Block Update Research Articles

Incremental Quasi-Newton Methods with Faster Superlinear Convergence Rates

We consider the finite-sum optimization problem, where each component function is strongly convex and has Lipschitz continuous gradient and Hessian. The recently proposed incremental quasi-Newton method is based on BFGS update and achieves a local superlinear convergence rate that is dependent on the condition number of the problem. This paper proposes a more efficient quasi-Newton method by incorporating the symmetric rank-1 update into the incremental framework, which results in the condition-number-free local superlinear convergence rate. Furthermore, we can boost our method by applying the block update on the Hessian approximation, which leads to an even faster local convergence rate. The numerical experiments show the proposed methods significantly outperform the baseline methods.

Detecting Weak Underwater Targets Using Block Updating of Sparse and Structured Channel Impulse Responses

In this paper, we considered the real-time modeling of an underwater channel impulse response (CIR), exploiting the inherent structure and sparsity of such channels. Building on the recent development in the modeling of acoustic channels using a Kronecker structure, we approximated the CIR using a structured and sparse model, allowing for a computationally efficient sparse block-updating algorithm, which can track the time-varying CIR even in low signal-to-noise ratio (SNR) scenarios. The algorithm employs a conjugate gradient formulation, which enables a gradual refinement if the SNR is sufficiently high to allow for this. This was performed by gradually relaxing the assumed Kronecker structure, as well as the sparsity assumptions, if possible. The estimated CIR was further used to form a residual signal containing (primarily) information of the time-varying signal responses, thereby allowing for the detection of weak target signals. The proposed method was evaluated using both simulated and measured underwater signals, clearly illustrating the better performance of the proposed method.

Multiperiod DER Coordination Using ADMM-Based Three-Block Distributed AC Optimal Power Flow Considering Inverter Volt-Var Control

The uptake of behind-the-meter distributed energy resources (DER) raises the likelihood of voltage problems in low-voltage distribution networks. Network operators increasingly require solar inverters to provide reactive power support using Volt-Var control (VVC) to reduce voltage stress. However, VVC can cause instability in real-time control because of its instantaneous response to voltage deviations, which has been previously addressed using delayed control methods. Coincidentally, optimization-based multiperiod DER coordination faces a similar problem, where numerical oscillations can prevent the convergence of a distributed algorithm. This paper aims to fill this gap by proposing a distributed three-block algorithm, based on the alternating direction method of multipliers (ADMM), for solving the DER coordination problem using AC optimal power flow (OPF) with VVC constraints. This approach decomposes the network at the prosumer level, resulting in an aggregator, a prosumer, and a VVC block. A key feature of the proposed algorithm is the introduction of carefully tuned delays in the VVC block update to circumvent unstable numerical behavior. This novel approach is numerically demonstrated to solve the distributed OPF problem to feasible solutions with (i) objective function values within less than 2.5% compared to those from centralized computations for tractable cases, (ii) robustness against changes in load/generation profiles and steepness of VVC curves, and (iii) an algorithmic performance that scales linearly with an increase in network size.

Real-time cable force identification based on block recursive Capon spectral estimation method

Cables are critical force-bearing components of cable-supported structures that greatly influence structure security. The changes in cable forces can reflect the cable service state and provide an important basis for structural health assessment. This paper proposes a method for real-time cable force identification (CFI) to tracking its varying rules. First, a recursive Capon method based on block updating is derived to estimate the amplitude spectrum at each observation moment. Second, determine the natural frequency (and corresponding mode order) in the transformed frequency domain and calculate the cable tension according to related formulas. Proper algorithm optimization and parameter selection are studied to ensure that the calculation cost meets the real-time requirement of CFI. The proposed method is applied to an experimental cable and the cables of a half-through arch bridge for validation.

