arXiv subjects

Xiaojun Chen

Publications and source records attributed to Xiaojun Chen.

At least 109 records · Page 6Linked to original sources

arXiv2020

An exact penalty approach for optimization with nonnegative orthogonality constraints

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single nonlinear constraint. Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed. By establishing a local error bound of the feasible set, we design a class of (smooth) exact penalty models via keeping the nonnegative and multiple spherical constraints. The penalty models are exact if the penalty parameter is sufficiently large other than going to infinity. A practical penalty algorithm with postprocessing is then developed. It uses a second-order method to approximately solve a series of subproblems with nonnegative and multiple spherical constraints. We study the asymptotic convergence of the penalty algorithm and establish that any limit point is a weakly stationary point of the original problem and becomes a stationary point under some additional mild conditions. Extensive numerical results on the projection problem, orthogonal nonnegative matrix factorization problems and the K-indicators model show the effectiveness of our proposed approach.

math.OC↗

arXiv2020

A Distributed Training Algorithm of Generative Adversarial Networks with Quantized Gradients

Training generative adversarial networks (GAN) in a distributed fashion is a promising technology since it is contributed to training GAN on a massive of data efficiently in real-world applications. However, GAN is known to be difficult to train by SGD-type methods (may fail to converge) and the distributed SGD-type methods may also suffer from massive amount of communication cost. In this paper, we propose a {distributed GANs training algorithm with quantized gradient, dubbed DQGAN,} which is the first distributed training method with quantized gradient for GANs. The new method trains GANs based on a specific single machine algorithm called Optimistic Mirror Descent (OMD) algorithm, and is applicable to any gradient compression method that satisfies a general $δ$-approximate compressor. The error-feedback operation we designed is used to compensate for the bias caused by the compression, and moreover, ensure the convergence of the new method. Theoretically, we establish the non-asymptotic convergence of {DQGAN} algorithm to first-order stationary point, which shows that the proposed algorithm can achieve a linear speedup in the parameter server model. Empirically, our experiments show that our {DQGAN} algorithm can reduce the communication cost and save the training time with slight performance degradation on both synthetic and real datasets.

cs.LG↗

arXiv2020

A weakly supervised registration-based framework for prostate segmentation via the combination of statistical shape model and CNN

Precise determination of target is an essential procedure in prostate interventions, such as the prostate biopsy, lesion detection and targeted therapy. However, the prostate delineation may be tough in some cases due to tissue ambiguity or lack of partial anatomical boundary. To address this problem, we proposed a weakly supervised registration-based framework for the precise prostate segmentation, by combining convolutional neural network (CNN) with statistical shape model (SSM). To obtain the prostate region, an inception-based neural network (SSM-Net) was firstly exploited to predict the model transform, shape control parameters and a fine-tuning vector, for the generation of prostate boundary. According to the inferred boundary, a normalized distance map was calculated. Then, a residual U-net (ResU-Net) was employed to predict a probability label map from the input images. Finally, the average of the distance map and the probability map was regarded as the prostate segmentation. After that, two public dataset PROMISE12 and NCI- ISBI 2013 were utilized for the model computation and for the network training and testing. The validation results demonstrate that the segmentation framework using a SSM with 9500 nodes achieved the best performance, with a dice of 0.904 and an average surface distance of 1.88 mm. In addition, we verified the impact of model elasticity augmentation and fine-tuning item on the network segmentation capability. As a result, both factors have improved the delineation accuracy, with dice increased by 10% and 7% respectively. In conclusion, via the combination of two weakly supervised neural networks, our segmentation method might be an effective and robust approach for prostate segmentation.

