics and field-driven dynamics in quasi one-dimensional biaxial nanowires under arbitrary uniform transverse magnetic fields (TMFs) based on the Landau-Lifshitz-Gilbert equation. Without axial driving fields, the static TDW should be symmetric about its center meanwhile twisted in its azimuthal angle distribution. By decoupling of polar and azimuthal degrees of freedom, an approximate solution is provided which reproduces these features to a great extent. When an axial driving field is applied, the dynamical behavior of a TDW is viewed as the response of its static profile to external excitations. By means of the asymptotic expansion method, the TDW velocity in traveling-wave mode is obtained, which provides the extent and boundary of the "velocity-enhancement" effect of TMFs to TDWs in biaxial nanowires. Finally numerical simulations are performed and strongly support our analytics.

cond-mat.mes-hall↗

arXiv2015

Dependent Indian Buffet Process-based Sparse Nonparametric Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix of papers by keywords). However, traditional NMF methods typically assume the number of latent factors (i.e., dimensionality of the loading matrices) to be fixed. This assumption makes them inflexible for many applications. In this paper, we propose a nonparametric NMF framework to mitigate this issue by using dependent Indian Buffet Processes (dIBP). In a nutshell, we apply a correlation function for the generation of two stick weights associated with each pair of columns of loading matrices, while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two loading matrices will be column-wise (indirectly) correlated. Under this same framework, two classes of correlation function are proposed (1) using Bivariate beta distribution and (2) using Copula function. Both methods allow us to adopt our work for various applications by flexibly choosing an appropriate parameter settings. Compared with the other state-of-the art approaches in this area, such as using Gaussian Process (GP)-based dIBP, our work is seen to be much more flexible in terms of allowing the two corresponding binary matrix columns to have greater variations in their non-zero entries. Our experiments on the real-world and synthetic datasets show that three proposed models perform well on the document clustering task comparing standard NMF without predefining the dimension for the factor matrices, and the Bivariate beta distribution-based and Copula-based models have better flexibility than the GP-based model.

stat.ML↗

arXiv2015

Flavour-changing top decays in the aligned two-Higgs-doublet model

We perform a complete one-loop computation of the two-body flavour-changing top decays $t \rightarrow c h$ and $t \rightarrow c V$ ($V= γ, Z$), within the aligned two-Higgs-doublet model. We evaluate the impact of the model parameters on the associated branching ratios, taking into account constraints from flavour data and measurements of the Higgs properties. Assuming that the $125$~GeV Higgs corresponds to the lightest CP-even scalar of the CP-conserving aligned two-Higgs-doublet model, we find that the rates for such flavour-changing top decays lie below the expected sensitivity of the future high-luminosity phase of the LHC. Measurements of the Higgs signal strength in the di-photon channel are found to play an important role in limiting the size of the $t \rightarrow c h$ decay rate when the charged scalar of the model is light.

hep-ph↗

arXiv2015

Nonnegative Multi-level Network Factorization for Latent Factor Analysis

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although networks between nodes with the same nature exist, standard NMF overlooks them, e.g., the social network between users. This problem leads to comparatively low recommendation accuracy because these networks are also reflections of the nature of the nodes, such as the preferences of users in a social network. Also, social networks, as complex networks, have many different structures. Each structure is a composition of links between nodes and reflects the nature of nodes, so retaining the different network structures will lead to differences in recommendation performance. To investigate the impact of these network structures on the factorization, this paper proposes four multi-level network factorization algorithms based on the standard NMF, which integrates the vertical network (e.g., rating matrix) with the structures of horizontal network (e.g., user social network). These algorithms are carefully designed with corresponding convergence proofs to retain four desired network structures. Experiments on synthetic data show that the proposed algorithms are able to preserve the desired network structures as designed. Experiments on real-world data show that considering the horizontal networks improves the accuracy of document clustering and recommendation with standard NMF, and various structures show their differences in performance on these two tasks. These results can be directly used in document clustering and recommendation systems.

