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Derivatives of local times for some Gaussian fields II

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arXiv 2020年

作者： Hong, Minhao Xu, Fangjun School of Statistics East China Normal University Shanghai200262 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai200062 China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai 3663 Zhongshan Road North Shanghai200062 China

Given a (2, d)-Gaussian field (formula presented), s where XH1 and XeH2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give the necessary condition for existence of de... 详细信息

关键词： Gaussian distribution

A hybrid deep learning method for finite-horizon mean-field game problems

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arXiv 2023年

作者： Zhang, Yu Jin, Zhuo Wei, Jiaqin Yin, George Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China Department of Actuarial Studies and Business Analytics Macquarie University NSW2109 Australia Department of Mathematics University of Connecticut Storrs CT06269-1009 United States

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved;two numerical examples are provided to illustrate the results. Copyright © 2023, The Authors. All rights reserved.

关键词： Markov chains

Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

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arXiv 2022年

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor’s attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results. Copyright © 2022, The Authors. All rights reserved.

关键词： Hidden Markov models

HYPOTHESIS TEST ON A MIXTURE FORWARD-INCUBATION-TIME EPIDEMIC MODEL WITH application TO COVID-19 OUTBREAK

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arXiv 2022年

作者： Wang, Chunlin Li, Pengfei Liu, Yukun Zhou, Xiao-Hua Qin, Jing Department of Statistics and Data Science School of Economics Wang Yanan Institute for Studies in Economics MOE Key Lab of Econometrics Fujian Key Lab of Statistics Xiamen University Xiamen China Department of Statistics and Actuarial Sciences University of Waterloo Canada Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai China Department of Biostatistics School of Public Health Peking University Beijing China National Institute of Allergy and Infectious Diseases National Institutes of Health United States

The distribution of the incubation period of the novel coronavirus disease that emerged in 2019 (COVID-19) has crucial clinical implications for understanding this disease and devising effective disease-control measures. Qin et al. (2020) designed a cross-sectional and forward follow-up study to collect the duration times between a specific observation time and the onset of COVID-19 symptoms for a number of individuals. They further proposed a mixture forward-incubation-time epidemic model, which is a mixture of an incubation-period distribution and a forward time distribution, to model the collected duration times and to estimate the incubation-period distribution of COVID-19. In this paper, we provide sufficient conditions for the identifiability of the unknown parameters in the mixture forward-incubation-time epidemic model when the incubation period follows a two-parameter distribution. Under the same setup, we propose a likelihood ratio test (LRT) for testing the null hypothesis that the mixture forward-incubation-time epidemic model is a homogeneous exponential distribution. The testing problem is non-regular because a nuisance parameter is present only under the alternative. We establish the limiting distribution of the LRT and identify an explicit representation for it. The limiting distribution of the LRT under a sequence of local alternatives is also obtained. Our simulation results indicate that the LRT has desirable type I errors and powers, and we analyze a COVID-19 outbreak dataset from China to illustrate the usefulness of the LRT. Copyright © 2022, The Authors. All rights reserved.

关键词： COVID-19

Robust Online Detection in Serially Correlated Directed Network

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arXiv 2021年

作者： Yu, Miaomiao Zhou, Yuhao Tsung, Fugee Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE Academy of Statistics and Interdisciplinary Sciences East China Normal University Shanghai China Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel HillNC27599 United States Department of Industrial Engineering and Decision Analytics Hong Kong University of Science and Technology Kowloon Hong Kong

As the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks robustly and sensitively. First, we consider a transition probability matrix to resolve the double correlation of primary data. Further, since the sum of each row of the transition probability matrix is one, it standardizes the data, facilitating subsequent modeling. Then we extend the spring length based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. This novel approach assumes only that the process observation is associated with nearby points without any parametric time series model, which is in line with reality. Simulation results and a real example from metro transportation demonstrate the superiority of our design. Copyright © 2021, The Authors. All rights reserved.

关键词： Digital storage

Class-Imbalanced Semi-Supervised Learning for Large-Scale Point Cloud Semantic Segmentation via Decoupling Optimization

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arXiv 2024年

作者： Li, Mengtian Lin, Shaohui Wang, Zihan Shen, Yunhang Zhang, Baochang Ma, Lizhuang Shanghai University China Shanghai Engineering Research Center of Motion Picture Special Effects China East China Normal University China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of Education China Beihang University China Tencent Youtu Lab China

Semi-supervised learning (SSL), thanks to the significant reduction of data annotation costs, has been an active research topic for large-scale 3D scene understanding. However, the existing SSL-based methods suffer from severe training bias, mainly due to class imbalance and long-tail distributions of the point cloud data. As a result, they lead to a biased prediction for the tail class segmentation. In this paper, we introduce a new decoupling optimization framework, which disentangles feature representation learning and classifier in an alternative optimization manner to shift the bias decision boundary effectively. In particular, we first employ two-round pseudo-label generation to select unlabeled points across head-to-tail classes. We further introduce multi-class imbalanced focus loss to adaptively pay more attention to feature learning across head-to-tail classes. We fix the backbone parameters after feature learning and retrain the classifier using ground-truth points to update its parameters. Extensive experiments demonstrate the effectiveness of our method outperforming previous state-of-the-art methods on both indoor and outdoor 3D point cloud datasets (i.e., S3DIS, ScanNet-V2, Semantic3D, and SemanticKITTI) using 1% and 1pt evaluation. Copyright © 2024, The Authors. All rights reserved.