eess.IV↗

arXiv2020

Equilibrium Oil Market Share under the COVID-19 Pandemic

Equilibrium models for energy markets under uncertain demand and supply have attracted considerable attentions. This paper focuses on modelling crude oil market share under the COVID-19 pandemic using two-stage stochastic equilibrium. We describe the uncertainties in the demand and supply by random variables and provide two types of production decisions (here-and-now and wait-and-see). The here-and-now decision in the first stage does not depend on the outcome of random events to be revealed in the future and the wait-and-see decision in the second stage is allowed to depend on the random events in the future and adjust the feasibility of the here-and-now decision in rare unexpected scenarios such as those observed during the COVID-19 pandemic. We develop a fast algorithm to find a solution of the two-stage stochastic equilibrium. We show the robustness of the two-stage stochastic equilibrium model for forecasting the oil market share using the real market data from January 2019 to May 2020.

math.OC↗

arXiv2020

Incorporating Uncertain Segmentation Information into Chinese NER for Social Media Text

Chinese word segmentation is necessary to provide word-level information for Chinese named entity recognition (NER) systems. However, segmentation error propagation is a challenge for Chinese NER while processing colloquial data like social media text. In this paper, we propose a model (UIcwsNN) that specializes in identifying entities from Chinese social media text, especially by leveraging ambiguous information of word segmentation. Such uncertain information contains all the potential segmentation states of a sentence that provides a channel for the model to infer deep word-level characteristics. We propose a trilogy (i.e., candidate position embedding -> position selective attention -> adaptive word convolution) to encode uncertain word segmentation information and acquire appropriate word-level representation. Experiments results on the social media corpus show that our model alleviates the segmentation error cascading trouble effectively, and achieves a significant performance improvement of more than 2% over previous state-of-the-art methods.

cs.CL↗

arXiv2020

Calabi-Yau algebras and the shifted noncommutative symplectic structure

In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg, on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its DG representation schemes, in the sense of Berest-Khachatryan-Ramadoss, have a shifted symplectic structure in the sense of Pantev-Toën-Vaquié-Vezzosi.

math.RA↗

arXiv2019

Improving Abstractive Text Summarization with History Aggregation

Recent neural sequence to sequence models have provided feasible solutions for abstractive summarization. However, such models are still hard to tackle long text dependency in the summarization task. A high-quality summarization system usually depends on strong encoder which can refine important information from long input texts so that the decoder can generate salient summaries from the encoder's memory. In this paper, we propose an aggregation mechanism based on the Transformer model to address the challenge of long text representation. Our model can review history information to make encoder hold more memory capacity. Empirically, we apply our aggregation mechanism to the Transformer model and experiment on CNN/DailyMail dataset to achieve higher quality summaries compared to several strong baseline models on the ROUGE metrics.

cs.CL↗

arXiv2019

Gravity algebra structure on the negative cyclic homology of Calabi-Yau algebras

In this paper, we study the gravity algebra structure on the negative cyclic homology or the cyclic cohomology of several classes of algebras. These algebras include: Calabi-Yau algebras, symmetric Frobenius algebras, unimodular Poisson algebras, and unimodular Frobenius Poisson algebras. The relationships among these gravity algebras are also discussed under some additional conditions.

math.RA↗

arXiv2019

Regularized two-stage stochastic variational inequalities for Cournot-Nash equilibrium under uncertainty

A convex two-stage non-cooperative multi-agent game under uncertainty is formulated as a two-stage stochastic variational inequality (SVI). Under standard assumptions, we provide sufficient conditions for the existence of solutions of the two-stage SVI and propose a regularized sample average approximation method for solving it. We prove the convergence of the method as the regularization parameter tends to zero and the sample size tends to infinity. Moreover, our approach is applied to a two-stage stochastic production and supply planning problem with homogeneous commodity in an oligopolistic market. Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVI in describing the market share of oil producing agents.

math.OC↗

arXiv2019

Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras

We study the noncommutative Poincaré duality between the Poisson homology and cohomology of unimodular Poisson algebras, and show that Kontsevich's deformation quantization as well as Koszul duality preserve the corresponding Poincaré duality. As a corollary, the Batalin-Vilkovisky algebra structures that naturally arise in these cases are all isomorphic.

