arXiv subjects

Long Yu

Publications and source records attributed to Long Yu.

36 records · Page 2Linked to original sources

arXiv2022

Testing Kronecker Product Covariance Matrices for High-dimensional Matrix-Variate Data

Kronecker product covariance structure provides an efficient way to modeling the inter-correlations of matrix-variate data. In this paper, we propose testing statistics for Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. Central limit theorem is proved for the linear spectral statistics with explicit formulas for mean and covariance functions, which fills the gap in the literature. We then theoretically justify that the proposed testing statistics have well-controlled sizes and strong powers. To facilitate practical usefulness, we further propose a bootstrap resampling algorithm to approximate the limiting distributions of associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. A more general model which allows the existence of noises will also be discussed. In the simulations, the empirical sizes of the proposed testing procedure and its bootstrapped version are close to corresponding theoretical values, while the powers converge to one quickly as the dimension and sample size grow.

math.ST↗

arXiv2021

Online Change-point Detection for Matrix-valued Time Series with Latent Two-way Factor Structure

This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a changepoint. Our procedure is based only on rates; at each point in time, we randomise the estimated eigenvalue, thus obtaining a normally distributed sequence which is $i.i.d.$ with mean zero under the null of no break, whereas it diverges to positive infinity in the presence of a changepoint. We base our monitoring procedures on such sequence. Extensive simulation studies and empirical analysis justify the theory.

stat.ME↗

arXiv2021

Tracy-Widom limit for the largest eigenvalue of high-dimensional covariance matrices in elliptical distributions

Let $X$ be an $M\times N$ random matrix consisting of independent $M$-variate elliptically distributed column vectors $\mathbf{x}_{1},\dots,\mathbf{x}_{N}$ with general population covariance matrix $Σ$. In the literature, the quantity $XX^{*}$ is referred to as the sample covariance matrix after scaling, where $X^{*}$ is the transpose of $X$. In this article, we prove that the limiting behavior of the scaled largest eigenvalue of $XX^{*}$ is universal for a wide class of elliptical distributions, namely, the scaled largest eigenvalue converges weakly to the same limit regardless of the distributions that $\mathbf{x}_{1},\dots,\mathbf{x}_{N}$ follow as $M,N\to\infty$ with $M/N\toϕ_0>0$ if the weak fourth moment of the radius of $\mathbf{x}_{1}$ exists . In particular, via comparing the Green function with that of the sample covariance matrix of multivariate normally distributed data, we conclude that the limiting distribution of the scaled largest eigenvalue is the celebrated Tracy-Widom law.

math.ST↗

arXiv2021

On New Quantum Codes From Matrix Product Codes

In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.

cs.IT↗

arXiv2021

A General 3D Non-Stationary Massive MIMO GBSM for 6G Communication Systems

A general three-dimensional (3D) non-stationary massive multiple-input multiple-output (MIMO) geometry-based stochastic model (GBSM) for the sixth generation (6G) communication systems is proposed in the paper. The novelty of the model is that the model is designed to cover a variety of channel characteristics, including space-time-frequency (STF) non-stationarity, spherical wavefront, spatial consistency, channel hardening, etc. Firstly, the introduction of the twin-cluster channel model is given in detail. Secondly, the key statistical properties such as space-time-frequency correlation function (STFCF), space cross-correlation function (CCF), temporal autocorrelation function (ACF), frequency correlation function (FCF), and performance indicators, e.g., singular value spread (SVS), and channel capacity are derived. Finally, the simulation results are given and consistent with some measurements in relevant literatures, which validate that the proposed channel model has a certain value as a reference to model massive MIMO channel characteristics.

eess.SP↗

arXiv2020

Projected Estimation for Large-dimensional Matrix Factor Models

In this study, we propose a projection estimation method for large-dimensional matrix factor models with cross-sectionally spiked eigenvalues. By projecting the observation matrix onto the row or column factor space, we simplify factor analysis for matrix series to that for a lower-dimensional tensor. This method also reduces the magnitudes of the idiosyncratic error components, thereby increasing the signal-to-noise ratio, because the projection matrix linearly filters the idiosyncratic error matrix. We theoretically prove that the projected estimators of the factor loading matrices achieve faster convergence rates than existing estimators under similar conditions. Asymptotic distributions of the projected estimators are also presented. A novel iterative procedure is given to specify the pair of row and column factor numbers. Extensive numerical studies verify the empirical performance of the projection method. Two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincides with financial, economic, or geographical interpretations.