Grant-Free Non-Orthogonal Multiple Access in Single-Carrier Frequency-Selective Fading Channels

Grant-free (GF) access is one key technology for massive machine-type communication (mMTC) in Internet-of-things. Single-carrier (SC) modulation has higher power-efficiency than multicarrier modulation such as orthogonal frequency division multiplexing, due to lower peak-to-average power ratio, and thus is specifically suitable for low-power-supply machine-type devices. In this paper, we study both the coherent and non-coherent grant-free non-orthogonal multiple access (GF-NOMA) schemes where SC modulation is employed in frequency selective fading channels. For coherent SC-GF-NOMA, the linear input-output relation is first presented, and two user-activity detection (UAD) algorithms, block covariance-based maximum-likelihood detection (CB-MLD) and turbo approximated message passing (Turbo AMP), are proposed. In block CB-MLD, a block update strategy is introduced in the coordinate descent iteration to utilize the special block-sparsity signal property inherent in coherent SC-GF-NOMA. Moreover, Turbo AMP consists of two components, AMP and message passing (MP), and turbo iteration between them. Concretely, AMP is designed for UAD-CE with fixed active user probability, and MP is designed to update the active user probability by utilizing the block sparsity. Moreover, the performance of Turbo AMP is analyzed by state-evolution (SE) formalism. For non-coherent SC-GF-NOMA, the linear input-output relation is first derived from which the hierarchical block-sparsity signal property is observed, and then block CB-MLD-based UAD algorithm is presented to utilize this signal property. Finally, computer simulation results are given to demonstrate the effectiveness of the proposed algorithms in both coherent and non-coherent SC-GF-NOMA.

Designing a Renewal Approach of Rejuvenating Historic Districts: Taking Nantong Temple Street as an Example

In recent years, people’s opinions have shifted with the continuous development and growth of cities. The category of historical heritage is increasingly being shifted from the city’s star fire to the backdrop color of the entire city. However, some cities are experiencing issues such as aging, regeneration, and stagnation. With the merging of sustainable development ideas with urban renewal techniques, sustainable urban renewal has developed as a new area of research. Data mining and analytics have played a significant role in extracting knowledge and decision-making in the revitalization of historic districts during the last decade. Machine learning, as a computational engine for learning analytics, is a fundamental technique for extracting information, data pattern detection, and prediction. From the perspective of machine learning, this study investigates the historical block update approach, which is utilized in feature space and culture at the same time. Furthermore, it investigates the development of countermeasures for injecting new energy into the historical block by using the functions of space and scale to search for the block transformation and the combination of natural and cultural landscapes. In addition, in order to interact with visitors and residents and realize the renewal of old blocks, in this research work, multifunctional culture is grafted into the historical block and buried underground, so that their life can be awakened. To highlight the efficiency of this work, we have taken the Nantong Temple Street in China as an example which verifies the validity of this study.

An Adaptive Rate Blocked Compressive Sensing Method for Video.

An adaptive rate Compressive Sensing (CS) method for video signals is proposed. The Blocked Compressive Sensing (BCS) scheme is adopted in this method. Firstly, each video frame is blocked and measured by the BCS scheme, and then the mean and variance of each image block are estimated by observing the CS measurement results. Using the mean and variance of each image block, the sparsity of the block is estimated and then the block can be classified. Adaptive rate sampling is realized by assigning different sampling rates to different classes. At the same time, in order to make better use of the correlation between video frames, a reference block subtraction method is also designed in this paper, which uses the estimates of the sparsity of image blocks as the basis for the reference block update. All operations of the proposed method only depend on the CS measurement results of image blocks and all calculations are simple. Thus, the proposed method is suitable for implementation in CS sampling devices with limited computational performance. Experiment results show that, compared with the actual values, the sparsity estimates and block classification results of the proposed method are accurate. Compared with the latest adaptive Compressive Video Sensing methods, the reconstructed image quality of the proposed method is better.

Solving Composite Fixed Point Problems with Block Updates

Abstract Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at each iteration, and the question of maintaining convergence while updating only blocks of operators is open. We propose a method that achieves this goal and analyze its asymptotic behavior. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays. Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to variational inequalities and minimization problems arising in data science.

