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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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Variational Bayesian Tensor Quantile Regression

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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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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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Hybrid Surrogate modeling Approach for data Reduction and Design Space Exploration of Turbine Blades

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Journal of Engineering for Gas Turbines and Power 2025年第7期147卷 071004页

作者： Ali, Sazeed S. Yadav, Vikas S. Nouri, Behnam Ghani, Abdulla Tools and Data Applications Siemens Energy AG Huttenstr. 12 Berlin10553 Germany Data Analysis and Modeling of Turbulent Flows Technische Universität Berlin Müller-Breslau-Straße 15 Berlin10623 Germany Chair of Data Analysis and Modeling of Turbulent Flows Technische Universität Berlin Müller-Breslau-Straße 15 Berlin10623 Germany

The conventional iterative optimization of turbine blades using computer-aided engineering simulations is resource-intensive, with high costs and time demands, as well as significant challenges in computational requirements and data management. The three-dimensional (3D) simulation data generated from computational fluid dynamics (CFD) and finite element analysis (FEA) for various blade geometries can range from hundreds of gigabytes to multiple terabytes, complicating long-term storage and access. To address this, we propose a machine learning-based methodology for data reduction and prediction of 3D surface field data. Our approach involves developing a convolutional variational auto-encoder (VAE), consisting of an encoder and a decoder. The encoder compresses the input data into a representation of reduced dimensionality in a latent space, while the decoder reconstructs the data from this latent space back to its original form. This significantly reduces the amount of stored data, facilitating long-term use. Additionally, we train a fully connected feedforward multilayer perceptron (MLP) to map geometry parameters, which generate blade variations, to the latent space. By combining the MLP with the VAE's trained decoder, we create our proposed multilayer perceptron-variational auto-encoder (MLP-VAE) hybrid model capable of predicting surface field data for new, unseen blade geometries. The MLP-VAE generates latent representations and surface field results with high accuracy (>97%) and without additional computational costs, offering a highly efficient and scalable solution for turbine blade optimization. Copyright © 2025 by Siemens Energy, Inc.

关键词： Computational fluid dynamics

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Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods? 41

Is Epistemic Uncertainty Faithfully Represented by Evidentia...

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41st International Conference on Machine Learning, ICML 2024

作者： Jürgens, Mira Meinert, Nis Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Department of Data Analysis and Mathematical Modeling Ghent University Belgium Neustrelitz Germany Germany

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures. Copyright 2024 by the author(s)

关键词： Contrastive Learning

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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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Forecasting stock market returns using deep learning and time series techniques: a comparative and empirical study using technical indicators

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Multimedia Tools and Applications 2024年 1-21页

作者： Fahd, Kalloubi Badr, Hirchoua Eddine, Labiad Salah Mouad, Aterhi LTI Laboratory National School of Applied Sciences El Jadida Morocco Casablanca Morocco Modeling Simulation and Data Analysis Mohammed VI Polytechnic University Ben Guerir Morocco

Deep learning models enable learning strategic and accurate behaviors. Nevertheless, training accurate models in dynamic environments, such as stock markets, has been a long-standing challenge. They suffer from partial observability, long-term dependencies, and require merging different handcrafted features. Moreover, selecting the model architecture and fine-tuning different parameters is very challenging. In this paper, we conduct a comparative and empirical study of different possible scenarios. We demonstrate and provide a solid recommendation for possible network architectures. Precisely, we compare different recurrent neural network models alongside time series techniques and report their influence on out-of-sample stock returns. Furthermore, we run an empirical study to determine the best features and hyperparameters using several feature importance techniques. Strong technical indicators have fueled the input prices to push the input representation forward. Extensive experiments have been presented to evaluate the performance of different models, and the results are critically analyzed and empirically verified. The results demonstrate that bidirectional recurrent neural networks and the autoregressive integrated moving average with explanatory variable model provide better performances in predicting the following day’s closing price and provide better references and insights for future investments. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Prediction models

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Feedback of Efficient Shock Acceleration on Magnetic-field Structure Inside Young Type Ia Supernova Remnants

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Research in Astronomy and Astrophysics 2024年第6期24卷 234-244页

作者： Jun-Yu Shen Bi-Wen Bao Li Zhang Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan ProvinceYunnan UniversityKunming 650091China Key Laboratory of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunming 650091China

Using an effective adiabatic index γ_(eff) to mimic the feedback of efficient shock acceleration,we simulate the temporal evolution of a young type Ia supernova remnant (SNR) with two different background magnetic field(BMF) topologies:a uniform and a turbulent *** density distribution and magnetic-field characteristics of our benchmark SNR are studied with two-dimensional cylindrical magnetohydrodynamic *** γ_(eff)is considered,we find that:(1) the two-shock structure shrinks and the downstream magnetic-field orientation is dominated by the Rayleigh–Taylor instability structures;(2) there exists more quasi-radial magnetic fields inside the shocked region;and (3) inside the intershock region,both the quasi-radial magnetic energy density and the total magnetic energy density are enhanced:in the radial direction,with γ_(eff)=1.1,they are amplified about 10–26 times more than those with γ_(eff)=5/*** in the angular direction,the total magnetic energy densities could be amplified about 350 times more than those with γ_(eff)=5/3,and there are more grid cells within the intershock region where the magnetic energy density is amplified by a factor greater than 100.

关键词： methods:numerical ISM:magnetic fields ISM:supernova remnants magnetohydrodynamics(MHD)

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Estimation of Treatment Effects in Nonlinear Models with Unobserved Confounding

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Acta Mathematicae Applicatae Sinica 2023年第2期39卷 320-336页

作者： Yu-ling LI Jun WANG Research Center for Applied Mathematics and Interdisciplinary Sciences Beijing Normal UniversityZhuhai 519087China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan UniversityKunming 650091China

Estimation of treatment effects is one of the crucial mainstays in economics and sociology *** problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved *** estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is *** this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear *** proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome *** proposed estimator is consistent and asymptotically normally *** studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error ***,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.

关键词： nonlinear models quasi likelihood estimator stable treatment effects unobserved confounding

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The superposition solution of positive quadratic function and arbitrary positive function of a (3+1)-dimensional soliton equation under vector representation

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Optical and Quantum Electronics 2025年第4期57卷 1-17页

作者： Sun, Wenlong Bilige, Sudao Shao, Hangbing Wang, Wenjing Department of Mathematics Inner Mongolia University of Technology Hohhot010051 China Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling Hohhot010051 China

The Hirota bilinear method was utilized to study a (3+1)-dimensional soliton equation, and we achieved success in obtaining a variety of solutions to the equation. Successfully yielding various solutions, such as lump solutions, rogue wave solutions, and interaction solutions. The first step in research is to transform the orginal equation into Hirota bilinear form. Through the symbolic calculation and the Cole-Hopf transformation, we obtain the solution of the original equation. Especially, we introduced vectors as tools to get the rational solutions of the equation. We make plots according to select different values of parameters, and the plots of various forms of solutions are dynamically analyzed to understand their physical significance. For the selection of trial functions, the first type is the positive quadratic functions, which can be used to obtain lump solutions and rogue wave solutions. The second type is the superposition of positive quadratic functions and positive arbitrary functions, resulting in an interaction solution consisting of both rational solution and arbitrary function solutions. We will provide examples to illustrate the interaction solutions formed by the superposition of positive quadratic and exponential functions, the superposition of positive quadratic, exponential and trigonometric functions, and the superposition of positive quadratic, exponential, trigonometric and hyperbolic functions. In short, we constructed different trial functions, so various new superposition solutions and wave motion were obtained. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Hyperbolic functions

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