谱归一化Wasserstein distance迁移网络

现有的Wasserstein distance在迁移学习中已经取得了巨大的成功,然而,以往方法对Lipschitz约束实施方式不好。为了克服这一问题,提出一种能够学习领域自适应能力的新方法,即谱归一化Wasserstein distance迁移网络(spectral normalization Wasserstein distance transfer network,SNWDTN)。该方法首先求出权值矩阵的谱范数,然后利用谱范数再对权值矩阵进行谱归一化处理,以设计出能够满足Lipschitz约束条件的谱归一化层,从而为Wasserstein distance的使用提供更好的约束条件满足。通过公共数据集的实验结果表明,SNWDTN取得了比以往方法更好的效果。

Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

A NEW PROCEDURE FOR TESTING NORMALITY BASED ON THE L_2 WASSERSTEIN DISTANCE

This paper proposes a new goodness-of-fit test for normality based on the L~ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval （0, 1） under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.

Data-driven Stochastic Programming with Distributionally Robust Constraints Under Wasserstein Distance:Asymptotic Properties

Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.

Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

We present a multi-phase image segmentation method based on the histogram of the Gabor feature space,which consists of a set of Gabor-filter responses with various orientations,scales and frequencies.Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function,which is a metric to measure the distance of two histograms.The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2.We test our model on both simple synthetic texture images and complex natural images with two or more phases.Experimental results are shown and compared to other recent results.

基于双扩张层和旋转框定位的群猪目标检测算法研究

目前猪群图像检测均为基于水平框的目标检测算法,对于图像中猪体粘连和相互遮挡情况检测率较低,针对图像中的猪只长宽比例较大和可能发生任意角度旋转的特点,提出了一种基于双扩张层和旋转框定位的群猪目标检测算法(Dual dilated layer and rotary box location network,DR Net)。采集3个猪场的群猪图像,利用数据增强保留9600幅图像制作数据集;基于膨胀卷积搭建提取图像全局信息的双扩张层,借鉴Res2Net模块改进CSP层融合多尺度特征,猪只目标以旋转框定位并采用五参数表示法在模型训练中利用Gaussian Wasserstein distance计算旋转框的回归损失。试验结果表明,DR Net对猪只目标识别的精确率、召回率、平均精确率、MAE、RMSE分别为98.57%、97.27%、96.94%、0.21、0.54,其检测效果优于YOLO v5,提高了遮挡与粘连场景下的识别精度和计数精度。利用可视化特征图分析算法在遮挡和粘连场景下能够利用猪只头颈部、背部或尾部特征准确定位目标。该研究有助于智能化猪场建设,可为后续猪只行为识别研究提供参考。

基于模型聚类的说话人识别研究

随着说话人识别技术的广泛应用,说话人规模不断增长,若采用传统的说话人辨别方式逐一比较,则计算量较大,难以实时响应,使说话人识别系统的性能与实用性大大降低。传统的K-L散度距离由于非对称性,并不是一种很好的聚类距离度量,聚类效果不佳。论文提出了一种基于Wasserstein distance聚类方法,相比于传统说话人识别方法,该方法的识别准确率提升了近4.7%,并且识别耗时仅为传统识别方法的25.5%,大大提升了说话人识别系统的性能与实用性。

Mesh‑free semi‑quantitative variance underestimation elimination method in Monte Caro algorithm

The inter-cycle correlation of fission source distributions(FSDs)in the Monte Carlo power iteration process results in variance underestimation of tallied physical quantities,especially in large local tallies.This study provides a mesh-free semiquantitative variance underestimation elimination method to obtain a credible confidence interval for the tallied results.This method comprises two procedures:Estimation and Elimination.The FSD inter-cycle correlation length is estimated in the Estimation procedure using the Sliced Wasserstein distance algorithm.The batch method was then used in the elimination procedure.The FSD inter-cycle correlation length was proved to be the optimum batch length to eliminate the variance underestimation problem.We exemplified this method using the OECD sphere array model and 3D PWR BEAVRS model.The results showed that the average variance underestimation ratios of local tallies declined from 37 to 87%to within±5%in these models.

Low-Dose CT Image Denoising Based on Improved WGAN-gp

In order to improve the quality of low-dose computational tomography (CT)images, the paper proposes an improved image denoising approach based on WGAN-gpwith Wasserstein distance. For improving the training and the convergence efficiency, thegiven method introduces the gradient penalty term to WGAN network. The novelperceptual loss is introduced to make the texture information of the low-dose imagessensitive to the diagnostician eye. The experimental results show that compared with thestate-of-art methods, the time complexity is reduced, and the visual quality of low-doseCT images is significantly improved.

A Study on Computer Consciousness on Intuitive Geometry Based on Mathematics Experiments and Statistical Analysis

In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.

