Searcharxiv⌕ Search

arXiv subjects

Weiming Li

Publications and source records attributed to Weiming Li.

54 records · Page 3Linked to original sources

Adversarial samples for deep monocular 6D object pose estimation

Estimating 6D object pose from an RGB image is important for many real-world applications such as autonomous driving and robotic grasping. Recent deep learning models have achieved significant progress on this task but their robustness received little research attention. In this work, for the first time, we study adversarial samples that can fool deep learning models with imperceptible perturbations to input image. In particular, we propose a Unified 6D pose estimation Attack, namely U6DA, which can successfully attack several state-of-the-art (SOTA) deep learning models for 6D pose estimation. The key idea of our U6DA is to fool the models to predict wrong results for object instance localization and shape that are essential for correct 6D pose estimation. Specifically, we explore a transfer-based black-box attack to 6D pose estimation. We design the U6DA loss to guide the generation of adversarial examples, the loss aims to shift the segmentation attention map away from its original position. We show that the generated adversarial samples are not only effective for direct 6D pose estimation models, but also are able to attack two-stage models regardless of their robust RANSAC modules. Extensive experiments were conducted to demonstrate the effectiveness, transferability, and anti-defense capability of our U6DA on large-scale public benchmarks. We also introduce a new U6DA-Linemod dataset for robustness study of the 6D pose estimation task. Our codes and dataset will be available at \url{https://github.com/cuge1995/U6DA}.

cs.CV↗

3D Adversarial Attacks Beyond Point Cloud

Recently, 3D deep learning models have been shown to be susceptible to adversarial attacks like their 2D counterparts. Most of the state-of-the-art (SOTA) 3D adversarial attacks perform perturbation to 3D point clouds. To reproduce these attacks in the physical scenario, a generated adversarial 3D point cloud need to be reconstructed to mesh, which leads to a significant drop in its adversarial effect. In this paper, we propose a strong 3D adversarial attack named Mesh Attack to address this problem by directly performing perturbation on mesh of a 3D object. In order to take advantage of the most effective gradient-based attack, a differentiable sample module that back-propagate the gradient of point cloud to mesh is introduced. To further ensure the adversarial mesh examples without outlier and 3D printable, three mesh losses are adopted. Extensive experiments demonstrate that the proposed scheme outperforms SOTA 3D attacks by a significant margin. We also achieved SOTA performance under various defenses. Our code is available at: https://github.com/cuge1995/Mesh-Attack.

cs.CV↗

Eigenvalue distribution of a high-dimensional distance covariance matrix with application

We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance covariance matrix when the dimensions of the vectors and the sample size tend to infinity simultaneously. This limit is valid when the vectors are independent or weakly dependent through a finite-rank perturbation. It is also universal and independent of the details of the distributions of the vectors. Furthermore, the top eigenvalues of this distance covariance matrix are shown to obey an exact phase transition when the dependence of the vectors is of finite rank. This finding enables the construction of a new detector for such weak dependence where classical methods based on large sample covariance matrices or sample canonical correlations may fail in the considered high-dimensional framework.

math.ST↗

Direct Flux Gradient Approximation to Close Moment Model for Kinetic Equations

To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure approach with remarkable advantages than the canonical approach. Instead of approximating the flux function, the new approach close the moment model by approximating the flux gradient. Precisely, we approximate the space derivative of the distribution function by an ansatz which is a weighted polynomial, and the derivative of the closing flux is computed by taking the moments of the ansatz. Consequently, the method provides us an improved framework to derive globally hyperbolic moment models, which preserve all those conservative variables in the low order moments. It is shown that the linearized system at the weight function, which is often the local equilibrium, of the moment model deduced by our new approach is automatically coincided with the system deduced from the classical perturbation theory, which can not be satisfied by previous hyperbolic regularization framework. Taking the Boltzmann equation as example, the linearlization of the moment model gives the correct Navier-Stokes-Fourier law same as that the Chapman-Enskog expansion gives. Most existing globally hyperbolic moment models are re-produced by our new approach, and several new models are proposed based on this framework.

physics.comp-ph↗

On eigenvalues of a high-dimensional spatial-sign covariance matrix

This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general enough to include the popular independent components model and the family of elliptical distributions. A first result of the paper establishes that the distribution of the eigenvalues converges to a deterministic limit that belongs to the family of generalized Marcenko-Pastur distributions. Furthermore, a new central limit theorem is established for a class of linear spectral statistics. We develop two applications of these results to robust statistics for a high-dimensional shape matrix. First, two statistics are proposed for testing the sphericity. Next, a spectrum-corrected estimator using the sample spatial-sign covariance matrix is proposed. Simulation experiments show that in high dimension, the sample spatial-sign covariance matrix provides a valid and robust tool for mitigating influence of outliers.

