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Two applications of Fourier Transform for Lévy Measures On Rp

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SSRN

SSRN 2023年

作者： Qiu, Rui Li, Lu Yin, Xiangrong Yu, Zhou School of Statistics East China Normal University Shanghai200062 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE Shanghai200062 China Department of Statistics University of Kentucky LexingtonKY40536-0082 United States

For univariate variable x ∈ R, the Lévy measures for the two real-valued continuous negative definite functions ln and lncosh(x) are shown in Böttcher et al. (2018). In this note, by utilizing the Fourier transform, we present the corresponding Lévy measures for ln and lncosh(|x|) with x ∈ Rp. These Lévy measures have significant potential applications across various domains. © 2023, The Authors. All rights reserved.

关键词： Fourier transforms

Rethinking Centered Kernel Alignment in Knowledge Distillation

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arXiv 2024年

作者： Zhou, Zikai Shen, Yunhang Shao, Shitong Gong, Linrui Lin, Shaohui School of Computer Science and Technology East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE China Youtu Lab Tencent Shanghai China Hunan University China

Knowledge distillation has emerged as a highly effective method for bridging the representation discrepancy between large-scale models and lightweight models. Prevalent approaches involve leveraging appropriate metrics to minimize the divergence or distance between the knowledge extracted from the teacher model and the knowledge learned by the student model. Centered Kernel Alignment (CKA) is widely used to measure representation similarity and has been applied in several knowledge distillation methods. However, these methods are complex and fail to uncover the essence of CKA, thus not answering the question of how to use CKA to achieve simple and effective distillation properly. This paper first provides a theoretical perspective to illustrate the effectiveness of CKA, which decouples CKA to the upper bound of Maximum Mean Discrepancy (MMD) and a constant term. Drawing from this, we propose a novel Relation-Centered Kernel Alignment (RCKA) framework, which practically establishes a connection between CKA and MMD. Furthermore, we dynamically customize the application of CKA based on the characteristics of each task, with less computational source yet comparable performance than the previous methods. The extensive experiments on the CIFAR-100, ImageNet-1k, and MS-COCO demonstrate that our method achieves state-of-the-art performance on almost all teacher-student pairs for image classification and object detection, validating the effectiveness of our approaches. Our code is available in https://***/Klayand/PCKA. Copyright © 2024, The Authors. All rights reserved.

关键词： Distillation

Studentized permutation method for comparing restricted mean survival times with small sample from randomized trials

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arXiv 2021年

作者： Ditzhaus, Marc Yu, Menggang Xu, Jin Department of Statistics TU Dortmund University Germany Department of Biostatistics and Medical Informatics University of Wisconsin MadisonWI United States Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE and School of Statistics East China Normal University China

Recent observations, especially in cancer immunotherapy clinical trials with time-to-event outcomes, show that the commonly used proportional hazard assumption is often not justifiable, hampering an appropriate analyse of the data by hazard ratios. An attractive alternative advocated is given by the restricted mean survival time (RMST), which does not rely on any model assumption and can always be interpreted intuitively. As pointed out recently by Horiguchi and Uno (2020a), methods for the RMST based on asymptotic theory suffer from inflated type-I error under small sample sizes. To overcome this problem, they suggested a permutation strategy leading to more convincing results in simulations. However, their proposal requires an exchangeable data set-up between comparison groups which may be limiting in practice. In addition, it is not possible to invert their testing procedure to obtain valid confidence intervals, which can provide more in-depth information. In this paper, we address these limitations by proposing a studentized permutation test as well as the corresponding permutation-based confidence intervals. In our extensive simulation study, we demonstrate the advantage of our new method, especially in situations with relative small sample sizes and unbalanced groups. Finally we illustrate the application of the proposed method by re-analysing data from a recent lung cancer clinical trial. Copyright © 2021, The Authors. All rights reserved.

关键词： Diseases

Diagnostic Tests Before Modeling Longitudinal Actuarial data

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arXiv 2023年

作者： Li, Yinhuan Fung, Tsz Chai Peng, Liang Qian, Linyi Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200241 China Department of Risk Management and Insurance Georgia State University AtlantaGA30303 United States

In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of the cross-sectional estimated parameters under a logistic regression model and the empirical residual correlations of the claim occurrence indicators across time, which serve as the indications to detect serial dynamics;ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach;iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamics

Diagnostic Tests Before Modeling Longitudinal Actuarial data

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SSRN

SSRN 2022年

In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of cross-sectional estimated model parameters and the empirical residual correlations of the claims across time, which serve as the indications to detect serial dynamics and peculiar serial dependence of claims;ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach;iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently. © 2022, The Authors. All rights reserved.