Image Denoising with GAN Based Model

Image denoising is often used as a preprocessing step in computer vision tasks,which can help improve the accuracy of image processing models.Due to the imperfection of imaging systems,transmission media and recording equipment,digital images are often contaminated with various noises during their formation,which troubles the visual effects and even hinders people’s normal recognition.The pollution of noise directly affects the processing of image edge detection,feature extraction,pattern recognition,etc.,making it difficult for people to break through the bottleneck by modifying the model.Many traditional filtering methods have shown poor performance since they do not have optimal expression and adaptation for specific images.Meanwhile,deep learning technology opens up new possibilities for image denoising.In this paper,we propose a novel neural network which is based on generative adversarial networks for image denoising.Inspired by U-net,our method employs a novel symmetrical encoder-decoder based generator network.The encoder adopts convolutional neural networks to extract features,while the decoder outputs the noise in the images by deconvolutional neural networks.Specially,shortcuts are added between designated layers,which can preserve image texture details and prevent gradient explosions.Besides,in order to improve the training stability of the model,we add Wasserstein distance in loss function as an optimization.We use the peak signal-to-noise ratio(PSNR)to evaluate our model and we can prove the effectiveness of it with experimental results.When compared to the state-of-the-art approaches,our method presents competitive performance.

On the mean field limit of the Random Batch Method for interacting particle systems

The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.

A novel image super-resolution reconstruction algorithm based on improved GANs and gradient penalty

Purpose–Conventional image super-resolution reconstruction by the conventional deep learning architectures suffers from the problems of hard training and gradient disappearing.In order to solve such problems,the purposeof this paperis to proposea novel image super-resolutionalgorithmbasedon improved generative adversarial networks(GANs)with Wasserstein distance and gradient penalty.Design/methodology/approach–The proposed algorithm first introduces the conventional GANs architecture,the Wasserstein distance and the gradient penalty for the task of image super-resolution reconstruction(SRWGANs-GP).In addition,a novel perceptual loss function is designed for the SRWGANs-GP to meet the task of image super-resolution reconstruction.The content loss is extracted from the deep model’s feature maps,and such features are introduced to calculate mean square error(MSE)for the loss calculation of generators.Findings–To validate the effectiveness and feasibility of the proposed algorithm,a lot of compared experiments are applied on three common data sets,i.e.Set5,Set14 and BSD100.Experimental results have shown that the proposed SRWGANs-GP architecture has a stable error gradient and iteratively convergence.Compared with the baseline deep models,the proposed GANs models have a significant improvement on performance and efficiency for image super-resolution reconstruction.The MSE calculated by the deep model’s feature maps gives more advantages for constructing contour and texture.Originality/value–Compared with the state-of-the-art algorithms,the proposed algorithm obtains a better performance on image super-resolution and better reconstruction results on contour and texture.

THE RANDOM BATCH METHOD FOR N-BODY QUANTUM DYNAMICS

This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N−1 other particles by the interaction with p≪N particles chosen at random at each time step,multiplied by(N−1)/p.This reduces the computational cost of computing the interaction potential per time step from O(N^(2))to O(N).For simplicity,we consider only in this work the case p=1—in other words,we assume that N is even,and that at each time step,the N particles are organized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time step.We obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N>1 and independent of the Planck constant h̵.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1(or Monge-Kantorovich-Rubinstein distance)on the set of Borel probability measures on Rd used in the context of optimal transport.

Convergence,boundedness,and ergodicity of regime-switching diusion processes with infinite memory

We study a class of diffusion processes, which are determined by solutions X(t) to stochastic functional differential equation with infinite memory and random switching represented by Markov chain Λ(t): Under suitable conditions, we investigate convergence and boundedness of both the solutions X(t) and the functional solutions Xt: We show that two solutions (resp., functional solutions) from different initial data living in the same initial switching regime will be close with high probability as time variable tends to infinity, and that the solutions (resp., functional solutions) are uniformly bounded in the mean square sense. Moreover, we prove existence and uniqueness of the invariant probability measure of two-component Markov-Feller process (Xt,Λ(t));and establish exponential bounds on the rate of convergence to the invariant probability measure under Wasserstein distance. Finally, we provide a concrete example to illustrate our main results.

Propagation of chaos and conditional McKean-Vlasov SDEs with regime-switching

We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching process.The switching process is allowed to be dependent on the particle system.The well-posedness and various properties of the limit conditional McKean-Vlasov SDEs are studied,and the conditional propagation of chaos is established with explicit estimate of the convergence rate.

Optimal Markovian Coupling and Exponential Convergence Rate for the TCP Process

In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications,distribution dependent stochastic differential equations(DDSDEs)have been intensively investigated.In this paper,we summarize some recent progresses in the study of DDSDEs,which include the correspondence of weak solutions and nonlinear Fokker-Planck equations,the well-posedness,regularity estimates,exponential ergodicity,long time large deviations,and comparison theorems.

Distributionally Robust Learning Based on Dirichlet Process Prior in Edge Networks

In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.