检索结果-内蒙古大学图书馆

Confidence intervals and hypothesis testing for high-dimensional quantile regression: convolution smoothing and debiasing

学校读者我要写书评

暂无评论

The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 11626-11674页

作者： Yibo Yan Xiaozhou Wang Riquan Zhang School of Statistics East China Normal University Shanghai China School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai China School of Statistics and Information Shanghai University of International Business and Economics Shanghai China

ℓ1-penalized quantile regression (ℓ1-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in the high-dimensional setting. Hypothesis tests can then be formulated based on the debiased ℓ1-QR estimator that reduces the bias induced by Lasso penalty. However, the nonsmoothness of the quantile loss brings great challenges to the computation, especially when the data dimension is high. Recently, the convolution-type smoothed quantile regression (SQR) model has been proposed to overcome such shortcoming, and people developed theory of estimation and variable selection therein. In this work, we combine the debiased method with SQR model and come up with the debiased ℓ1-SQR estimator, based on which we then establish confidence intervals and hypothesis testing in the high-dimensional setup. Theoretically, we provide the non-asymptotic Bahadur representation for our proposed estimator and also the Berry-Esseen bound, which implies the empirical coverage rates for the studentized confidence intervals. Furthermore, we build up the theory of hypothesis testing on both a single variable and a group of variables. Finally, we exhibit extensive numerical experiments on both simulated and real data to demonstrate the good performance of our method.

关键词： high-dimensional quantile regression convolution-based smoothing debiased method hypothesis testing non-asymptotic statistics

A Very-Short-Term Online PV Power Prediction Model Based on RAN With Secondary Dynamic Adjustment

学校读者我要写书评

暂无评论

IEEE Transactions on Artificial Intelligence

IEEE Transactions on Artificial Intelligence 2023年第5期4卷 1214-1224页

作者： Zhang, Tengfei Ma, Fumin Peng, Chen Yu, Yang Yue, Dong Dou, Chunxia O'Hare, Gregory M. P. Nanjing University of Posts and Telecommunications College of Automation College of Artificial Intelligence The Jiangsu Engineering Laboratory of Big Data Analysis and Control for Active Distribution Network Nanjing210023 China Nanjing University of Finance and Economics College of Information Engineering Nanjing210023 China Shanghai University School of Mechatronic Engineering and Automation Shanghai200072 China Nanjing University of Posts and Telecommunications Institute of Advanced Technology Nanjing210023 China Trinity College Dublin School of Computer Science and Statistics Dublin 2 Ireland

Photovoltaic (PV) power is progressively being subsumed into power grids. As a consequence, reliable PV power forecasting has become essential in order to ensure the optimal functioning of the power grid. Neural networks remain the dominant prediction model utilized. Conventional neural network forecasting models are wholly dependent upon offline data. Subsequent to offline training, no further structural adjustments can be made during the forecasting process, which therefore they fail to cater for PV power supply fluctuations that are fundamentally dynamic. To address this failing, this article proposes a very-short-term online prediction model based on a resource-allocating network (RAN) incorporating a secondary dynamic adjustment. The RAN is initially trained offline to obtain a basic forecasting model. Thereafter, in an online prediction process, those samples with large prediction errors that exceed a preset value are recorded in a specific buffer. When the set conditions are triggered, the secondary dynamic adjustment strategy is employed, which enables the online prediction model to effectively relearn previously unmodeled samples while shielding external interference. Experimental results obtained from actual testing demonstrate the validity of the secondary dynamic adjustment strategy for online learning while also providing higher accuracy levels from the prediction model. © 2020 IEEE.

关键词： Forecasting

Combining Experimental and Historical data for Policy Evaluation

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Li, Ting Shi, Chengchun Wen, Qianglin Sui, Yang Qin, Yongli Lai, Chunbo Zhu, Hongtu School of Statistics and Management Shanghai University of Finance and Economics China Department of Statistics London School of Economics and Political Science United Kingdom Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University China Didi Chuxing China Department of Biostatistics The University of North Carolina Chapel Hill United States

This paper studies policy evaluation with multiple data sources, especially in scenarios that involve one experimental dataset with two arms, complemented by a historical dataset generated under a single control arm. We propose novel data integration methods that linearly integrate base policy value estimators constructed based on the experimental and historical data, with weights optimized to minimize the mean square error (MSE) of the resulting combined estimator. We further apply the pessimistic principle to obtain more robust estimators, and extend these developments to sequential decision making. Theoretically, we establish non-asymptotic error bounds for the MSEs of our proposed estimators, and derive their oracle, efficiency and robustness properties across a broad spectrum of reward shift scenarios. Numerical experiments and real-data-based analyses from a ridesharing company demonstrate the superior performance of the proposed estimators. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

Deep generative network for image inpainting with gradient semantics and spatial-smooth attention

学校读者我要写书评

暂无评论

Journal of Visual Communication and Image Representation 2024年 98卷

作者： Sheng, Ziqi Xu, Wenbo Lin, Cong Lu, Wei Ye, Long School of Computer Science and Engineering Guangdong Province Key Laboratory of Information Security Technology Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Guangzhou510006 China Applied Laboratory of Dig Data and Education Statistics School of Statistics and Mathematics Guangdong University of Finance and Economics Guangzhou510320 China State Key Laboratory of Media Convergence and Communication Communication University of China Beijing100024 China

As a powerful forgery operation in the image content security area, image inpainting based on deep generative networks can yield visually appealing outputs but often produces ambiguous artifacts, especially in boundary and high semantic areas. To address this issue, a novel end-to-end network with gradient semantics and spatial-smooth attention (GS-SSA) is proposed, which combines a gradient learning network and an image inpainting network. The gradient learning network is meant to properly anticipate the gradient semantics in the hole region and get a complete gradient semantic map. The image inpainting network utilizes the complete gradient semantic map to better repair the missing pixels and obtain the final inpainting results. Moreover, spatial-smooth attention is introduced into the image inpainting network, considering both the spatial structural relations and the surrounding information in the hole region. Experimental results on public datasets show the superiority of the proposed method, especially in large-hole region tasks. © 2023 Elsevier Inc.