cs.SI↗

arXiv2015

Infinite Author Topic Model based on Mixed Gamma-Negative Binomial Process

Incorporating the side information of text corpus, i.e., authors, time stamps, and emotional tags, into the traditional text mining models has gained significant interests in the area of information retrieval, statistical natural language processing, and machine learning. One branch of these works is the so-called Author Topic Model (ATM), which incorporates the authors's interests as side information into the classical topic model. However, the existing ATM needs to predefine the number of topics, which is difficult and inappropriate in many real-world settings. In this paper, we propose an Infinite Author Topic (IAT) model to resolve this issue. Instead of assigning a discrete probability on fixed number of topics, we use a stochastic process to determine the number of topics from the data itself. To be specific, we extend a gamma-negative binomial process to three levels in order to capture the author-document-keyword hierarchical structure. Furthermore, each document is assigned a mixed gamma process that accounts for the multi-author's contribution towards this document. An efficient Gibbs sampling inference algorithm with each conditional distribution being closed-form is developed for the IAT model. Experiments on several real-world datasets show the capabilities of our IAT model to learn the hidden topics, authors' interests on these topics and the number of topics simultaneously.

stat.ML↗

arXiv2015

Nonparametric Relational Topic Models through Dependent Gamma Processes

Traditional Relational Topic Models provide a way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, link prediction, benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known in advance, and this is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model in this paper. Instead of using fixed-dimensional probability distributions in its generative model, we use stochastic processes. Specifically, a gamma process is assigned to each document, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different gamma process from the global gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics.

stat.ML↗

arXiv2015

Convergence analysis of approximate primal solutions in dual first-order methods

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have only been established under global Lipschitz continuity of the dual gradient. This is a rather restrictive assumption that does not hold for several important classes of problems. In this paper, we demonstrate that primal convergence rate guarantees can also be obtained when the dual gradient is only locally Lipschitz. The class of problems that we analyze admits general convex constraints including nonlinear inequality, linear equality, and set constraints. As an approximate primal solution, we take the minimizer of the Lagrangian, computed when evaluating the dual gradient. We derive error bounds for this approximate primal solution in terms of the errors of the dual variables, and establish convergence rates of the dual variables when the dual problem is solved using a projected gradient or fast gradient method. By combining these results, we show that the suboptimality and infeasibility of the approximate primal solution at iteration $k$ are no worse than $O(1/\sqrt{k})$ when the dual problem is solved using a projected gradient method, and $O(1/k)$ when a fast dual gradient method is used.

math.OC↗

arXiv2014

$B_{s,d}^0 \to \ell^+\ell^-$ Decays in Two-Higgs Doublet Models

We study the rare leptonic decays $B_{s,d}^0 \to \ell^+\ell^-$ within the general framework of the aligned two-Higgs doublet model. A complete one-loop calculation of the relevant short-distance Wilson coefficients is presented, with a detailed technical summary of the results. The phenomenological constraints imposed by present data on the model parameters are also investigated.

hep-ph↗

arXiv2014

Effective Theories for QCD-like at TeV Scale

We study the Effective Field Theory of three QCD-like theories, which can be classified by having quarks in a complex, real or pseudo-real representations of the gauge group. The Lagrangians are written in a very similar way so that the calculations can be done using techniques from Chiral Perturbation Theory (ChPT). We calculated the vacuum-expectation-value, the mass and the decay constant of pseudo-Goldstone Bosons up to next-to-next-to leading order (NNLO) \cite{Bijnens:2009qm}. The various channels of general $n$ flavour meson-meson scattering of the three theories are systematically studied and calculated up to NNLO \cite{Bijnens:2011fm}. We also calculated the vector, axial-vector, scalar, pseudo-scalar two-point functions and pseudo-scalar decay constant up NNLO order \cite{Bijnens:2011xt}. The analytic expressions of the S parameter for the three different QCD-like theories are obtained at TeV scale. Our results are useful for chiral extrapolation in lattice calculation on theory of strong dynamical and finite baryon density.

hep-ph↗