math.ST↗

A hybrid moment method for multi-scale kinetic equations based on maximum entropy principle

We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When transiting from the fluid regime to the kinetic regime, the maximum entropy principle is adopted to reconstruct the kinetic distribution function, so that the information in the fluid region can be utilized thoroughly. Moreover, only one uniform set of numerical scheme is needed for both the fluid and kinetic regions. Numerical tests show the high efficiency of this new hybrid method.

physics.comp-ph↗

Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multiscale photon transport. In this method, the photon free streaming and scattering processes are treated in an un-splitting way. The duality descriptions, namely the simulation particle and distribution function, are utilized to describe the photon. By accurately recovering the governing equations of the unified gas-kinetic scheme (UGKS), the UGKWP preserves the multiscale dynamics of photon transport from optically thin to optically thick regime. In the optically thin regime, the UGKWP becomes a Monte Carlo type particle tracking method, while in the optically thick regime, the UGKWP becomes a diffusion equation solver. The local photon dynamics of the UGKWP, as well as the proportion of wave-described and particle-described photons are automatically adapted according to the numerical resolution and transport regime. Compared to the $S_n$ -type UGKS, the UGKWP requires less memory cost and does not suffer ray effect. Compared to the implicit Monte Carlo (IMC) method, the statistical noise of UGKWP is greatly reduced and computational efficiency is significantly improved in the optically thick regime. Several numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the UGKWP method. In comparison to the $S_n$ -type UGKS and IMC method, the UGKWP method may have several-order-of-magnitude reduction in computational cost and memory requirement in solving some multsicale transport problems.

physics.comp-ph↗

A Nonlinear Three-Moment Model for Radiative Transfer in Spherical Symmetry

We study the approximation of the radiative transfer equation with a relatively few moments in the spherically symmetric case. We propose a three-moment model based on choosing the beta distribution as the ansatz for the specific intensity. This ansatz enables our model to capture the anisotropy in the distribution function. The characteristic structure of the Riemann problem of the model is studied in detail. Numerical simulations demonstrate its validity in approximating the radiative transfer equation in the spherically symmetric case and its advantage in approximating highly anisotropic distribution functions in comparison to the $P_n$ method.

physics.comp-ph↗

A Unified Gas-kinetic Particle Method for Multiscale Photon Transport

In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes from the recovery of the time evolution flux function in the unified gas-kinetic scheme (UGKS) through a coupled dynamic process of particle transport and collision. This practice improves the original operator splitting approach in the Monte Carlo method, such as the separated treatment of particle transport and collision. As a result, with the variation of the ratio between numerical time step and local photon's collision time, different transport physics can be fully captured in a single computation. In the diffusive limit, the UGKP method could recover the solution of the diffusion equation with the cell size and time step being much larger than the photon's mean free path and the mean collision time. In the free transport limit, it presents an exact particle tracking process as the original Monte Carlo method. In the transition regime, the weights of particle free transport and collision are determined by the ratio of local numerical time step to the photon's collision time. Several one-dimensional numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the current scheme. In comparison with the $S_N$ discrete ordinate method, the UGKP method is based on particles and avoids the discretization of particle velocity space, which does not suffer from the ray effect.

physics.comp-ph↗

High-dimensional covariance matrices in elliptical distributions with application to spherical test

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of elliptical populations. This general theoretical result has wide applications and, as an example, it is then applied to test the sphericity of elliptical populations.

math.ST↗

Joint CLT for eigenvalue statistics from several dependent large dimensional sample covariance matrices with application

Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices $\mathbf{B}_{nr}=\frac1n \mathbf{Q}_r \mathbf{X}_n \mathbf{X}_n^*\mathbf{Q}_r^\top,~1\le r\le R$, where the $\mathbf{Q}_{r}$'s are nonrandom real matrices with common dimensions $p\times k~(k\geq p)$. Assuming that both the dimension $p$ and the sample size $n$ grow to infinity, the limiting distributions of the eigenvalues of the matrices $\{\mathbf{B}_{nr}\}$ are identified, and as the main result of the paper, we establish a joint central limit theorem for linear spectral statistics of the $R$ matrices $\{\mathbf{B}_{nr}\}$. Next, this new CLT is applied to the problem of testing a high dimensional white noise in time series modelling. In experiments the derived test has a controlled size and is significantly faster than the classical permutation test, though it does have lower power. This application highlights the necessity of such joint CLT in the presence of several dependent sample covariance matrices. In contrast, all the existing works on CLT for linear spectral statistics of large sample covariance matrices deal with a single sample covariance matrix ($R=1$).

