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Variational Bayesian Tensor Quantile Regression

Acta Mathematica Sinica,English Series 2025年第2期41卷 733-756页

作者： Yunzhi Jin Yanqing Zhang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091P.R.China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Southwest United Graduate SchoolYunnan UniversityKunming 650091P.R.China

Quantile regression is widely used in variable relationship research for statistical *** quantile regression model is based on vector-valued covariates and can be efficiently estimated via traditional estimation ***,many modern applications involve tensor data with the intrinsic tensor *** quantile regression can not deal with tensor regression issues *** this end,we consider a tensor quantile regression with tensor-valued covariates and develop a novel variational Bayesian estimation approach to make estimation and prediction based on the asymmetric Laplace model and the CANDECOMP/PARAFAC decomposition of tensor *** incorporate the sparsity of tensor coefficients,we consider the multiway shrinkage priors for marginal factor vectors of tensor *** key idea of the proposed method is to efficiently combine the prior structural information of tensor and utilize the matricization of tensor decomposition to simplify the complexity of tensor coefficient *** coordinate ascent algorithm is employed to optimize variational lower *** studies and a real example show the numerical performances of the proposed method.

关键词： Asymmetric Laplace model CANDECOMP PARAFAC decomposition matricization tensor quantile regression variational Bayesian

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Efficient Estimation of Single-index Models with Deep ReQU Neural Networks

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Acta Mathematica Sinica,English Series 2025年第2期41卷 640-676页

作者： Zhihuang Yang Siming Zheng Niansheng Tang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091P.R.China School of Medicine Yale UniversityNew HavenCT 06520USA

Single-index model offers the greater flexibility of modelling than generalized linear models and also retains the interpretability of the model to some extent. Although many standard approaches such as kernels or penalized/smooothing splines were proposed to estimate smooth link function, they cannot approximate complicated unknown link functions together with the corresponding derivatives effectively due to their poor approximation ability for a finite sample size. To alleviate this problem, this paper proposes a semiparametric least squares estimation approach for a single-index model using the rectifier quadratic unit (ReQU) activated deep neural networks, called deep semiparametric least squares (DSLS) estimation method. Under some regularity conditions, we show non-asymptotic properties of the proposed DSLS estimator, and evidence that the index coefficient estimator can achieve the semiparametric efficiency. In particular, we obtain the consistency and the convergence rate of the proposed DSLS estimator when response variable is conditionally sub-exponential. This is an attempt to incorporate deep learning technique into semiparametrically efficient estimation in a single index model. Several simulation studies and a real example data analysis are conducted to illustrate the proposed DSLS estimator.

关键词： Asymptotical normality deep neural networks non-asymptotic estimation error bound semiparametric efficiency single-index models

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Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 84-98页

作者： Meng WANG Ming-liang SHU Jian-jun ZHOU Si-xin WU Min CHEN School of Management University of Science and Technology of ChinaHefei 230026China Academy of Mathematics and System Science Chinese Academy of SciencesBeijing 100190China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.

关键词： multiple functional linear model autoregressive errors principal component analysis consistency

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Testing High-Dimensional Means for Sparse Signals

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Communications in Mathematics and Statistics 2025年 1-31页

作者： Zhu, Jiayan Yu, Xiaochen Pan, Dongdong Li, Zhengbang School of Information Engineering Hubei University of Chinese Medicine Wuhan China School of Mathematics and Statistics Central China Normal University Wuhan China Yunnan Key Laboratory of Statistical Modeling and Data Analysis School of Mathematics and Statistics Yunnan University Kunming China

In this paper, we investigate the high-dimensional mean vector testing problem with fewer observations than the dimension. We revisit a kind of test which belongs to the supremum-type statistic and propose a novel test by the combination of the maximum and minimum values among all component tests. The asymptotic null distributions of two tests are obtained and the asymptotical powers against sparse alternatives are also investigated under weak conditions. Simulation results show that these two tests can control empirical sizes well. Our novel test can gain desirable powers. A real data example about Electro-Encephalo Gram measurements also demonstrates that our proposed test has desirable numerical performances. © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

