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A data-driven line search rule for support recovery in high-dimensional data analysis

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arXiv 2021年

作者： Li, Peili Jiao, Yuling Lu, Xiliang Kang, Lican School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai200062 China School of Mathematics and Statistics Hubei Key Laboratory of Computational Science Wuhan University Wuhan430072 China School of Mathematics and Statistics Wuhan University Wuhan430072 China

In this work, we consider the algorithm to the (nonlinear) regression problems with 0penalty. The existing algorithms for 0based optimization problem are often carried out with a fixed step size, and the selection of an appropriate step size depends on the restricted strong convexity and smoothness for the loss function, hence it is difficult to compute in practical calculation. In sprite of the ideas of support detection and root finding Huang et al. (2021), we proposes a novel and efficient data-driven line search rule to adaptively determine the appropriate step size. We prove the 2error bound to the proposed algorithm without much restrictions for the cost functional. A large number of numerical comparisons with state-of-the-art algorithms in linear and logistic regression problems show the stability, effectiveness and superiority of the proposed algorithms. Copyright © 2021, The Authors. All rights reserved.

关键词： Machine learning

ID-Unet: Iterative soft and hard deformation for view synthesis

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arXiv 2021年

作者： Yin, Mingyu Sun, Li Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing Shanghi China Key Laboratory of Advanced Theory and Application in Statistics & Data Science East China Normal University Shanghai200241 China

View synthesis is usually done by an autoencoder, in which the encoder maps a source view image into a latent content code, and the decoder transforms it into a target view image according to the condition. However, the source contents are often not well kept in this setting, which leads to unnecessary changes during the view translation. Although adding skipped connections, like Unet, alleviates the problem, but it often causes the failure on the view conformity. This paper proposes a new architecture by performing the source-to-target deformation in an iterative way. Instead of simply incorporating the features from multiple layers of the encoder, we design soft and hard deformation modules, which warp the encoder features to the target view at different resolutions, and give results to the decoder to complement the details. Particularly, the current warping flow is not only used to align the feature of the same resolution, but also as an approximation to coarsely deform the high resolution feature. Then the residual flow is estimated and applied in the high resolution, so that the deformation is built up in the coarse-to-fine fashion. To better constrain the model, we synthesize a rough target view image based on the intermediate flows and their warped features. The extensive ablation studies and the final results on two different data sets show the effectiveness of the proposed model. https://***/MingyuY/Iterative-view-synthesis © 2021, CC BY.

关键词： Signal encoding

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