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Derivatives of local times for some Gaussian fields

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arXiv 2019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

In this article, we consider derivatives of local time for a (2, d)-Gaussian field Z = {Z(t, s) = XtH1 − XeH2 , s, t ≥ 0}, s where XH1 and XeH2 are two independent processes from a class of d-dimensional centered Gaussian processes satisfying certain local nondeterminism property. We first give a condition for existence of derivatives of the local time. Then, under this condition, we show that derivatives of the local time are Hölder continuous in both time and space variables. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time at the origin. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

Kernel entropy estimation for long memory linear processes with infinite variance

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arXiv 2022年

作者： Liu, Hui 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

Let X = {Xn : n ∈ N} be a long memory linear process with innovations in the domain of attraction of an α-stable law (0 RR f 2(x) dx by using the kernel estimator X 2 Tn(hn) = n(n − 1)hn 1≤jn K (Xih−nXj) . The simulation study for long memory linear processes with symmetric α-stable innovations is also given. © 2022, CC BY-NC-SA.

关键词： Probability density function

Derivatives of local times for some Gaussian fields II

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arXiv 2020年

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

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

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

CLIP-Driven Open-Vocabulary 3D Scene Graph Generation via Cross-Modality Contrastive Learning

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CLIP-Driven Open-Vocabulary 3D Scene Graph Generation via Cr...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Lianggangxu Chen Xuejiao Wang Jiale Lu Shaohui Lin Changbo Wang Gaoqi He School of Computer Science and Technology East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of Education China Chongqing Key Laboratory of Precision Optics Chongqing Institute of East China Normal University Chongqing China

ISBN: (数字)9798350353006

ISBN: (纸本)9798350353013

3D Scene Graph Generation (3DSGG) aims to classify objects and their predicates within 3D point cloud scenes. However, current 3DSGG methods struggle with two main challenges. 1) The dependency on labor-intensive ground-truth annotations. 2) Closed-set classes training hampers the recognition of novel objects and predicates. Addressing these issues, our idea is to extract cross-modality features by CLIP from text and image data naturally related to 3D point clouds. Cross-modality features are used to train a robust 3D scene graph (3DSG)feature extractor. Specifically, we propose a novel Cross-Modality Contrastive Learning 3DSGG (CCL-3DSGG) method. Firstly, to align the text with 3DSG, the text is parsed into word level that are consistent with the 3DSG annotation. To enhance robustness during the alignment, adjectives are exchanged for different objects as negative samples. Then, to align the image with 3DSG, the camera view is treated as a positive sample and other views as negatives. Lastly, the recognition of novel object and predicate classes is achieved by calculating the cosine similarity between prompts and 3DSG features. Our rigorous experiments confirm the superior open-vocabulary capability and applicability of CCL-3DSGG in real-world contexts.

关键词： Point cloud compression Training Computer vision Three-dimensional displays Annotations Contrastive learning Feature extraction

Cross Attention Based Style Distribution for Controllable Person Image Synthesis

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arXiv 2022年

作者： Zhou, Xinyue Yin, Mingyu Chen, Xinyuan Sun, Li Gao, Changxin Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai China Shanghai AI Laboratory Shanghai China Huazhong University of Science and Technology Wuhan China

Controllable person image synthesis task enables a wide range of applications through explicit control over body pose and appearance. In this paper, we propose a cross attention based style distribution module that computes between the source semantic styles and target pose for pose transfer. The module intentionally selects the style represented by each semantic and distributes them according to the target pose. The attention matrix in cross attention expresses the dynamic similarities between the target pose and the source styles for all semantics. Therefore, it can be utilized to route the color and texture from the source image, and is further constrained by the target parsing map to achieve a clearer objective. At the same time, to encode the source appearance accurately, the self attention among different semantic styles is also added. The effectiveness of our model is validated quantitatively and qualitatively on pose transfer and virtual try-on tasks. Codes are available at https://***/xyzhouo/CASD. Copyright © 2022, The Authors. All rights reserved.

关键词： Semantics

NOVEL ENSEMBLE ALGORITHMS FOR RANDOM TWO-DOMAIN PARABOLIC PROBLEMS

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arXiv 2023年

作者： Sun, Yizhong Wang, Jiangshan Zheng, Haibiao 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 Shanghai China

In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction parameter due to its complexity and uncertainty. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic fluid-fluid numerical models and use the ensemble idea to realize the fast computation of multiple problems. Our remarkable feature of these algorithms is employing the same coefficient matrix for multiple linear systems, significantly reducing the computational cost. By data-passing partitioned techniques, we can decouple the numerical models into two smaller sub-domain problems and achieve parallel computation. Theoretically, we derive that both algorithms are unconditionally stable and convergent. Finally, numerical experiments are conducted not only to support the theoretical results but also to validate the exclusive feature of the proposed algorithms. © 2023, CC BY-NC-SA.

关键词： Numerical models