关键词： Semantic Segmentation

ENSEMBLE DOMAIN DECOMPOSITION ALGORITHM FOR THE FULLY-MIXED RANDOM STOKES-DARCY MODEL WITH THE BEAVERS-JOSEPH INTERFACE CONDITIONS

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arXiv 2022年

作者： Shi, Feng Sun, Yizhong Zheng, Haibiao College of Science Harbin Institute of Technology Shenzhen China School of Mathematical Sciences East China Normal University Shanghai China School of Mathematical Sciences East China Normal University Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai China

In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully-mixed random Stokes-Darcy model with the physically realistic Beavers-Joseph (BJ) interface conditions. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic Stokes-Darcy numerical models and use the idea of the ensemble to realize the fast computation of multiple problems. One remarkable feature of the algorithm is that multiple linear systems share a common coefficient matrix in each deterministic numerical model, which significantly reduces the computational cost and achieves comparable accuracy with the traditional methods. Moreover, by domain decomposition, we can decouple the Stokes-Darcy system into two smaller sub-physics problems naturally. Both mesh-dependent and mesh-independent convergence rates of the algorithm are rigorously derived by choosing suitable Robin parameters. Optimized Robin parameters are derived and analyzed to accelerate the convergence of the proposed algorithm. Especially, for small hydraulic conductivity in practice, the almost optimal geometric convergence can be obtained by finite element discretization. Finally, two groups of numerical experiments are conducted to validate the exclusive features of the proposed algorithm. © 2022, CC BY-NC-ND.

关键词： Numerical models

Click-Through Rate Prediction Models based on Interest Modeling 5

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Click-Through Rate Prediction Models based on Interest Model...

5th International Conference on Big data Engineering, BDE 2023

作者： Luo, Zhen Zhang, Yingfang Hu, Chengxuan Xia, Yuxuan Zhu, Shengxin Department of Statistical Science University College London United Kingdom Department of Statistics and Actuarial Science University of Hong Kong Hong Kong Hong Kong Department of Industrial and Systems Engineering Polytechnic University of Hong Kong Hong Kong Hong Kong School of Mathematics University of Southampton United Kingdom Research Center for Mathematics Advanced Institute of Natural Science Beijing Normal University Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College China

ISBN: (纸本)9798400708695

Deep learning frameworks have achieved extraordinary results in popular technological frontiers, which also greatly inspires considerable researchers in recommender system. As one of the mainstream research frontiers, click-through rate (CTR) predictions have received increasing attention from both industrial and academic circles. Recently, Alibaba group has come up with novel idea of interest modeling that can effectively overcome the limitations brought by previous deep learning CTR prediction models, which is also the key to improve performance. For the past few years, more and more relevant works begin to explore approaches taking advantage of the learning, representation, and interpretation ability from neural networks. However, there are few comprehensive surveys targeted at this topic. In this paper, we systematically review and summarize recent CTR prediction models based on interest modeling. First, we elaborate their different design ideas and pay additional attention to their intrinsic relationship including improvements and extensions, similarities and differences, advantages and disadvantages and so on. Next, we deploy them separately according to official open-source code and compare their performance assessment in terms of accuracy and speed, looking for best optimizers and other hyperparameters. Furthermore, we briefly discuss some possible refinement directions and future research trends. © 2023 ACM.

关键词： Recommender systems

Boundary-aware Supervoxel-level Iteratively Refined Interactive 3D Image Segmentation with Multi-agent Reinforcement Learning

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arXiv 2023年

作者： Ma, Chaofan Xu, Qisen Wang, Xiangfeng Jin, Bo Zhang, Xiaoyun Wang, Yanfeng Zhang, Ya The Cooperative Medianet Innovation Center Shanghai Jiao Tong University Shanghai200240 China The MOE Key Laboratory for Advanced Theory and Application in Statistics and Data Science School of Computer Science and Technology East China Normal University Shanghai200062 China The Shanghai Institute of Intelligent Science and Technology Tongji University Shanghai200092 China

Interactive segmentation has recently been explored to effectively and efficiently harvest high-quality segmentation masks by iteratively incorporating user hints. While iterative in nature, most existing interactive segmentation methods tend to ignore the dynamics of successive interactions and take each interaction independently. We here propose to model iterative interactive image segmentation with a Markov decision process (MDP) and solve it with reinforcement learning (RL) where each voxel is treated as an agent. Considering the large exploration space for voxel-wise prediction and the dependence among neighboring voxels for the segmentation tasks, multi-agent reinforcement learning is adopted, where the voxel-level policy is shared among agents. Considering that boundary voxels are more important for segmentation, we further introduce a boundary-aware reward, which consists of a global reward in the form of relative cross-entropy gain, to update the policy in a constrained direction, and a boundary reward in the form of relative weight, to emphasize the correctness of boundary predictions. To combine the advantages of different types of interactions, i.e., simple and efficient for point-clicking, and stable and robust for scribbles, we propose a supervoxel-clicking based interaction design. Experimental results on four benchmark datasets have shown that the proposed method significantly outperforms the state-of-the-arts, with the advantage of fewer interactions, higher accuracy, and enhanced robustness. Copyright © 2023, The Authors. All rights reserved.

关键词： Reinforcement learning