arXiv subjects

Xiaohui Chen

Publications and source records attributed to Xiaohui Chen.

At least 91 records · Page 5Linked to original sources

arXiv2019

Estimation of dynamic networks for high-dimensional nonstationary time series

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified based on comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered based on a kernelized time-varying constrained $L_1$-minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S\&P 500 index between 2003 and 2008.

math.ST↗

arXiv2019

Approximating high-dimensional infinite-order $U$-statistics: statistical and computational guarantees

We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction intervals that quantify the uncertainty of ensemble methods such as subbagging and random forests. A major obstacle in using the IOUS is their computational intractability when the sample size and/or order are large. In this article, we derive non-asymptotic Gaussian approximation error bounds for an incomplete version of the IOUS with a random kernel. We also study data-driven inferential methods for the incomplete IOUS via bootstraps and develop their statistical and computational guarantees.

math.ST↗

arXiv2019

An End-to-End Block Autoencoder For Physical Layer Based On Neural Networks

Deep Learning has been widely applied in the area of image processing and natural language processing. In this paper, we propose an end-to-end communication structure based on autoencoder where the transceiver can be optimized jointly. A neural network roles as a combination of channel encoder and modulator. In order to deal with input sequences parallelly, we introduce block scheme, which means that the autoencoder divides the input sequence into a series of blocks. Each block contains fixed number of bits for encoding and modulating operation. Through training, the proposed system is able to produce the modulated constellation diagram of each block. The simulation results show that our autoencoder performs better than other autoencoder-based systems under additive Gaussian white noise (AWGN) and fading channels. We also prove that the bit error rate (BER) of proposed system can achieve an acceptable range with increasing the number of symbols.

cs.IT↗

arXiv2019

Jackknife multiplier bootstrap: finite sample approximations to the $U$-process supremum with applications

This paper is concerned with finite sample approximations to the supremum of a non-degenerate $U$-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the $U$-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the $U$-process supremum by the supremum of a Gaussian process, and derive coupling and Kolmogorov distance bounds. Such Gaussian approximations are, however, not often directly applicable in statistical problems since the covariance function of the approximating Gaussian process is unknown. This motivates us to study bootstrap-type approximations to the $U$-process supremum. We propose a novel jackknife multiplier bootstrap (JMB) tailored to the $U$-process, and derive coupling and Kolmogorov distance bounds for the proposed JMB method. All these results are non-asymptotic, and established under fairly general conditions on function classes and underlying distributions. Key technical tools in the proofs are new local maximal inequalities for $U$-processes, which may be useful in other problems. We also discuss applications of the general approximation results to testing for qualitative features of nonparametric functions based on generalized local $U$-processes.

math.ST↗

arXiv2019

Randomized incomplete $U$-statistics in high dimensions

This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of Big Data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of the $U$-statistic is prohibitively demanding. Data-dependent inferential procedures such as the empirical bootstrap for $U$-statistics is even more computationally expensive. To overcome such computational bottleneck, incomplete $U$-statistics obtained by sampling fewer terms of the $U$-statistic are attractive alternatives. In this paper, we introduce randomized incomplete $U$-statistics with sparse weights whose computational cost can be made independent of the order of the $U$-statistic. We derive non-asymptotic Gaussian approximation error bounds for the randomized incomplete $U$-statistics in high dimensions, namely in cases where the dimension $d$ is possibly much larger than the sample size $n$, for both non-degenerate and degenerate kernels. In addition, we propose generic bootstrap methods for the incomplete $U$-statistics that are computationally much less-demanding than existing bootstrap methods, and establish finite sample validity of the proposed bootstrap methods. Our methods are illustrated on the application to nonparametric testing for the pairwise independence of a high-dimensional random vector under weaker assumptions than those appearing in the literature.

math.ST↗

arXiv2018

Hybrid Beamforming Design and Performance with Imperfect Phase Shifters in Multiuser Millimeter Wave Systems

Hybrid beamforming (HBF) includes analog beamforming with phase shifted array in RF domain and digital beamforming in baseband domain. Phase shifted array is usually made up with a large amount of phase shifters. Limited to the manufacturing techniques, phase shifters are unavoidable to have phaseshifting error and gain error. In the paper we study the influence of imperfect phase shifters upon the performance of multiuser mmWave massive MIMO systems1 with the wireless channel modeled by Rice fading. We derive the upper bound of the achievable sum rate with imperfect phase shifters, which can be very tight when the number of the antennas at the base station is much larger than the number of users. Results show that there is a performance ceiling due to phase-shifting error and gain error. Then we propose a novel channel estimation and hybrid beamforming method to settle this problem with low training overhead. It performs well when the channel paths are few and the channel Rician K-factor is large, which can be easily satisfied in outdoor mmWave communication environment. We further make a tradeoff between the performance and the training overhead so that the algorithm can work well in more kinds of propagation environment.