stat.ME↗

arXiv2020

DT-Net: A novel network based on multi-directional integrated convolution and threshold convolution

Since medical image data sets contain few samples and singular features, lesions are viewed as highly similar to other tissues. The traditional neural network has a limited ability to learn features. Even if a host of feature maps is expanded to obtain more semantic information, the accuracy of segmenting the final medical image is slightly improved, and the features are excessively redundant. To solve the above problems, in this paper, we propose a novel end-to-end semantic segmentation algorithm, DT-Net, and use two new convolution strategies to better achieve end-to-end semantic segmentation of medical images. 1. In the feature mining and feature fusion stage, we construct a multi-directional integrated convolution (MDIC). The core idea is to use the multi-scale convolution to enhance the local multi-directional feature maps to generate enhanced feature maps and to mine the generated features that contain more semantics without increasing the number of feature maps. 2. We also aim to further excavate and retain more meaningful deep features reduce a host of noise features in the training process. Therefore, we propose a convolution thresholding strategy. The central idea is to set a threshold to eliminate a large number of redundant features and reduce computational complexity. Through the two strategies proposed above, the algorithm proposed in this paper produces state-of-the-art results on two public medical image datasets. We prove in detail that our proposed strategy plays an important role in feature mining and eliminating redundant features. Compared with the existing semantic segmentation algorithms, our proposed algorithm has better robustness.

cs.CV↗

arXiv2020

Large-dimensional Factor Analysis without Moment Constraints

Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model typically requires finite fourth moment of the data, which ignores the effect of heavy-tailedness and thus may result in unrobust or even inconsistent estimation of the factor space and common components. In this paper, we propose to recover the factor space by performing principal component analysis to the spatial Kendall's tau matrix instead of the sample covariance matrix. In a second step, we estimate the factor scores by the ordinary least square (OLS) regression. Theoretically, we show that under the elliptical distribution framework the factor loadings and scores as well as the common components can be estimated consistently without any moment constraint. The convergence rates of the estimated factor loadings, scores and common components are provided. The finite sample performance of the proposed procedure is assessed through thorough simulations. An analysis of a financial data set of asset returns shows the superiority of the proposed method over the classical PCA method.

stat.ME↗

arXiv2020

A New Multiple Max-pooling Integration Module and Cross Multiscale Deconvolution Network Based on Image Semantic Segmentation

To better retain the deep features of an image and solve the sparsity problem of the end-to-end segmentation model, we propose a new deep convolutional network model for medical image pixel segmentation, called MC-Net. The core of this network model consists of four parts, namely, an encoder network, a multiple max-pooling integration module, a cross multiscale deconvolution decoder network and a pixel-level classification layer. In the network structure of the encoder, we use multiscale convolution instead of the traditional single-channel convolution. The multiple max-pooling integration module first integrates the output features of each submodule of the encoder network and reduces the number of parameters by convolution using a kernel size of 1. At the same time, each max-pooling layer (the pooling size of each layer is different) is spliced after each convolution to achieve the translation invariance of the feature maps of each submodule. We use the output feature maps from the multiple max-pooling integration module as the input of the decoder network; the multiscale convolution of each submodule in the decoder network is cross-fused with the feature maps generated by the corresponding multiscale convolution in the encoder network. Using the above feature map processing methods solves the sparsity problem after the max-pooling layer-generating matrix and enhances the robustness of the classification. We compare our proposed model with the well-known Fully Convolutional Networks for Semantic Segmentation (FCNs), DecovNet, PSPNet, U-net, SgeNet and other state-of-the-art segmentation networks such as HyperDenseNet, MS-Dual, Espnetv2, Denseaspp using one binary Kaggle 2018 data science bowl dataset and two multiclass dataset and obtain encouraging experimental results.

cs.CV↗

arXiv2020

Network-Assisted Estimation for Large-dimensional Factor Model with Guaranteed Convergence Rate Improvement

Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between individuals is observed. To fully excavate the prior network information, we construct two different penalties to regularize the factor loadings and shrink the idiosyncratic errors. Closed-form solutions are provided for the penalized optimization problems. Theoretical results demonstrate that the modified estimators achieve faster convergence rates and lower asymptotic mean squared errors when the underlying network structure among individuals is correct. An interesting finding is that even if the priori network is totally misleading, the proposed estimators perform no worse than conventional state-of-art methods. Furthermore, to facilitate the practical application, we propose a data-driven approach to select the tuning parameters, which is computationally efficient. We also provide an empirical criterion to determine the number of common factors. Simulation studies and application to the S&P100 weekly return dataset convincingly illustrate the superiority and adaptivity of the new approach.

