arXiv subjects

Xu Guo

Publications and source records attributed to Xu Guo.

At least 91 records · Page 5Linked to original sources

arXiv2024

Test and Measure for Partial Mean Dependence Based on Machine Learning Methods

It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based on machine learning methods and data splitting. The test statistic converges to the standard chi-squared distribution under the null hypothesis while it converges to a normal distribution under the fixed alternative hypothesis. Power enhancement and algorithm stability are also discussed. If the null hypothesis is rejected, we propose a partial Generalized Measure of Correlation (pGMC) to measure the partial mean dependence of $Y$ given $W$ after controlling for the nonlinear effect of $Z$. We present the appealing theoretical properties of the pGMC and establish the asymptotic normality of its estimator with the optimal root-$N$ convergence rate. Furthermore, the valid confidence interval for the pGMC is also derived. As an important special case when there are no conditional covariates $Z$, we introduce a new test of overall significance of covariates for the response in a model-free setting. Numerical studies and real data analysis are also conducted to compare with existing approaches and to demonstrate the validity and flexibility of our proposed procedures.

stat.ME↗

arXiv2024

A class of new linear, efficient and high-order implicit-explicit methods for the coupled free flow-porous media system based on nonlinear Lions interface condition

In this paper, we construct and analyze new first- and second-order implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system, which is based on the scalar auxiliary variable (SAV) approach in time and finite element method in space. The constructed schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and can decouple the Navier-Stokes and Darcy systems. The unconditional stability of both the first- and second-order IMEX schemes can be derived for the coupled system equipped with the Lions interface condition, where the key point is that we should construct a new trilinear form to balance the fully explicit discretizations of the nonlinear terms in the complex system. We can also establish rigorous error estimates for the velocity and hydraulic head of the first-order scheme without any time step restriction. Numerical examples are presented to validate the proposed schemes.

math.NA↗

arXiv2024

Model-free controlled variable selection via data splitting

Addressing the simultaneous identification of contributory variables while controlling the false discovery rate (FDR) in high-dimensional data is a crucial statistical challenge. In this paper, we propose a novel model-free variable selection procedure in sufficient dimension reduction framework via a data splitting technique. The variable selection problem is first converted to a least squares procedure with several response transformations. We construct a series of statistics with global symmetry property and leverage the symmetry to derive a data-driven threshold aimed at error rate control. Our approach demonstrates the capability for achieving finite-sample and asymptotic FDR control under mild theoretical conditions. Numerical experiments confirm that our procedure has satisfactory FDR control and higher power compared with existing methods.

stat.ME↗

arXiv2024

Estimation and Inference in Ultrahigh Dimensional Partially Linear Single-Index Models

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference problem very challenging. In this paper, we first propose a profile partial penalized least squares estimator and establish the sparsity, consistency and asymptotic representation of the proposed estimator in ultrahigh dimensional setting. We then propose an $F$-type test statistic for parameters of primary interest and show that the limiting null distribution of the test statistic is $χ^2$ distribution, and the test statistic can detect local alternatives, which converge to the null hypothesis at the root-$n$ rate. We further propose a new test for the specification testing problem of the nonparametric function. The test statistic is shown to be asymptotically normal. Simulation studies are conducted to examine the finite sample performance of the proposed estimators and tests. A real data example is used to illustrate the proposed procedures.

stat.ME↗

arXiv2024

Gradient based Feature Attribution in Explainable AI: A Technical Review

The surge in black-box AI models has prompted the need to explain the internal mechanism and justify their reliability, especially in high-stakes applications, such as healthcare and autonomous driving. Due to the lack of a rigorous definition of explainable AI (XAI), a plethora of research related to explainability, interpretability, and transparency has been developed to explain and analyze the model from various perspectives. Consequently, with an exhaustive list of papers, it becomes challenging to have a comprehensive overview of XAI research from all aspects. Considering the popularity of neural networks in AI research, we narrow our focus to a specific area of XAI research: gradient based explanations, which can be directly adopted for neural network models. In this review, we systematically explore gradient based explanation methods to date and introduce a novel taxonomy to categorize them into four distinct classes. Then, we present the essence of technique details in chronological order and underscore the evolution of algorithms. Next, we introduce both human and quantitative evaluations to measure algorithm performance. More importantly, we demonstrate the general challenges in XAI and specific challenges in gradient based explanations. We hope that this survey can help researchers understand state-of-the-art progress and their corresponding disadvantages, which could spark their interest in addressing these issues in future work.