Accelerating block coordinate descent for nonnegative tensor factorization

AbstractThis paper is concerned with improving the empirical convergence speed of block‐coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in‐between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates the empirical convergence speed of most existing block‐coordinate algorithms for NTF, in particular for challenging computational scenarios, while requiring a negligible additional computational budget.

First-Order Methods for Constrained Convex Programming Based on Linearized Augmented Lagrangian Function

First-order methods (FOMs) have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two FOMs for constrained convex programs, where the constraint set is represented by affine equations and smooth nonlinear inequalities. Both methods are based on the classical augmented Lagrangian function. They update the multipliers in the same way as the augmented Lagrangian method (ALM) but use different primal updates. The first method, at each iteration, performs a single proximal gradient step to the primal variable, and the second method is a block update version of the first one. For the first method, we establish its global iterate convergence and global sublinear and local linear convergence, and for the second method, we show a global sublinear convergence result in expectation. Numerical experiments are carried out on the basis pursuit denoising, convex quadratically constrained quadratic programs, and the Neyman-Pearson classification problem to show the empirical performance of the proposed methods. Their numerical behaviors closely match the established theoretical results.

Guide star catalog generation of star sensors for interstellar navigation

In interstellar travel, parallax and stellar aberration have a non-negligible influence on the star identification of star sensors. Through the analysis of the working principle of star sensors, only the guide star catalog generation can solve this problem. The influence mechanism of parallax and stellar aberration is synthetically analyzed by four-dimensional time-space diagrams, and a generation algorithm of the guide star catalog for the interstellar star identification is presented. The update cycle of the catalog is studied, and a block update method based on the distance distribution is given. The Hipparcos catalog is adopted as the fundamental catalog. On the premise of meeting the accuracy requirement of star identification, the maximum travel distance supported by the catalog is about 0.3 light-years. In order to balance the star identification and the influence of parallax, eliminating 30% to 40% of the nearby guide stars is an optimal criterion for the guide star selection. The analysis of the catalog distribution shows that the parallax and the stellar aberration have opposite effects on the distribution of guide stars. The methods and conclusions provide a theoretical basis for interstellar celestial navigation.

Empirical comparison of skewed t-copula models for insurance and financial data

Skewed t-copulas recently became popular as a modeling tool of non-linear dependence in statistics. In this paper we consider three different versions of skewed t-copulas introduced by Demarta and McNeill; Smith, Gan and Kohn; and Azzalini and Capitanio. Each of these versions represents a generalization of the symmetric t-copula model, allowing for a different treatment of lower and upper tails. Each of them has certain advantages in mathematical construction, inferential tools and interpretability. Our objective is to apply models based on different types of skewed t-copulas to the same financial and insurance applications. We consider comovements of stock index returns and times-to-failure of related vehicle parts under the warranty period. In both cases the treatment of both lower and upper tails of the joint distributions is of a special importance. Skewed t-copula model performance is compared to the benchmark cases of Gaussian and symmetric Student t-copulas. Instruments of comparison include information criteria, goodness-of-fit and tail dependence. A special attention is paid to methods of estimation of copula parameters. Some technical problems with the implementation of maximum likelihood method and the method of moments suggest the use of Bayesian estimation. We discuss the accuracy and computational efficiency of Bayesian estimation versus MLE. Metropolis-Hastings algorithm with block updates was suggested to deal with the problem of intractability of conditionals.