stat.ME↗

arXiv2019

Robust Factor Number Specification for Large-dimensional Elliptical Factor Model

The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that the fourth moments of the factors and idiosyncratic errors are bounded. In this paper we propose efficient and robust estimators for the factor number via considering a more general static Elliptical Factor Model (EFM) framework. We innovatively propose to exploit the multivariate Kendall's tau matrix, which captures the correlation structure of elliptical random vectors. Theoretically we show that the proposed estimators are consistent without exerting any moment condition when both cross-sections N and time dimensions T go to infinity. Simulation study shows that the new estimators perform much better in heavy-tailed data setting while performing comparably with the state-of-the-art methods in the light-tailed Gaussian setting. At last, a real macroeconomic data example is given to illustrate its empirical advantages and usefulness.

stat.ME↗

arXiv2018

Entanglement-assisted quantum codes from Galois LCD codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the parameter of ebits $c$ is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on $k$-Galois LCD MDS codes for some certain code lengths, where the parameter of ebits $c$ can be easily generated algebraically and not by computational search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs.

cs.IT↗

arXiv2018

Two types of permutation polynomials with special forms

Let $q$ be a power of a prime and $\mathbb{F}_q$ be a finite field with $q$ elements. In this paper, we propose four families of infinite classes of permutation trinomials having the form $cx-x^s + x^{qs}$ over $\mathbb{F}_{q^2}$, and investigate the relationship between this type of permutation polynomials with that of the form $(x^q-x+δ)^s+cx$. Based on this relation, many classes of permutation trinomials having the form $(x^q-x+δ)^s+cx$ without restriction on $δ$ over $\mathbb{F}_{q^2}$ are derived from known permutation trinomials having the form $cx-x^s + x^{qs}$.

cs.IT↗

arXiv2017

Constant composition codes derived from linear codes

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.

cs.IT↗

arXiv2017

Constant Composition Codes as Subcodes of Linear Codes

In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on LVFC bound. On the other hand, a class of constant composition codes is derived from known linear codes.

cs.IT↗

arXiv2016

Self-Dual Codes over $\mathbb{Z}_2\times (\mathbb{Z}_2+u\mathbb{Z}_2)$

In this paper, we study self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $, where $u^2=0$. Three types of self-dual codes are defined. For each type, the possible values $α,β$ such that there exists a code $\mathcal{C}\subseteq \mathbb{Z}_{2}^α\times (\mathbb{Z}_2+u\mathbb{Z}_2)^β$ are established. We also present several approaches to construct self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $. Moreover, the structure of two-weight self-dual codes is completely obtained for $α\cdotβ\neq 0$.

cs.IT↗

arXiv2014

A class of $p$-ary cyclic codes and their weight enumerators

Let $m$, $k$ be positive integers such that $\frac{m}{\gcd(m,k)}\geq 3$, $p$ be an odd prime and $π$ be a primitive element of $\mathbb{F}_{p^m}$. Let $h_1(x)$ and $h_2(x)$ be the minimal polynomials of $-π^{-1}$ and $π^{-\frac{p^k+1}{2}}$ over $\mathbb{F}_p$, respectively. In the case of odd $\frac{m}{\gcd(m,k)}$, when $k$ is even, $\gcd(m,k)$ is odd or when $\frac{k}{\gcd(m,k)}$ is odd, Zhou et~al. in \cite{zhou} obtained the weight distribution of a class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ with parity-check polynomial $h_1(x)h_2(x)$. In this paper, we further investigate this class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ in the rest case of odd $\frac{m}{\gcd(m,k)}$ and the case of even $\frac{m}{\gcd(m,k)}$. Moreover, we determine the weight distribution of cyclic codes $\mathcal{C}$.

cs.IT↗

arXiv2014

The weight distribution of a family of p-ary cyclic codes

Let m, k be positive integers, p be an odd prime and $π$ be a primitive element of $\mathbb{F}_{p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\mathcal{C}_t$ over $\mathbb{F}_p$, whose duals have two zeros $π^{-t}$ and $-π^{-t}$, where $t$ satisfies $t\equiv \frac{p^k+1}{2}p^τ\ ({\rm mod}\ \frac{p^m-1}{2}) $ for some $τ\in \{0,1,\cdots, m-1\}$.

cs.IT↗