In this paper, we propose a general framework for tensor singular value decomposition (tensor (SVD)), which focuses on the methodology and theory extracting hidden low-rank structure from high-dimensional data. Comprehensive results are developed both statistical computational limits SVD. This problem exhibits three different phases according to signal-to-noise ratio (SNR). particular, with strong SNR, show that classical higher-order orthogonal iteration achieves minimax optimal rate of...

Rate adaptation varies the transmission rate of a wireless sender to match channel conditions, in order achieve best possible performance. It is key component IEEE 802.11 networks. Minstrel popular algorithm due its efficiency and availability commonly used drivers. However, despite popularity, little work has been done on evaluating performance or comparing it fixed rates. In this paper, we conduct an experimental study that compares against rates 802.11g testbed. The experiment results...

In this article, we develop methods for estimating a low rank tensor from noisy observations on subset of its entries to achieve both statistical and computational efficiencies. There have been lot recent interests in problem completion. Much the attention has focused fundamental challenges often associated with problems involving higher order tensors, yet very little is known about their performance. To fill void, characterize limits completion by establishing minimax optimal rates...

The 2D limit equilibrium method is widely used for slope stability analysis. However, with the advancement of dump engineering, composite slopes often exhibit significant 3D mechanical effects. Consequently, it importance to develop an effective calculation enhance design and control open-pit engineering. Using formed by mining stope inner in Baiyinhua No. 1 2 coal mine as a case study, this research investigates failure mode establishes spatial shape equations sliding mass. By integrating...

To date, social network analysis has been largely focused on pairwise interactions. The study of higher-order interactions, via a hypergraph network, brings in new insights. We community detection network. A popular approach is to project the graph and then apply methods for networks, but we show that this may cause unwanted information loss. propose method operates directly hypergraph. At heart our regularized orthogonal iteration (reg-HOOI) algorithm computes an approximate low-rank...

We study the problem of community detection in multilayer networks, where pairs nodes can be related multiple modalities. introduce a general framework, that is, mixture stochastic block model (MMSBM), which includes many earlier models as special cases. propose tensor-based algorithm (TWIST) to reveal both global/local memberships nodes, and layers. show TWIST procedure accurately detect communities with small misclassification error number and/or layers increases. Numerical studies confirm...

Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory low-rank tensor decomposition with auxiliary covariates. models extend factor by incorporating covariates in loading matrices. We propose an algorithm iteratively projected singular value (IP-SVD) for semi-parametric estimation. It projects data onto linear space spanned basis functions applies matricized tensors over each mode. establish convergence...

Network method of moments (Ann. Statist. 39 (2011) 2280–2301) is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions the sampling distributions moment statistics. In this paper, we present first higher-order approximation to CDF a studentized by Edgeworth expansion. sharp contrast classical literature noiseless U-statistics, show that expansion statistic as noisy U-statistic can achieve accuracy without nonlattice or...

We investigate a generalized framework to estimate latent low-rank plus sparse tensor, where the tensor often captures multi-way principal components and accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by part. The flexibly covers both linear models, can easily handle continuous categorical variables. propose fast algorithm integrating Riemannian gradient descent novel pruning procedure. Under suitable conditions, converges linearly...

In this paper, a novel concept called uniquely factorable constellation pair (UFCP) is proposed for the systematic design of noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes wireless communication system having transmitter antennas and single receiver antenna. It proved that such UFCP assures unique identification both channel coefficients transmitted signals in noise-free case as well maximum likelihood noise case. To further improve...

Abstract We introduce a flexible framework for making inferences about general linear forms of large matrix based on noisy observations subset its entries. In particular, under mild regularity conditions, we develop universal procedure to construct asymptotically normal estimators through double-sample debiasing and low-rank projection whenever an entry-wise consistent estimator the is available. These allow us subsequently confidence intervals test hypotheses forms. Our proposal was...

We introduce a unified framework, formulated as general latent space models, to study complex higher-order network interactions among multiple entities. Our framework covers several popular models in recent analysis literature, including mixture multi-layer model and hypergraph model. formulate the relationship between positions observed data via generalized multilinear kernel link function. While our enjoys decent generality, its maximum likelihood parameter estimation is also convenient...

IEEE 802.11 wireless systems usually contain rate control algorithms which are designed to adapt the transmission between several available rates in response varying channel conditions. The efficiency of algorithm selecting optimal data for conditions directly impacts on throughput system. Minstrel is a that has good performance compared with other algorithms, and widely implemented popular drivers such as MadWiFi, Ath5k Ath9k. However, surprisingly, there very little literature studying...

This paper is on the normal approximation of singular subspaces when noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula empirical spectral projectors. The neat and holds for deterministic perturbations. Second, calculate expected projection distance between true subspaces. method allows obtaining arbitrary k-th order distance. Third, prove non-asymptotical with different levels bias corrections. By ⌈log(d1+d2)⌉-th...

This letter presents a novel harmonic impedance matching technique by using parallel LC resonate block after the combining point to design fully integrated high-efficiency Doherty power amplifier (DPA). The second impedances of both carrier and peaking amplifiers can be matched optimal area with only one tuner easily. insertion loss size output network (OMN) reduced. For verification, 4.6-5.2-GHz monolithic microwave circuit DPA was designed fabricated 0.25-μm gallium nitride (GaN)-HEMT...

Low-rank matrix regression refers to the instances of recovering a low-rank based on specially designed measurements and corresponding noisy outcomes. Numerous statistical methods have been developed over recent decade for efficiently reconstructing unknown matrices. It is often interesting, in certain applications, estimate singular subspaces. In this paper, we revisit model introduce two-step procedure construct confidence regions We investigate distributions joint projection distance...

In this paper, we investigate the sample size requirement for exact recovery of a high order tensor low rank from subset its entries. We show that gradient descent algorithm with initial value obtained spectral method can, in particular, reconstruct ${d\times d\times d}$ multilinear ranks $(r,r,r)$ probability as few $O(r^{7/2}d^{3/2}\log^{7/2}d+r^7d\log^6d)$ case when $r=O(1)$, our matches those nuclear norm minimization (Yuan and Zhang, 2016a), or alternating least squares assuming...

Let $\mathcal{S}_{m}$ be the set of all $m\times m$ density matrices (Hermitian positively semi-definite unit trace). Consider a problem estimation an unknown matrix $\rho\in\mathcal{S}_{m}$ based on outcomes $n$ measurements observables $X_{1},\dots,X_{n}\in\mathbb{H}_{m}$ ($\mathbb{H}_{m}$ being space Hermitian matrices) for quantum system identically prepared times in state $\rho.$ Outcomes $Y_{1},\dots,Y_{n}$ such could described by trace regression model which...