关键词： Semantics

Lattice Boltzmann equation for convection-diffusion flows with Neumann boundary condition

学校读者我要写书评

暂无评论

Physical Review E 2025年第3期111卷 035311-035311页

作者： Lin Zheng Song Zheng Qinglan Zhai MIIT Key Laboratory of Thermal Control of Electronic Equipment School of Energy and Power Engineering Nanjing University of Science and Technology Nanjing 210094 People's Republic of China School of Data Science Zhejiang University of Finance and Economic Hangzhou 310018 People's Republic of China School of Economics Management and Law Chaohu University Chaohu 238000 People's Republic of China

In this work, a lattice Boltzmann equation (LBE) is developed to convection-diffusion flows with Neumann boundary condition in complex geometry. The physical fluid domain together with the physical boundary is extended to a large domain similar to the fictitious domain method, and the original convection-diffusion equation (CDE) is reformulated for the large domain, where the Neumann boundary condition is naturally incorporated to CDE without separated explicit treatment. Based on this extended CDE for the large domain, the LBE solver is designed accordingly. Several classical simulations of pure thermal diffusion/natural convection between two concentrated cylinders, natural convection flow around a circular cylinder with constant heat flux in square cavity, and mixed convection flow in a square lid-driven cavity with a circular cylinder are carried out to validate the present method. Numerical results show that the predictions by present LBE agree well with theoretical or other results.

关键词： Circular cylinders

Competitive and exclusion and oscillation phenomena of an eco-epidemiological model: An invasive approach

学校读者我要写书评

暂无评论

International Journal of Biomathematics 2023年第5期16卷 23-47页

作者： Ke-Lu Li Jun-Yuan Yang Xue-Zhi Li School of Mathematics and Information Science Henan Normal University 453007XinriangHenanP.R.China Comple Systems Research Center Shanri University 030006TaiyuanShanciP.R.China Shanci Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention Shanri University 030006TaiyuanShanriP.R.China School of Statistics and Mathematics Henan Finance University 450046ZhengzhouHenanP.R.China

Eco-epidemiological model plays a crucial role in maintaining ecological balance and biological *** this paper,we propose a predator-prey model where the predator population is infected by the *** non-negativity and boundedness of the solution are *** existence and stability of equilibrium are discussed by an invasive *** simulations are used to demonstrate the competitive and exclusion,and oscillation behaviors of the ***,the predation rate of the infected predator is shown to have far-reaching implications for the structure and stability of ecological communities.

关键词： Eco-epidemiological model Hopf bifurcation competitive and exclusion global stability

Deep Conditional Distribution Learning via Conditional Föllmer Flow

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Chang, Jinyuan Ding, Zhao Jiao, Yuling Li, Ruoxuan Yang, Jerry Zhijian Joint Laboratory of Data Science and Business Intelligence Southwestern University of Finance and Economics Sichuan Chengdu611130 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics Wuhan University Hubei Wuhan430072 China Hubei Key Laboratory of Computational Science Hubei Wuhan430072 China

We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional Föllmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate the target conditional distribution very well when the time is close to 1. For effective implementation, we discretize the flow with Euler’s method where we estimate the velocity field nonparametrically using a deep neural network. Furthermore, we also establish the convergence result for the Wasserstein-2 distance between the distribution of the learned samples and the target conditional distribution, providing the first comprehensive end-to-end error analysis for conditional distribution learning via ODE flow. Our numerical experiments showcase its effectiveness across a range of scenarios, from standard nonparametric conditional density estimation problems to more intricate challenges involving image data, illustrating its superiority over various existing conditional density estimation methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

High-dimensional inference for single-index model with latent factors

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Shi, Yanmei Hao, Meiling Tang, Yanlin Lian, Heng Guo, Xu School of Statistics Beijing Normal University Beijing China School of Statistics University of International Business and Economics Beijing China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE School of Statistics East China Normal University Shanghai China Department of Mathematics City University of Hong Kong Hong Kong

Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index Model. We first address the concern whether it is necessary to consider the augmented part by introducing a score-type test statistic. Compared with previous test statistics, our proposed test statistic does not need to estimate the high-dimensional regression coefficients, nor high-dimensional precision matrix, making it simpler in implementation. We also propose a Gaussian multiplier bootstrap to determine the critical value. The validity of our procedure is theoretically established under suitable conditions. We further investigate the penalized estimation of the regression model. With estimated latent factors, we establish the error bounds of the estimators. Lastly, we introduce debiased estimator and construct confidence interval for individual coefficient based on the asymptotic normality. No moment condition for the error term is imposed for our proposal. Thus our procedures work well when random error follows heavy-tailed distributions or when outliers are present. We demonstrate the finite sample performance of the proposed method through comprehensive numerical studies and its application to an FRED-MD macroeconomics dataset. Copyright © 2025, The Authors. All rights reserved.

关键词： Random errors

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

学校读者我要写书评

暂无评论

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