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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

Large and moderate deviations for record numbers in some non–nearest neighbor random walks

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arXiv 2019年

作者： Li, Yuqiang Yao, Qiang Key Laboratory of Advanced Theory and Application in Statistics and Data Science–MOE School of Statistics East China Normal University China NYU–ECNU Institute of Mathematical Sciences NYU Shanghai China

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non–nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations for the number of "weak records" (or "ladder points") in two kinds of one–dimensional non–nearest neighbor random walks. The proofs depend only on the direct analysis of random walks. We illustrate that the traditional method of analyzing the local time of Brownian motions, which is often adopted for the simple random walks, would lead to wrong conjectures for our *** Codes 60F10, 60G50 Copyright © 2019, The Authors. All rights reserved.

关键词： Brownian movement

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

Spatially Clustered Varying Coefficient Model

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arXiv 2020年

作者： Lin, Fangzheng Tang, Yanlin Zhu, Huichen Zhu, Zhongyi Department of Statistics Fudan University China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University China Department of Mathematics Hong Kong University of Science and Technology China

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the regression coefficients are allowed to vary smoothly within each cluster but change abruptly across the boundaries of adjacent clusters, and we develop a unified approach for simultaneous coefficient estimation and cluster identification. The varying coefficients are approximated by penalized splines, and the clusters are identified through a fused concave penalty on differences in neighboring locations, where the spatial neighbors are specified by the minimum spanning tree (MST). The optimization is solved efficiently based on the alternating direction method of multipliers, utilizing the sparsity structure from MST. Furthermore, we establish the oracle property of the proposed method considering the structure of MST. Numerical studies show that the proposed method can efficiently incorporate spatial neighborhood information and automatically detect possible spatially clustered patterns in the regression coefficients. An empirical study in oceanography illustrates that the proposed method is promising to provide informative results. Copyright © 2020, The Authors. All rights reserved.

关键词： Constrained optimization

RecursiveDet: End-to-End Region-based Recursive Object Detection

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RecursiveDet: End-to-End Region-based Recursive Object Detec...

International Conference on Computer Vision (ICCV)

作者： Jing Zhao Li Sun Qingli Li 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

End-to-end region-based object detectors like Sparse R-CNN usually have multiple cascade bounding box decoding stages, which refine the current predictions according to their previous results. Model parameters within each stage are independent, evolving a huge cost. In this paper, we find the general setting of decoding stages is actually redundant. By simply sharing parameters and making a recursive decoder, the detector already obtains a significant improvement. The recursive decoder can be further enhanced by positional encoding (PE) of the proposal box, which makes it aware of the exact locations and sizes of input bounding boxes, thus becoming adaptive to proposals from different stages during the recursion. Moreover, we also design centerness-based PE to distinguish the RoI feature element and dynamic convolution kernels at different positions within the bounding box. To validate the effectiveness of the proposed method, we conduct intensive ablations and build the full model on three recent mainstream region-based detectors. The RecusiveDet is able to achieve obvious performance boosts with even fewer model parameters and slightly increased computation cost. Codes are available at https://***/bravezzzzzz/RecursiveDet.

关键词：

RecursiveDet: End-to-End Region-based Recursive Object Detection

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arXiv 2023年

作者： Zhao, Jing Sun, Li 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

关键词： Object detection

IoU-Enhanced Attention for End-to-End Task Specific Object Detection

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arXiv 2022年

作者： Zhao, Jing Wu, Shengjian Sun, Li 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

Without densely tiled anchor boxes or grid points in the image, sparse R-CNN achieves promising results through a set of object queries and proposal boxes updated in the cascaded training manner. However, due to the sparse nature and the one-to-one relation between the query and its attending region, it heavily depends on the self attention, which is usually inaccurate in the early training stage. Moreover, in a scene of dense objects, the object query interacts with many irrelevant ones, reducing its uniqueness and harming the performance. This paper proposes to use IoU between different boxes as a prior for the value routing in self attention. The original attention matrix multiplies the same size matrix computed from the IoU of proposal boxes, and they determine the routing scheme so that the irrelevant features can be suppressed. Furthermore, to accurately extract features for both classification and regression, we add two lightweight projection heads to provide the dynamic channel masks based on object query, and they multiply with the output from dynamic convs, making the results suitable for the two different tasks. We validate the proposed scheme on different datasets, including MS-COCO and CrowdHuman, showing that it significantly improves the performance and increases the model convergence speed. Codes are available at https://***/bravezzzzzz/IoU-Enhanced-Attention. Copyright © 2022, The Authors. All rights reserved.

关键词： Object detection

Causal Mediation Analysis with a Three-Dimensional Image Mediator

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arXiv 2023年

作者： Chen, Minghao Zhou, Yingchun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE Institute of Brain and Education Innovation School of Statistics East China Normal University 3663 North Zhongshan Road Shanghai200062 China

Causal mediation analysis is increasingly abundant in biology, psychology, and epidemiology studies, etc. In particular, with the advent of the big data era, the issue of high-dimensional mediators is becoming more prevalent. In neuroscience, with the widespread application of magnetic resonance technology in the field of brain imaging, studies on image being a mediator emerged. In this study, a novel causal mediation analysis method with a three-dimensional image mediator is proposed. We define the average casual effects under the potential outcome framework, explore several sufficient conditions for the valid identification, and develop techniques for estimation and inference. To verify the effectiveness of the proposed method, a series of simulations under various scenarios is performed. Finally, the proposed method is applied to a study on the causal effect of mother's delivery mode on child's IQ development. It is found that the white matter in certain regions of the frontal-parietal and brainstem-cerebellum areas has mediating effects. © 2023, CC BY.

关键词： Magnetic resonance

A hybrid deep learning method for controlled stochastic Kolmogorov systems with regime-switching

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A hybrid deep learning method for controlled stochastic Kolm...

International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Yu Zhang Zhuo Jin Jiaqin Wei School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai China Department of Actuarial Studies and Business Analytics Macquarie University NSW Australia

ISBN: (数字)9798350373974

ISBN: (纸本)9798350373981

In this paper, we employ numerical methods based on deep learning algorithms for solving controlled stochastic Kolmogorov systems with regime-switching. Different from classical control problems, each component of the state in controlled Kolmogorov systems is nonnegative. Due to the nonlinearity and complexity of the controlled stochastic Kolmogorov systems, we develop a hybrid deep learning method to numerically solve the optimal controls under this system. Subsequently, we apply the hybrid deep learning method to solve a specific case of a controlled stochastic Kolmogorov system, specifically controlled SIS (susceptible-infected-susceptible) systems. Finally, the effectiveness of the proposed hybrid deep learning method is verified through numerical results.

关键词： Deep learning Closed-form solutions Neural networks Optimal control Aerospace electronics Control systems Complexity theory Approximation methods Information technology Method of moments