关键词： Asymptotic theories for extremes Asymptotic theories for extremes Behrens-Fisher problem Behrens-Fisher problem High-dimensional central limit theorems High-dimensional central limit theorems High-dimensional data High-dimensional data

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Evidence for Magneto-gravitational Processes in Supermassive Black Hole Binary PG 1553+113

arXiv

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arXiv 2025年

作者： Haiyun, Zhang Dahai, Yan Li, Zhang Niansheng, Tang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan Province Yunnan University Kunming650091 China

PG 1553+113 has drawn significant attention for its quasi-periodic oscillation (QPO) in Υ-ray variability, though the origin of its variability remains uncertain. In this study, we propose a physical mechanism to explain the observed Υ-ray variability within the framework of a supermassive black hole binary (SMBHB) system, supported by a newly identified component hidden in the light curve. A detailed analysis for its ∼16-year light curve obtained from Fermi-LAT observations is performed by Gaussian process (GP). As anticipated, the QPO of 2.1 years (771 ± 8 days) is effectively captured by the stochastically-driven damped simple harmonic oscillator (SHO) kernel within the under-damped regime, and the overall stochastic nature of the variability is described by the damped random walk (DRW) kernel albeit with an unconstrained damping timescale. Additionally, our results reveal a previously unrecognized component in active galactic nuclei variability, characterized by the Matérn−3/2 kernel, which is typically associated with systems undergoing abrupt energy release. These findings can be consistently interpreted within the SMBHB framework. The QPO of ∼2.1 years is likely attributed to the orbital motion in a SMBHB system. The Matérn−3/2 component is interpreted as resulting from magnetic reconnection events triggered by gravitational perturbations of the magnetic field within the jet, occurring as one black hole approaches the other. Meanwhile, in this case, the damping timescale of the common DRW kernel remains unconstrained due to the influence of new perturbations within the system. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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statistical inference for smoothed quantile regression with streaming data

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Journal of Econometrics 2025年 249卷

作者： Xie, Jinhan Yan, Xiaodong Jiang, Bei Kong, Linglong Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Mathematical and Statistical Sciences University of Alberta Edmonton AlbertaT6G 2G1 Canada School of Mathematics and Statistics Xi'an Jiaotong University China

In this paper, we tackle the problem of conducting valid statistical inference for quantile regression with streaming data. The main difficulties are that the quantile regression loss function is non-smooth and it is often infeasible to store the entire dataset in memory, rendering traditional methodologies ineffective. We introduce a fully online updating method for statistical inference in smoothed quantile regression with streaming data to overcome these issues. Our main contributions are twofold. First, for low-dimensional data, we present an incremental updating algorithm to obtain the smoothed quantile regression estimator with the streaming data set. The proposed estimator allows us to construct asymptotically exact statistical inference procedures. Second, within the realm of high-dimensional data, we develop an online debiased lasso procedure to accommodate the special sparse structure of streaming data. The proposed online debiased approach is updated with only the current data and summary statistics of historical data and corrects an approximation error term from online updating with streaming data. Furthermore, theoretical results such as estimation consistency and asymptotic normality are established to justify its validity in both settings. Our findings are supported by simulation studies and illustrated through applications to Seoul's bike-sharing demand data and index fund data. © 2024

关键词： Logistic regression

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Pattern and Origin for the Extreme γ-ray Flares of 3C 454.3 and 3C 279: An Astrophysical Critical Damper?

arXiv

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arXiv 2025年

作者： Zhang, Haiyun Yan, Dahai Zhou, Jianeng Zhang, Li Tang, Niansheng Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan Province Yunnan University Kunming650091 China Shanghai Astronomical Observatory Chinese Academy of Sciences 80 Nandan Road Shanghai200030 China