math.ST↗

3D B_2 Model for Radiative Transfer Equation Part I: Modelling

We extend to three-dimensional space the approximate M_2 model for the slab geometry studied in our previous paper. The B_2 model therein, as a special case of the second order extended quadrature method of moments (EQMOM), is proved to be globally hyperbolic. The model we proposed here extends EQMOM to multiple dimensions following the idea to approximate the maximum entropy closure for the slab geometry case. Like the M_2 closure, the ansatz of the new model has the capacity to capture both isotropic and beam-like solutions, while the new model has fluxes in closed-form, thus is applicable to practical numerical simulations. The rotational invariance, realizability, and hyperbolicity of the model are studied.

math.NA↗

On spectral properties of high-dimensional spatial-sign covariance matrices in elliptical distributions with applications

Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations, where both the dimension $p$ of observations and the sample size $n$ tend to infinity with their ratio $p/n\to c\in (0, \infty)$. The empirical spectral distribution of this nonparametric scatter matrix is shown to converge in distribution to a generalized Marčenko-Pastur law. Beyond this, a new central limit theorem (CLT) for general linear spectral statistics of the SSCM is also established. For polynomial spectral statistics, explicit formulae of the limiting mean and covarance functions in the CLT are provided. The derived results are then applied to an estimation procedure and a test procedure for the spectrum of the shape component of population covariance matrices.

math.ST↗

On structure testing for component covariance matrices of a high-dimensional mixture

By studying the family of $p$-dimensional scale mixtures, this paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix {\em does not converge} to the celebrated Marčenko-Pastur law. A different and new limit is found and characterized. The reasons of failure of the Marčenko-Pastur limit in this situation are found to be a strong dependence between the $p$-coordinates of the mixture. Next, we address the problem of testing whether the mixture has a spherical covariance matrix. To analize the traditional John's type test we establish a novel and general CLT for linear statistics of eigenvalues of the sample covariance matrix. It is shown that the John's test and its recent high-dimensional extensions both fail for high-dimensional mixtures, precisely due to the different spectral limit above. As a remedy, a new test procedure is constructed afterwards for the sphericity hypothesis. This test is then applied to identify the covariance structure in model-based clustering. It is shown that the test has much higher power than the widely used ICL and BIC criteria in detecting non spherical component covariance matrices of a high-dimensional mixture.

stat.ME↗

An Approximate $M_2$ Model for Radiative Transfer in Slab Geometry

We propose an approximate second order maximum entropy ($M_2$) model for radiative transfer in slab geometry. The model is based on the ansatz of the specific intensity in the form of a $\Beta$-distribution. This gives us an explicit form in its closure. The closure is very close to that of the maximum entropy, thus an approximation of the $M_2$ model. We prove that the new model is globally hyperbolic, sharing most of the advantages of the maximum entropy closure. Numerical examples illustrate that it provides solutions with satisfactory agreement with the $M_2$ model.

physics.comp-ph↗

Testing the independence of two random vectors where only one dimension is large

For testing the independence of two vectors with respective dimensions $p_1$ and $p_2$, the existing literature in high-dimensional statistics all assume that both dimensions $p_1$ and $p_2$ grow to infinity with the sample size. However, as evidenced in the RNA-sequencing data analysis discussed in the paper, it happens frequently that one of the dimension is quite small and the other quite large compared to the sample size. In this paper, we address this new asymptotic framework for the independence test. A new test procedure is introduced and its asymptotic normality is established when the vectors are normal distributed. A Mote-Carlo study demonstrates the consistency of the procedure and exhibits its superiority over some existing high-dimensional procedures. Applied to the RNA-sequencing data mentioned above, we obtain very convincing results on pairwise independence/dependence of gene isoform expressions as attested by prior knowledge established in that field. Lastly, Monte-Carlo experiments show that the procedure is robust against the normality assumption on the population vectors.

stat.ME↗

Estimation of the population spectral distribution from a large dimensional sample covariance matrix

This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Marcenko-Pastur equation, originally defined in the complex plan, to the real line. Beyond its easy implementation and the established asymptotic consistency, the new estimator outperforms two existing estimators from the literature in almost all the situations tested in a simulation experiment. An application to the analysis of the correlation matrix of S&P stocks data is also given.

stat.ME↗

A local moment estimator of the spectrum of a large dimensional covariance matrix

This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment estimation procedure. Compared with the original one, the new procedure can be applied successfully to models where the asymptotic clusters of sample eigenvalues generated by different population eigenvalues are not all separate. The proposed estimates are proved to be consistent. Numerical results illustrate the implementation of the estimation procedure and demonstrate its efficiency in various cases.

stat.ME↗