关键词： Insurance

SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space

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arXiv 2023年

作者： Li, Yunchen Yu, Zhou He, Gaoqi Shen, Yunhang Li, Ke Sun, Xing Lin, Shaohui East China Normal University China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of Education China Youtu Lab Tencent Shanghai China

Symmetric positive definite (SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models, where predictions are made directly on E(X|y), where y is a vector and X is an SPD matrix. However, these methods are challenging to handle for large-scale data, as they need to access and process the whole data. In this paper, inspired by denoising diffusion probabilistic model (DDPM), we propose a novel generative model, termed SPD-DDPM, by introducing Gaussian distribution in the SPD space to estimate E(X|y). Moreover, our model is able to estimate p(X) unconditionally and flexibly without giving y. On the one hand, the model conditionally learns p(X|y) and utilizes the mean of samples to obtain E(X|y) as a prediction. On the other hand, the model unconditionally learns the probability distribution of the data p(X) and generates samples that conform to this distribution. Furthermore, we propose a new SPD net which is much deeper than the previous networks and allows for the inclusion of conditional factors. Experiment results on toy data and real taxi data demonstrate that our models effectively fit the data distribution both unconditionally and unconditionally and provide accurate predictions. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

Style Transformer for Image Inversion and Editing

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arXiv 2022年

作者： Hu, Xueqi Huang, Qiusheng Shi, Zhengyi Li, Siyuan Gao, Changxin Sun, Li Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai China Huazhong University of Science and Technology Wuhan China

Existing GAN inversion methods fail to provide latent codes for reliable reconstruction and flexible editing simultaneously. This paper presents a transformer-based image inversion and editing model for pretrained StyleGAN which is not only with less distortions, but also of high quality and flexibility for editing. The proposed model employs a CNN encoder to provide multi-scale image features as keys and values. Meanwhile it regards the style code to be determined for different layers of the generator as queries. It first initializes query tokens as learnable parameters and maps them into W+ space. Then the multi-stage alternate selfand cross-attention are utilized, updating queries with the purpose of inverting the input by the generator. Moreover, based on the inverted code, we investigate the referenceand label-based attribute editing through a pretrained latent classifier, and achieve flexible image-to-image translation with high quality results. Extensive experiments are carried out, showing better performances on both inversion and editing tasks within StyleGAN. Codes are available at https://***/sapphire497/style-transformer. Copyright © 2022, The Authors. All rights reserved.

关键词： Generative adversarial networks

Assessment of Effects of Age and Gender on the Incubation Period of COVID-19 with a Mixture Regression Model

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Journal of data science 2021年第1期19卷 p1-16页

作者： SIMING ZHENG JING QIN YONG ZHOU Academy of Mathematics and Systems Science University of Chinese Academy of Sciences Beijing China National Institute of Allergy and Infectious Diseases National Institutes of Health Bethesda Maryland USA Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE Academy of Statistics and Interdisciplinary Sciences Faculty of Economics and Management East China Normal University Shanghai China

Following the outbreak of COVID-19, various containment measures have been taken, including the use of quarantine. At present, the quarantine period is the same for everyone, since it is implicitly assumed that the incubation period distribution of COVID-19 is the same regardless of age or gender. For testing the effects of age and gender on the incubation period of COVID-19, a novel two-component mixture regression model is proposed. An expectation-maximization (EM) algorithm is adopted to obtain estimates of the parameters of interest, and the simulation results show that the proposed method outperforms the simple regression method and has robustness. The proposed method is applied to a Zhejiang COVID-19 dataset, and it is found that age and gender statistically have no effect on the incubation period of COVID-19, which indicates that the quarantine measure currently in operation is reasonable. [ABSTRACT FROM AUTHOR]

关键词： EM algorithm incubation period length-biased data mixture model

A General and Efficient Training for Transformer via Token Expansion

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A General and Efficient Training for Transformer via Token E...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Wenxuan Huang Yunhang Shen Jiao Xie Baochang Zhang Gaoqi He Ke Li Xing Sun Shaohui Lin School of Computer Science and Technology East China Normal University Shanghai China Tencent Youtu Lab China Xiamen University China Beihang University China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE China

ISBN: (数字)9798350353006

ISBN: (纸本)9798350353013

The remarkable performance of Vision Transformers (ViTs) typically requires an extremely large training cost. Existing methods have attempted to accelerate the training of ViTs, yet typically disregard method universality with accuracy dropping. Meanwhile, they break the training consistency of the original transformers, including the consistency of hyperparameters, architecture, and strategy, which prevents them from being widely applied to different Transformer networks. In this paper, we propose a novel token growth scheme Token Expansion (termed ToE) to achieve consistent training acceleration for ViTs. We introduce an “initialization-expansion-merging” pipeline to maintain the integrity of the intermediate feature distribution of original transformers, preventing the loss of crucial learnable information in the training process. ToE can not only be seamlessly integrated into the training and fine-tuning process of transformers (e.g., DeiT and LV-ViT), but also effective for efficient training frameworks (e.g., EfficientTrain), without twisting the original training hyperparameters, architecture, and introducing additional training strategies. Extensive experiments demonstrate that ToE achieves about 1.3× faster for the training of ViTs in a lossless manner, or even with performance gains over the full-token training baselines. Code is available at https://***/Osilly/TokenExpansion.

关键词： Training Computer vision Accuracy Costs Codes Pipelines Computer architecture