cs.IT↗

arXiv2018

TCP Decoupling for Next Generation Communication System

In traditional networks, interfaces of network nodes are duplex. But, emerging communication technologies such as visible light communication, millimeter-wave communications, can only provide a unidirectional interface when cost is limited. It's urgent to find effective solutions to utilize such new unidirectional communication skills. Decoupling implies separating one single resource to two independent resources. This idea can be applied at physical layer, link layer, network layer, even transport layer. TCP decoupling is an end to end solution provided at transport layer. With decoupled TCP, two distinct unidirectional path can be created to meet the requirements of reliable information transfer. However, it is not an easy task to decouple a bidirectional logical path at transport layer. In this paper, we dwell on the idea of TCP decoupling. Advantages of decoupling at transport layer are analyzed also. In addition, an experiment is carried out to figure out how to implement a decouple TCP. Our results show decoupling at transport layer is possible and the modified protocol is available.

cs.NI↗

arXiv2018

Comprehensive Optimization of Parametric Kernels for Graphics Processing Units

This work deals with the optimization of computer programs targeting Graphics Processing Units (GPUs). The goal is to lift, from programmers to optimizing compilers, the heavy burden of determining program details that are dependent on the hardware characteristics. The expected benefit is to improve robustness, portability and efficiency of the generated computer programs. We address these requirements by: (1) treating machine and program parameters as unknown symbols during code generation, and (2) generating optimized programs in the form of a case discussion, based on the possible values of the machine and program parameters. By taking advantage of recent advances in the area of computer algebra, preliminary experimentation yield promising results.

cs.DC↗

arXiv2017

Sparse transition matrix estimation for high-dimensional and locally stationary vector autoregressive models

We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose a hybridized kernel smoothing and $\ell^1$-regularized method to directly estimate the sequence of time-varying transition matrices. Under the sparsity assumption on the transition matrix, we establish the rate of convergence of the proposed estimator and show that the convergence rate depends on the smoothness of the locally stationary VAR processes only through the smoothness of the transition matrix function. In addition, for our estimator followed by thresholding, we prove that the false positive rate (type I error) and false negative rate (type II error) in the pattern recovery can asymptotically vanish in the presence of weak signals without assuming the minimum nonzero signal strength condition. Favorable finite sample performances over the $\ell^2$-penalized least-squares estimator and the unstructured maximum likelihood estimator are shown on simulated data. We also provide two real examples on estimating the dependence structures on financial stock prices and economic exchange rates datasets.

math.ST↗

arXiv2017

Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications

This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed. Subject to mild moment conditions on the kernel, we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in $\mathbb{R}^d$ that decays polynomially in sample size for a high-dimensional scaling limit, where the dimension can be much larger than the sample size. We also provide computable approximation methods for the quantiles of the maxima of centered U-statistics. Specifically, we provide a unified perspective for the empirical bootstrap, the randomly reweighted bootstrap, and the Gaussian multiplier bootstrap with the jackknife estimator of covariance matrix as randomly reweighted quadratic forms and we establish their validity. We show that all three methods are inferentially first-order equivalent for high-dimensional U-statistics in the sense that they achieve the same uniform rate of convergence over all $d$-dimensional hyperrectangles. In particular, they are asymptotically valid when the dimension $d$ can be as large as $O(e^{n^c})$ for some constant $c \in (0,1/7)$. (Full abstract can be found in the paper.)

math.ST↗

arXiv2017

Inference of high-dimensional linear models with time-varying coefficients

We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge regression estimator. Due to the non-stationarity feature of the model, dynamic bias-variance decomposition of the estimator is obtained. With a bias-correction procedure, the local null distribution of the estimator of the time-varying coefficient vector is characterized for iid Gaussian and heavy-tailed errors. The limiting null distribution is also established for Gaussian process errors, and we show that the asymptotic properties differ between short-range and long-range dependent errors. Here, p-values are adjusted by a Bonferroni-type correction procedure to control the familywise error rate (FWER) in the asymptotic sense at each time point. The finite sample size performance of the proposed inference algorithm is illustrated with synthetic data and an application to learn brain connectivity by using the resting-state fMRI data for Parkinson's disease.

stat.ME↗

arXiv2016

Gaussian approximation for the sup-norm of high-dimensional matrix-variate U-statistics and its applications