math-ph↗

arXiv2019

Triple Trustworthiness Measurement for Knowledge Graph

The Knowledge graph (KG) uses the triples to describe the facts in the real world. It has been widely used in intelligent analysis and applications. However, possible noises and conflicts are inevitably introduced in the process of constructing. And the KG based tasks or applications assume that the knowledge in the KG is completely correct and inevitably bring about potential deviations. In this paper, we establish a knowledge graph triple trustworthiness measurement model that quantify their semantic correctness and the true degree of the facts expressed. The model is a crisscrossing neural network structure. It synthesizes the internal semantic information in the triples and the global inference information of the KG to achieve the trustworthiness measurement and fusion in the three levels of entity level, relationship level, and KG global level. We analyzed the validity of the model output confidence values, and conducted experiments in the real-world dataset FB15K (from Freebase) for the knowledge graph error detection task. The experimental results showed that compared with other models, our model achieved significant and consistent improvements.

cs.AI↗

arXiv2019

Exploring Communities in Large Profiled Graphs

Given a graph $G$ and a vertex $q\in G$, the community search (CS) problem aims to efficiently find a subgraph of $G$ whose vertices are closely related to $q$. Communities are prevalent in social and biological networks, and can be used in product advertisement and social event recommendation. In this paper, we study profiled community search (PCS), where CS is performed on a profiled graph. This is a graph in which each vertex has labels arranged in a hierarchical manner. Extensive experiments show that PCS can identify communities with themes that are common to their vertices, and is more effective than existing CS approaches. As a naive solution for PCS is highly expensive, we have also developed a tree index, which facilitate efficient and online solutions for PCS.

cs.DB↗

arXiv2018

On transitive action on quiver varieties

Associated with each finite subgroup $Γ$ of $\rm{SL}_2(\mathbb{C})$ there is a family of noncommutative algebras $O_τ(Γ)$ quantizing $\mathbb{C}^2/\!\!/Γ$. Let $G_Γ$ be the group of $Γ$-equivariant automorphisms of $O_τ$. One of the authors earlier defined and studied a natural action of $G_Γ$ on certain quiver varieties associated with $Γ$. He established a $G_Γ$-equivariant bijective correspondence between quiver varieties and the space of isomorphism classes of $O_τ$-ideals. The main theorem in this paper states that when $Γ$ is a cyclic group, the action of $G_Γ$ on each quiver variety is transitive. This generalizes an earlier result due to Berest and Wilson who showed the transitivity of the automorphism group of the first Weyl algebra on the Calogero-Moser spaces. Our result has two important implications. First, it confirms the Bockland-Le Bruyn conjecture for cyclic quiver varieties. Second, it will be used to give a complete classification of algebras Morita equivalent to $O_τ(Γ)$.

math.QA↗

arXiv2018

Leveraging Long and Short-term Information in Content-aware Movie Recommendation

Movie recommendation systems provide users with ranked lists of movies based on individual's preferences and constraints. Two types of models are commonly used to generate ranking results: long-term models and session-based models. While long-term models represent the interactions between users and movies that are supposed to change slowly across time, session-based models encode the information of users' interests and changing dynamics of movies' attributes in short terms. In this paper, we propose an LSIC model, leveraging Long and Short-term Information in Content-aware movie recommendation using adversarial training. In the adversarial process, we train a generator as an agent of reinforcement learning which recommends the next movie to a user sequentially. We also train a discriminator which attempts to distinguish the generated list of movies from the real records. The poster information of movies is integrated to further improve the performance of movie recommendation, which is specifically essential when few ratings are available. The experiments demonstrate that the proposed model has robust superiority over competitors and sets the state-of-the-art. We will release the source code of this work after publication.

cs.IR↗

arXiv2018

A Non-monotone Alternating Updating Method for A Class of Matrix Factorization Problems