Network Pseudohealth Information Recognition Model: An Integrated Architecture of Latent Dirichlet Allocation and Data Block Update

The wanton dissemination of network pseudohealth information has brought great harm to people’s health, life, and property. It is important to detect and identify network pseudohealth information. Based on this, this paper defines the concepts of pseudohealth information, data block, and data block integration, designs an architecture that combines the latent Dirichlet allocation (LDA) algorithm and data block update integration, and proposes the combination algorithm model. In addition, crawler technology is used to crawl the pseudohealth information transmitted on the Sina Weibo platform during the “epidemic situation” from February to March 2020 for the simulation test on the experimental case dataset. The research results show that (1) the LDA model can deeply mine the semantic information of network pseudohealth information, obtain the features of document-topic distribution, and classify and train topic features as input variables; (2) the dataset partitioning method can effectively block data according to the text attributes and class labels of network pseudohealth information and can accurately classify and integrate the block data through the data block reintegration method; and (3) considering that the combination model has certain limitations on the detection of network pseudohealth information, the support vector machine (SVM) model can extract the granularity content of data blocks in pseudohealth information in real time, thus greatly improving the recognition performance of the combination model.

Enabling Ternary Hash Tree Based Integrity Verification for Secure Cloud Data Storage

Cloud Computing enables the remote users to access data, services, and applications in on-demand from the shared pool of configurable computing resources, without the consideration of storage, hardware, and software management. On the other hand, it is not easy for cloud users to identify whether Cloud Service Provider's (CSP) tag along with the data security legal expectations. So, cloud users could not rely on CSP's in terms of trust. So, it is significant to build a secure and efficient data auditing framework for increasing and maintaining cloud users trust with CSP. Researchers suggested introducing Third Party Auditor (TPA) on behalf of cloud user for verifying the outsourced data integrity, which may reduce the computation overhead of cloud users. In this work, we proposed a novel integrity verification framework for securing cloud storage based on Ternary Hash Tree (THT) and Replica based Ternary Hash Tree (R-THT), which will be used by TPA to perform data auditing. Differing from existing work, the proposed framework performs Block-level, File-level and Replica-level auditing with tree block ordering, storage block ordering for verifying the data integrity and ensuring data availability in the cloud. We further extend our framework to support error localization with data correctness, dynamic updates with block update, insert, and delete operations in the cloud. The structure of THT and R-THT will reduce the computation cost and provide efficiency in data updates compared to the existing schemes. The security analysis of the proposed public auditing framework indicates the achievement of desired properties and performance has been evaluated with the detailed experiment set. The results show that the proposed secure cloud auditing framework is highly secure and efficient in storage, communication, and computation costs.

Efficient Solution of Electromagnetic Scattering Problems Using Multilevel Adaptive Cross Approximation and LU Factorization

The multilevel adaptive cross approximation (MLACA), previously described in the literature, extends the single-level ACA with a recursive multilevel algorithm that significantly improves compression of off-diagonal matrix blocks resulting from electromagnetic integral equations (IE) discretized via the method of moments (MoM). In this article, the MLACA approach is extended and applied to a direct solution of the MoM matrix system via LU factorization. It will be shown through numerical experiments that the off-diagonal LU blocks are also compressible using MLACA, yielding a compression rate superior to the single-level ACA and a memory complexity of O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4/3</sup> log N). In addition, the MLACA LU block updates are performed in rank-reduced form, yielding a very efficient software implementation via a Level 3 BLAS optimized for the CPU or GPU.

Modeling material stress using integrated Gaussian Markov random fields

The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMises stress for each of the more than 94,000 tetrahedra within the finite element discretization. In this paper, we define an intricate statistical model for the spatial field of vonMises stress which uses the given grain geometry in a fundamental way. Our model relates the three-dimensional field to integrals of latent stochastic processes defined on the vertices of the one- and two-dimensional grain boundaries. An intuitive neighborhood structure of the said boundary nodes suggested the use of a latent Gaussian Markov random field (GMRF). However, despite the potential for computational gains afforded by GMRFs, the integral nature of our model and the sheer number of data points pose substantial challenges for a full Bayesian analysis. To overcome these problems and encourage efficient exploration of the posterior distribution, a number of techniques are now combined: parallel computing, sparse matrix methods, and a modification of a block update strategy within the sampling routine. In addition, we use an auxiliary variables approach to accommodate the presence of outliers in the data.

Learning a mixture of microbial networks using minorization-maximization.

