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OD-DETR: Online Distillation for Stabilizing Training of Detection Transformer

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arXiv 2024年

作者： Wu, Shengjian Sun, Li Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University China FinVolution Group Iran Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University China

DEtection TRansformer (DETR) becomes a dominant paradigm, mainly due to its common architecture with high accuracy and no post-processing. However, DETR suffers from unstable training dynamics. It consumes more data and epochs to converge compared with CNN-based detectors. This paper aims to stabilize DETR training through the online distillation. It utilizes a teacher model, accumulated by Exponential Moving Average (EMA), and distills its knowledge into the online model in following three aspects. First, the matching relation between object queries and ground truth (GT) boxes in the teacher is employed to guide the student, so queries within the student are not only assigned labels based on their own predictions, but also refer to the matching results from the teacher. Second, the teacher’s initial query is given to the online student, and its prediction is directly constrained by the corresponding output from the teacher. Finally, the object queries from teacher’s different decoder stages are used to build the auxiliary group to accelerate the convergence. For each GT, two queries with the least matching costs are selected into this extra group, and they predict the GT box and participate the optimization. Extensive experiments show that the proposed OD-DETR successfully stabilizes the training, and significantly increases the performance without bringing in more parameters. Copyright © 2024, The Authors. All rights reserved.

关键词： Students

Time-Consistent Portfolio Selection for Rank-Dependent Utilities in an Incomplete Market

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arXiv 2024年

作者： Wei, Jiaqin Xia, Jianming Zhao, Qian Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Statistics and Information Shanghai University of International Business and Economics Shanghai201620 China

We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium strategies. In the case of time-invariant probability weighting function, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique non-zero equilibrium, if exists, can be determined by solving an autonomous ODE. In the case of time-variant probability weighting functions, we observe that there may be infinitely many non-zero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available. © 2024, CC BY-NC-ND.

关键词： Commerce

An efficient semismooth Newton method for adaptive sparse signal recovery problems

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arXiv 2021年

作者： Ding, Yanyun Zhang, Haibin Li, Peili Xiao, Yunhai Department of Operations Research and Information Engineering Beijing University of Technology Beijing100124 China 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 Henan University Kaifeng475000 China

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional methods might work not so well. Recently, it was shown that using the difference between l1- and l2-norm as a regularization always has superior performance. In this paper, we propose an adaptive lp-l1−2 model where the lp-norm with p ≥ 1 measures the data fidelity and the l1−2-term measures the sparsity. This proposed model has the ability to deal with different types of noises and extract the sparse property even under high coherent condition. We use a proximal majorization-minimization technique to handle the nonconvex regularization term and then employ a semismooth Newton method to solve the corresponding convex relaxation subproblem. We prove that the sequence generated by the semismooth Newton method admits fast local convergence rate to the subproblem under some technical assumptions. Finally, we do some numerical experiments to demonstrate the superiority of the proposed model and the progressiveness of the proposed algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Compressed sensing

Variable screening in multivariate linear regression with high-dimensional covariates

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Statistical theory and Related Fields 2022年第3期6卷 241-253页

作者： Shiferaw B.Bizuayehu Lu Li Jin Xu School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal UniversityShanghaiPeople’s Republic of China

We propose two variable selection methods in multivariate linear regression with highdimensional *** first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low *** second method extends the univariate forward regression of Wang[(2009).Forward regression for ultra-high dimensional variable *** of the American Statistical Association,104(488),1512–***://***/10.1198/***08516]in a unified way such that the variable selection and model estimation can be obtained *** establish the sure screening property for both *** and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.

关键词： Dimension reduction forward regression multiple correlation coefficient multivariate regression variable selection

An asymptotic analysis of minibatch-based momentum methods for linear regression models

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arXiv 2021年

作者： Gao, Yuan Zhu, Xuening Qi, Haobo Li, Guodong Zhang, Riquan Wang, Hansheng School of Statistics East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE East China Normal University Shanghai China School of Data Science Fudan University Shanghai China Guanghua School of Management Peking University Beijing China Department of Statistics and Actuarial Science University of Hong Kong Hong Kong

Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the minibatch-based gradient descent methods with momentum (MGDM) are widely used to solve large-scale optimization problems with massive datasets. Despite the success of the MGDM methods in practice, their theoretical properties are still underexplored. To this end, we investigate the theoretical properties of MGDM methods based on the linear regression models. We first study the numerical convergence properties of the MGDM algorithm and further provide the theoretically optimal tuning parameters specification to achieve faster convergence rate. In addition, we explore the relationship between the statistical properties of the resulting MGDM estimator and the tuning parameters. Based on these theoretical findings, we give the conditions for the resulting estimator to achieve the optimal statistical efficiency. Finally, extensive numerical experiments are conducted to verify our theoretical results. © 2021, CC BY.

关键词： Gradient methods

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