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and non-Lipschitz problem, we develop a non-monotone alternating updating method based on a potential function. Our method essentially updates two blocks of variables in turn by inexactly minimizing this potential function, and updates another auxiliary block of variables using an explicit formula. The special structure of our potential function allows us to take advantage of efficient computational strategies for non-negative matrix factorization to perform the alternating minimization over the two blocks of variables. A suitable line search criterion is also incorporated to improve the numerical performance. Under some mild conditions, we show that the line search criterion is well defined, and establish that the sequence generated is bounded and any cluster point of the sequence is a stationary point. Finally, we conduct some numerical experiments using real datasets to compare our method with some existing efficient methods for non-negative matrix factorization and matrix completion. The numerical results show that our method can outperform these methods for these specific applications.

math.OC↗

arXiv2018

Clinical evaluation of semi-automatic opensource algorithmic software segmentation of the mandibular bone: Practical feasibility and assessment of a new course of action

Computer assisted technologies based on algorithmic software segmentation are an increasing topic of interest in complex surgical cases. However - due to functional instability, time consuming software processes, personnel resources or licensed-based financial costs many segmentation processes are often outsourced from clinical centers to third parties and the industry. Therefore, the aim of this trial was to assess the practical feasibility of an easy available, functional stable and licensed-free segmentation approach to be used in the clinical practice. In this retrospective, randomized, controlled trail the accuracy and accordance of the open-source based segmentation algorithm GrowCut (GC) was assessed through the comparison to the manually generated ground truth of the same anatomy using 10 CT lower jaw data-sets from the clinical routine. Assessment parameters were the segmentation time, the volume, the voxel number, the Dice Score (DSC) and the Hausdorff distance (HD). Overall segmentation times were about one minute. Mean DSC values of over 85% and HD below 33.5 voxel could be achieved. Statistical differences between the assessment parameters were not significant (p<0.05) and correlation coefficients were close to the value one (r > 0.94). Complete functional stable and time saving segmentations with high accuracy and high positive correlation could be performed by the presented interactive open-source based approach. In the cranio-maxillofacial complex the used method could represent an algorithmic alternative for image-based segmentation in the clinical practice for e.g. surgical treatment planning or visualization of postoperative results and offers several advantages. Systematic comparisons to other segmentation approaches or with a greater data amount are areas of future works.

cs.CV↗

arXiv2018

In-depth Assessment of an Interactive Graph-based Approach for the Segmentation for Pancreatic Metastasis in Ultrasound Acquisitions of the Liver with two Specialists in Internal Medicine

The manual outlining of hepatic metastasis in (US) ultrasound acquisitions from patients suffering from pancreatic cancer is common practice. However, such pure manual measurements are often very time consuming, and the results repeatedly differ between the raters. In this contribution, we study the in-depth assessment of an interactive graph-based approach for the segmentation for pancreatic metastasis in US images of the liver with two specialists in Internal Medicine. Thereby, evaluating the approach with over one hundred different acquisitions of metastases. The two physicians or the algorithm had never assessed the acquisitions before the evaluation. In summary, the physicians first performed a pure manual outlining followed by an algorithmic segmentation over one month later. As a result, the experts satisfied in up to ninety percent of algorithmic segmentation results. Furthermore, the algorithmic segmentation was much faster than manual outlining and achieved a median Dice Similarity Coefficient (DSC) of over eighty percent. Ultimately, the algorithm enables a fast and accurate segmentation of liver metastasis in clinical US images, which can support the manual outlining in daily practice.

cs.CV↗

arXiv2018

Convergence Analysis of Sample Average Approximation of Two-stage Stochastic Generalized Equations

A solution of two-stage stochastic generalized equations is a pair: a first stage solution which is independent of realization of the random data and a second stage solution which is a function of random variables.This paper studies convergence of the sample average approximation of two-stage stochastic nonlinear generalized equations. In particular an exponential rate of the convergence is shown by using the perturbed partial linearization of functions. Moreover, sufficient conditions for the existence, uniqueness, continuity and regularity of solutions of two-stage stochastic generalized equations are presented under an assumption of monotonicity of the involved functions. These theoretical results are given without assuming relatively complete recourse, and are illustrated by two-stage stochastic non-cooperative games of two players.

math.OC↗