We apply a Gaussian process method to the extreme γ-ray flares of 3C 454.3 and 3C 279 to discover the variable patterns and then to investigate the physical origins of the giant flares. The kernels of stochastically driven damped simple harmonic oscillator (SHO), the damped random-walk (DRW), and Matérn−3/2 are respectively used to describe the adaptive-binning γ-ray light curves of the two flares. Our findings show that both the extreme γ-ray flares of 3C 454.3 and 3C 279 clearly prefer the SHO kernel in the over-damped mode and the Matérn−3/2 kernel over the DRW kernel. The resulted SHO and Matérn−3/2 power spectral densities (PSDs) are the same for each object, with the index changing from -4 at high frequencies to 0 at low frequencies. The patterns of the two flares are both approaching the critical damping mode with the quality factor Q ≈ 0.4 (i.e., the damping ratio η ≈ 1.25), but with slightly different damping timescales. The characteristic timescale (corresponding to the broken frequency in the PSD) for 3C 454.3 is 2-3 days and 3-5 days for 3C 279. The variable patterns found here suggest that once the system responds to the energy injection disturbance, the release of the energy in the system is finished abruptly. The obtained timescale provides a constraint on the size of energy dissipation region for each source. Copyright © 2025, The Authors. All rights reserved.

关键词： Gamma rays

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Self-supervised distributional and contrastive learning model for image anomaly detection

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Knowledge-Based Systems 2025年 316卷

作者： Pu, Yannan Sun, Jian Tang, Niansheng Xu, Zongben Department of Surgical Intensive Care Unit The First Affiliated Hospital of Xi'an Jiaotong University Xi'an Shaanxi710061 China School of Mathematics and Statistic Xi'an Jiaotong University Xi'an China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650500 China

Anomaly detection is a critical task in computer vision and machine learning, which aims to detect anomalies that are away from the distribution of normal data. Prevalent methods perform anomaly detection via pretraining the model or constructing pretext tasks based on instance-level contrastive learning. However, they ignore the underlying distribution of features for normal data, which is crucial for detecting anomalies. In this paper, we propose a self-supervised distributional and contrastive learning model for anomaly detection. For distributional modeling, based on the augmented dataset with given rotated images, we propose to model latent features of normal sample set under each rotation transformation via a Gaussian Mixture Model (GMM). By the proposed GMM clustering loss, we maximize the probability of data to the GMM model with rotation that is applied to the data, and minimize its probability to the GMMs of other rotations. For contrastive learning, we discriminate augmented features via rotation-based contrastive learning that constructs positive pairs augmented from the same instance under the same rotation and negative pairs augmented from different instances under rotations. Our approach jointly conducts distributional modeling of image features considering feature clustering properties, and discriminative learning of features in a self-supervised way. We also design detection scores from different modules to detect anomalies. Extensive experiments on image datasets (e.g., CIFAR-10, CIFAR-100 and ImageNet-30) demonstrate that our method achieves favorable performance compared with several state-of-the-art methods on unsupervised image anomaly detection tasks. Ablation studies demonstrate the effectiveness of the key modules in our model. © 2025 Elsevier B.V.

关键词： Self-supervised learning

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Moment Selection and Generalized Empirical Likelihood Estimation in High-Dimensional Unconditional Moment Conditions

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Journal of Systems Science & Complexity 2024年第6期37卷 2738-2770页

作者： WANG Wenjun YANG Zhihuang Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.

关键词： Fantope projection and selection generalized empirical likelihood high dimensionality moment selection unconditional moment condition

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Diagnostic Measures for Functional Linear Model with Nonignorable Missing Responses

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Communications in Mathematics and Statistics 2024年第3期12卷 543-562页

作者： Yujian Zhu Puying Zhao Key Lab of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunmingPeople’s Republic of China

Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to *** this paper,we introduce three case-deletion diagnostic measures to identify influential observations in functional linear models when the covariate is functional and observations on the scalar response are subject to nonignorable *** nonignorable missing data mechanism is modeled via an exponential tilting semiparametric functional model.A semiparametric imputation procedure is developed to mitigate the effects of missing *** estimations of the functional coefficients are based on functional principal components analysis using the imputed dataset.A smoothed bootstrap samplingmethod is introduced to estimate the diagnostic probability for each proposed diagnostic measure,which is helpful to unveil which observations have the larger influence on estimation and *** studies and a real data example are conducted to illustrate the finite performance of the proposed methods.

关键词： Case deletion Diagnostic measure Functional linear model Nonignorable nonresponse Semiparametric imputation

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