This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution. Specifically, subject to mild moment conditions on the kernel, we establish the explicit rate of convergence that decays polynomially in sample size for a high-dimensional scaling limit, where the dimension can be much larger than the sample size. We also supplement a practical Gaussian wild bootstrap method to approximate the quantiles of the maxima of centered U-statistics and prove its asymptotic validity. The wild bootstrap is demonstrated on statistical applications for high-dimensional non-Gaussian data including: (i) principled and data-dependent tuning parameter selection for regularized estimation of the covariance matrix and its related functionals; (ii) simultaneous inference for the covariance and rank correlation matrices. In particular, for the thresholded covariance matrix estimator with the bootstrap selected tuning parameter, we show that the Gaussian-like convergence rates can be achieved for heavy-tailed data, which are less conservative than those obtained by the Bonferroni technique that ignores the dependency in the underlying data distribution. In addition, we also show that even for subgaussian distributions, error bounds of the bootstrapped thresholded covariance matrix estimator can be much tighter than those of the minimax estimator with a universal threshold.

math.ST↗

arXiv2016

Regularized estimation of linear functionals of precision matrices for high-dimensional time series

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d. samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. It is shown that the convergence rates depend on the degree of temporal dependence and the moment conditions of the underlying linear processes. The Dantzig-selector estimator is applied to the sparse Markowitz portfolio allocation and the optimal linear prediction for time series, in which the ratio consistency when compared with an oracle estimator is established. The effect of dependence and innovation moment conditions is further illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real fMRI dataset and to portfolio optimization on a financial dataset.

math.ST↗

arXiv2016

Many Access for Small Packets Based on Precoding and Sparsity-aware Recovery

Modern mobile terminals produce massive small data packets. For these short-length packets, it is inefficient to follow the current multiple access schemes to allocate transmission resources due to heavy signaling overhead. We propose a non-orthogonal many-access scheme that is well suited for the future communication systems equipped with many receive antennas. The system is modeled as having a block-sparsity pattern with unknown sparsity level (i.e., unknown number of transmitted messages). Block precoding is employed at each single-antenna transmitter to enable the simultaneous transmissions of many users. The number of simultaneously served active users is allowed to be even more than the number of receive antennas. Sparsity-aware recovery is designed at the receiver for joint user detection and symbol demodulation. To reduce the effects of channel fading on signal recovery, normalized block orthogonal matching pursuit (BOMP) algorithm is introduced, and based on its approximate performance analysis, we develop interference cancellation based BOMP (ICBOMP) algorithm. The ICBOMP performs error correction and detection in each iteration of the normalized BOMP. Simulation results demonstrate the effectiveness of the proposed scheme in small packet services, as well as the advantages of ICBOMP in improving signal recovery accuracy and reducing computational cost.

cs.IT↗

arXiv2014

Multiple Access for Small Packets Based on Precoding and Sparsity-Aware Detection

Modern mobile terminals often produce a large number of small data packets. For these packets, it is inefficient to follow the conventional medium access control protocols because of poor utilization of service resources. We propose a novel multiple access scheme that employs block-spreading based precoding at the transmitters and sparsity-aware detection schemes at the base station. The proposed scheme is well suited for the emerging massive multiple-input multiple-output (MIMO) systems, as well as conventional cellular systems with a small number of base-station antennas. The transmitters employ precoding in time domain to enable the simultaneous transmissions of many users, which could be even more than the number of receive antennas at the base station. The system is modeled as a linear system of equations with block-sparse unknowns. We first adopt the block orthogonal matching pursuit (BOMP) algorithm to recover the transmitted signals. We then develop an improved algorithm, named interference cancellation BOMP (ICBOMP), which takes advantage of error correction and detection coding to perform perfect interference cancellation during each iteration of BOMP algorithm. Conditions for guaranteed data recovery are identified. The simulation results demonstrate that the proposed scheme can accommodate more simultaneous transmissions than conventional schemes in typical small-packet transmission scenarios.

cs.IT↗

arXiv2014

A Novel Uplink Data Transmission Scheme For Small Packets In Massive MIMO System

Intelligent terminals often produce a large number of data packets of small lengths. For these packets, it is inefficient to follow the conventional medium access control (MAC) protocols because they lead to poor utilization of service resources. We propose a novel multiple access scheme that targets massive multiple-input multiple-output (MIMO) systems based on compressive sensing (CS). We employ block precoding in the time domain to enable the simultaneous transmissions of many users, which could be even more than the number of receive antennas at the base station. We develop a block-sparse system model and adopt the block orthogonal matching pursuit (BOMP) algorithm to recover the transmitted signals. Conditions for data recovery guarantees are identified and numerical results demonstrate that our scheme is efficient for uplink small packet transmission.

cs.IT↗

arXiv2014

A Note on Moment Inequality for Quadratic Forms

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagonal structures and detect the sparsity in the high-dimensional covariance matrix are presented.

math.ST↗

arXiv2014

Covariance and precision matrix estimation for high-dimensional time series

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate of convergence. Asymptotic properties are also obtained for the precision matrix estimate which is based on the graphical Lasso principle. Our theory substantially generalizes earlier ones by allowing dependence, by allowing nonstationarity and by relaxing the associated moment conditions.

math.ST↗