cs.AI↗

arXiv2024

Generative AI for Synthetic Data Generation: Methods, Challenges and the Future

The recent surge in research focused on generating synthetic data from large language models (LLMs), especially for scenarios with limited data availability, marks a notable shift in Generative Artificial Intelligence (AI). Their ability to perform comparably to real-world data positions this approach as a compelling solution to low-resource challenges. This paper delves into advanced technologies that leverage these gigantic LLMs for the generation of task-specific training data. We outline methodologies, evaluation techniques, and practical applications, discuss the current limitations, and suggest potential pathways for future research.

cs.LG↗

arXiv2024

Optimal design of fast topological pumping

Utilizing synthetic dimensions generated by spatial or temporal modulation, topological pumping enables the exploration of higher-dimensional topological phenomena through lower-dimensional physical systems. In this letter, we propose a rational design paradigm of fast topological pumping based on 1D and 2D time-modulated discrete elastic lattices for the first time. Firstly, the realization of topological pumping is ensured by introducing quantitative indicators to drive a transition of the edge or corner state in the lattice spectrum. Meanwhile, with the help of limiting speed for adiabaticity to calculate the modulation time, a mathematical formulation of designing topological pumping with the fastest modulation speed is presented. By applying the proposed design paradigm, topological edge-bulk-edge and corner-bulk-corner energy transport are successfully achieved, with 11.2 and 4.0 times of improvement in modulation speed compared to classical pumping systems in the literature. In addition, applying to 1D and 2D space-modulated systems, the optimized modulation schemes can reduce the number of stacks to 5.3% and 26.8% of the classical systems while ensuring highly concentrated energy transport. This design paradigm is expected to be extended to the rational design of fast topological pumping in other physical fields.

cond-mat.other↗

arXiv2024

Real-time generative design of diverse, "truly" optimized structures with controllable structural complexities

Compared with traditional design methods, generative design significantly attracts engineers in various disciplines. In thiswork, howto achieve the real-time generative design of optimized structures with various diversities and controllable structural complexities is investigated. To this end, a modified Moving Morphable Component (MMC) method together with novel strategies are adopted to generate high-quality dataset. The complexity level of optimized structures is categorized by the topological invariant. By improving the cost function, the WGAN is trained to produce optimized designs with the input of loading position and complexity level in real time. It is found that, diverse designs with a clear load transmission path and crisp boundary, even not requiring further optimization and different from any reference in the dataset, can be generated by the proposed model. This method holds great potential for future applications of machine learning enhanced intelligent design.

cs.CE↗

arXiv2024

Shell-infill composite structure design based on a hybrid explicit-implicit topology optimization method

The present paper introduces a hybrid explicit-implicit topology optimization method for shell-infill composite structure design. The proposed approach effectively combines the advantages of the explicit Moving Morphable Component (MMC) method, which describes structural topology only using a set of geometric parameters, and the implicit Solid Isotropic Material with Penalization (SIMP) method, which offers greater design freedom for characterizing the structural features. Compared to the existing methods for shell-infill structure design, the proposed approach can obtain optimized shell-infill structures with complex infill topology without resorting to complex filtering/projection operations. Numerical examples demonstrate the effectiveness of the proposed approach.

math.OC↗

arXiv2024

Explicit design optimization of air rudders for maximizing stiffness and fundamental frequency