MotivationThe interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose nodes represent microbial taxa and edges represent pairwise interactions. A microbial network is typically constructed from a sample-taxa count matrix that is obtained by sequencing multiple biological samples and identifying taxa counts. From large-scale microbiome studies, it is evident that microbial community compositions and interactions are impacted by environmental and/or host factors. Thus, it is not unreasonable to expect that a sample-taxa matrix generated as part of a large study involving multiple environmental or clinical parameters can be associated with more than one microbial network. However, to our knowledge, microbial network inference methods proposed thus far assume that the sample-taxa matrix is associated with a single network.ResultsWe present a mixture model framework to address the scenario when the sample-taxa matrix is associated with K microbial networks. This count matrix is modeled using a mixture of K Multivariate Poisson Log-Normal distributions and parameters are estimated using a maximum likelihood framework. Our parameter estimation algorithm is based on the minorization–maximization principle combined with gradient ascent and block updates. Synthetic datasets were generated to assess the performance of our approach on absolute count data, compositional data and normalized data. We also addressed the recovery of sparse networks based on an l1-penalty model.Availability and implementationMixMPLN is implemented in R and is freely available at https://github.com/sahatava/MixMPLN.Supplementary information Supplementary data are available at Bioinformatics online.

Sampling Strategies for Fast Updating of Gaussian Markov Random Fields

Gaussian Markov random fields (GMRFs) are popular for modeling dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by the sparse precision matrices needed for random variable generation. Typically in Bayesian computation, GMRFs are updated jointly in a block Gibbs sampler or componentwise in a single-site sampler via the full conditional distributions. The former approach can speed convergence by updating correlated variables all at once, while the latter avoids solving large matrices. We consider a sampling approach in which the underlying graph can be cut so that conditionally independent sites are updated simultaneously. This algorithm allows a practitioner to parallelize updates of subsets of locations or to take advantage of “vectorized” calculations in a high-level language such as R. Through both simulated and real data, we demonstrate computational savings that can be achieved versus both single-site and block updating, regardless of whether the data are on a regular or an irregular lattice. The approach provides a good compromise between statistical and computational efficiency and is accessible to statisticians without expertise in numerical analysis or advanced computing.

REACT: Read/Write Error Rate Aware Coding Technique for Emerging STT-MRAM Caches

Spin-transfer torque magnetic RAMs (STT-MRAMs) are the most promising alternative for static random-access memories in large last-level on-chip caches due to their higher density and near-zero leakage power. However, the reliability of STT-MRAMs is threatened by high probability of read disturbance and write failure . Both read disturbance and write failure, which cause a soft error in the cache cells, have an asymmetric behavior. Read disturbance occurs only in STT-MRAM cells storing “1” value, and write failure error rate in a $0\rightarrow 1$ transition is much higher than that in a $1\rightarrow 0$ transition. In this paper, we propose Read/write Error-rate Aware Coding Technique (REACT) to improve the reliability of the emerging STT-MRAM caches. REACT decreases the read disturbance and write failure rates by reducing the total number of “1”s and $0\rightarrow 1$ transitions on a cache block update. Our simulation results show that REACT reduces the probability of read disturbance and write failure up to 58% and 71%, respectively. These improvements are achieved by imposing negligible area, power, and performance overheads (less than 1%).

Computation of maximum likelihood estimates in cyclic structural equation models

Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from nonlinear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is often required to avoid convergence issues. As an alternative approach, we propose a block-coordinate descent method that cycles through the considered variables, updating only the parameters related to a given variable in each step. We show that the resulting block update problems can be solved in closed form even when the structural equation model comprises feedback cycles. Furthermore, we give a characterization of the models for which the block-coordinate descent algorithm is well defined, meaning that for generic data and starting values all block optimization problems admit a unique solution. For the characterization, we represent each model by its mixed graph (also known as path diagram), which leads to criteria that can be checked in time that is polynomial in the number of considered variables.