In aerospace engineering, there is a growing demand for lightweight design through topology optimization. This paper presents a novel design optimization method for stiffened air rudders, commonly used for aircraft attitude control, based on the Moving Morphable Components (MMC) method. The stiffeners within the irregular enclosed design domain are modeled as MMCs and discretized by shell elements, accurately capturing their geometry and evolution during optimization process using explicit parameters. In order to maximize the stiffness and fundamental frequency of the rudder structures, numerical analysis algorithms were developed with shape sensitivity analysis conducted. To comply with the manufacturing requirement, a minimum thickness is prescribed for the stiffeners. Penalty strategies were developed for the thickness and density of stiffeners with thickness smaller than the threshold to meet the thickness requirement and suppress spurious modes. The method's effectiveness was demonstrated through optimization examples of two typical air rudders, illustrating the significance of stiffener's distribution on design objectives. The explicit modeling characteristics allow for directly importing the optimization results into CAD systems, significantly enhancing the engineering applicability.

math.OC↗

arXiv2023

Training on Synthetic Data Beats Real Data in Multimodal Relation Extraction

The task of multimodal relation extraction has attracted significant research attention, but progress is constrained by the scarcity of available training data. One natural thought is to extend existing datasets with cross-modal generative models. In this paper, we consider a novel problem setting, where only unimodal data, either text or image, are available during training. We aim to train a multimodal classifier from synthetic data that perform well on real multimodal test data. However, training with synthetic data suffers from two obstacles: lack of data diversity and label information loss. To alleviate the issues, we propose Mutual Information-aware Multimodal Iterated Relational dAta GEneration (MI2RAGE), which applies Chained Cross-modal Generation (CCG) to promote diversity in the generated data and exploits a teacher network to select valuable training samples with high mutual information with the ground-truth labels. Comparing our method to direct training on synthetic data, we observed a significant improvement of 24.06% F1 with synthetic text and 26.42% F1 with synthetic images. Notably, our best model trained on completely synthetic images outperforms prior state-of-the-art models trained on real multimodal data by a margin of 3.76% in F1. Our codebase will be made available upon acceptance.

cs.AI↗

arXiv2023

Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe3Sn Kagome and Sn2 honeycomb layers. On the Fe3Sn layer terminated FeSn thin films epitaxially grown on SrTiO3(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the transitional symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

cond-mat.mtrl-sci↗

arXiv2023

Compressing the memory variables in constant-Q viscoelastic wave propagation via an improved sum-of-exponentials approximation

Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a reliable model for frequency-independent Q anelastic behavior. Nonetheless, the numerical resolution of this equation poses considerable challenges due to the requirement of storing a complete time history of wavefields. To address this computational challenge, we present a novel approach: a nearly optimal sum-of-exponentials (SOE) approximation to the Caputo fractional derivative with very small fractional exponent, utilizing the machinery of generalized Gaussian quadrature. This method minimizes the number of memory variables needed to approximate the power attenuation law within a specified error tolerance. We establish a mathematical equivalence between this SOE approximation and the continuous fractional stress-strain relationship, relating it to the generalized Maxwell body model. Furthermore, we prove an improved SOE approximation error bound to thoroughly assess the ability of rheological models to replicate the power attenuation law. Numerical simulations on constant-Q viscoacoustic equation in 3D homogeneous media and variable-order P- and S- viscoelastic wave equations in 3D inhomogeneous media are performed. These simulations demonstrate that our proposed technique accurately captures changes in amplitude and phase resulting from material anelasticity. This advancement provides a significant step towards the practical usage of the time-fractional wave equation in seismic inversion.

math.NA↗

arXiv2023

Training Multimedia Event Extraction With Generated Images and Captions

Contemporary news reporting increasingly features multimedia content, motivating research on multimedia event extraction. However, the task lacks annotated multimodal training data and artificially generated training data suffer from distribution shift from real-world data. In this paper, we propose Cross-modality Augmented Multimedia Event Learning (CAMEL), which successfully utilizes artificially generated multimodal training data and achieves state-of-the-art performance. We start with two labeled unimodal datasets in text and image respectively, and generate the missing modality using off-the-shelf image generators like Stable Diffusion and image captioners like BLIP. After that, we train the network on the resultant multimodal datasets. In order to learn robust features that are effective across domains, we devise an iterative and gradual training strategy. Substantial experiments show that CAMEL surpasses state-of-the-art (SOTA) baselines on the M2E2 benchmark. On multimedia events in particular, we outperform the prior SOTA by 4.2% F1 on event mention identification and by 9.8% F1 on argument identification, which indicates that CAMEL learns synergistic representations from the two modalities. Our work demonstrates a recipe to unleash the power of synthetic training data in structured prediction.

cs.MM↗

arXiv2023

A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components

In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues, including topology optimization, reinforced-rib layout optimization, and sandwich structure design problems. The complexity of thin-walled structures mainly comes from flexible geometries and the variation of thickness. On the one hand, the geometric complexity of thin-walled structures leads to the difficulty in automatically describing material distribution (e.g., reinforced ribs). On the other hand, thin-walled structures with different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell theory and Reissner-Mindlin shell theory) to ensure the precision of structural responses. Whereas for cases that do not fit the shell hypothesis, the precision loss of response solutions is nonnegligible in the optimization process since the accumulation of errors will cause entirely different designs. Hence, the current article proposes a novel embedded solid component to tackle these challenges. The geometric constraints that make the components fit to the curved thin-walled structure are whereby satisfied. Compared with traditional strategies, the proposed method is free from the limit of shell assumptions of structural analysis and can achieve optimized designs with clear load transmission paths at the cost of few design variables and degrees of freedom for finite element analysis (FEA). Finally, we apply the proposed method to several representative examples to demonstrate its effectiveness, efficiency, versatility, and potential to handle complex industrial structures.

cs.GR↗

arXiv2023

Semiparametric efficient estimation of genetic relatedness with machine learning methods

In this paper, we propose semiparametric efficient estimators of genetic relatedness between two traits in a model-free framework. Most existing methods require specifying certain parametric models involving the traits and genetic variants. However, the bias due to model misspecification may yield misleading statistical results. Moreover, the semiparametric efficient bounds for estimators of genetic relatedness are still lacking. In this paper, we develop semiparametric efficient estimators with machine learning methods and construct valid confidence intervals for two important measures of genetic relatedness: genetic covariance and genetic correlation, allowing both continuous and discrete responses. Based on the derived efficient influence functions of genetic relatedness, we propose a consistent estimator of the genetic covariance as long as one of genetic values is consistently estimated. The data of two traits may be collected from the same group or different groups of individuals. Various numerical studies are performed to illustrate our introduced procedures. We also apply proposed procedures to analyze Carworth Farms White mice genome-wide association study data.

stat.ME↗

arXiv2023

Tests for ultrahigh-dimensional partially linear regression models

In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt machine learning methods to estimate the unknown nuisance function and introduce quadratic-form test statistics. Interestingly, though the machine learning methods can be very complex, under suitable conditions, we establish the asymptotic normality of our introduced test statistics under the null hypothesis and local alternative hypotheses. We further propose a power-enhanced procedure to improve the test statistics' performance. Two thresholding determination methods are provided for the power-enhanced procedure. We show that the power-enhanced procedure is powerful to detect signals under either sparse or dense alternatives and it can still control the type-I error asymptotically under the null hypothesis. Numerical studies are carried out to illustrate the empirical performance of our introduced procedures.

stat.ME↗

arXiv2023

Distributed local spline simulator for wave propagation

Numerical simulation of wave propagation in elastic media faces the challenges arising from increasing demand of high resolution in modern 3-D imaging applications, which requires a balance between efficiency and accuracy in addition to being friendly to the distributed high-performance computing environment. In this paper, we propose a distributed local spline simulator (LOSS) for solving the wave equation. LOSS uses patched cubic B-splines to represent the wavefields and attains an accurate evaluation of spatial derivatives with linear complexity. In order to link the adjacent patches, a perfectly matched boundary condition is introduced to give a closure of local spline coefficients. Owing to the rapid decay property of the local wavelets in dual space, it can recover the global spline as accurately as possible only at the cost of local communications among adjacent neighbors. Several typical numerical examples, including 2-D acoustic wave equation and P- and S- wave propagation in 3-D homogenous or heterogenous media, are provided to validate its convergence, accuracy and parallel scalability.

math.NA↗