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arXiv 2024年

作者： Wijayawardhana, Anjana Gunawan, David Suesse, Thomas School of Mathematics and Applied Statistics University of Wollongong WollongongNSW Australia

The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has significant limitations when it comes to handling missing data in the response variable due to its high computational cost. Variational Bayes (VB) approximation offers an alternative solution to this problem. Two VB-based algorithms employing Gaussian variational approximation with factor covariance structure are presented, joint VB (JVB) and hybrid VB (HVB), suitable for both missing at random and not at random inference. When dealing with many missing values, the JVB is inaccurate, and the standard HVB algorithm struggles to achieve accurate inferences. Our modified versions of HVB enable accurate inference within a reasonable computational time, thus improving its performance. The performance of the VB methods is evaluated using simulated and real datasets. © 2024, CC BY.

关键词： approximation algorithms

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Causal Discovery under Off-Target Interventions

arXiv

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arXiv 2024年

作者： Choo, Davin Shiragur, Kirankumar Uhler, Caroline National University of Singapore Singapore Broad Institute of MIT and Harvard United States Massachusetts Institute of Technology United States

Causal graph discovery is a significant problem with applications across various disciplines. However, with observational data alone, the underlying causal graph can only be recovered up to its Markov equivalence class, and further assumptions or interventions are necessary to narrow down the true graph. This work addresses the causal discovery problem under the setting of stochastic interventions with the natural goal of minimizing the number of interventions performed. We propose the following stochastic intervention model which subsumes existing adaptive noiseless interventions in the literature while capturing scenarios such as fat-hand interventions and CRISPR gene knockouts: any intervention attempt results in an actual intervention on a random subset of vertices, drawn from a distribution dependent on attempted action. Under this model, we study the two fundamental problems in causal discovery of verification and search and provide approximation algorithms with polylogarithmic competitive ratios and provide some preliminary experimental results. Copyright © 2024, The Authors. All rights reserved.

关键词： approximation algorithms

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Space Complexity of Minimum Cut Problems in Single-Pass Streams

arXiv

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arXiv 2024年

作者： Ding, Matthew Garces, Alexandro Li, Jason Lin, Honghao Nelson, Jelani Shah, Vihan Woodruff, David P. Department of Electrical Engineering and Computer Sciences University of California Berkeley United States Department of Mathematics Massachusetts Institute of Technology United States Computer Science Department Carnegie Mellon University United States Department of Computer Science University of Waterloo Canada

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less well-studied. To this end, we show upper and lower bounds on minimum cut problems in insertion-only streams for a variety of settings, including for both randomized and deterministic algorithms, for both arbitrary and random order streams, and for both approximate and exact algorithms. One of our main results is an Oe(n/Ε) space algorithm with fast update time for approximating a spectral cut query with high probability on a stream given in an arbitrary order. Our result breaks the Ω(n/Ε2) space lower bound required of a sparsifier that approximates all cuts simultaneously. Using this result, we provide streaming algorithms with near optimal space of Oe(n/Ε) for minimum cut and approximate all-pairs effective resistances, with matching space lower-bounds. The amortized update time of our algorithms is Oe(1), provided that the number of edges in the input graph is at least (n/Ε2)1+o(1). We also give a generic way of incorporating sketching into a recursive contraction algorithm to improve the post-processing time of our algorithms. In addition to these results, we give a random-order streaming algorithm that computes the exact minimum cut on a simple, unweighted graph using Oe(n) space. Finally, we give an Ω(n/Ε2) space lower bound for deterministic minimum cut algorithms which matches the best-known upper bound up to polylogarithmic factors. Copyright © 2024, The Authors. All rights reserved.

关键词： approximation algorithms

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Image Messages Security Using the Elkamchouchi-Elshenawy-Shaban Algorithm, Logistic Chaos, and XOR

Image Messages Security Using the Elkamchouchi-Elshenawy-Sha...

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International Conference on Electrical, Telecommunication and Computer Engineering (ELTICOM)

作者： Dian Rachmawati Mohammad Andri Budiman Wilbert Departemen Ilmu Komputer Fakultas Ilmu Komputer dan Teknologi Informasi Universitas Sumatera Utara Medan Indonesia

ISBN: (数字)9798331531249

ISBN: (纸本)9798331531256

The rise of digital technology necessitates robust methods for securing image transmissions against interception and theft. This research presents a web-based application for encrypting and decrypting image files using the Elkamchouchi-Elshenawy-Shaban algorithm, Logistic Map, and XOR operations. The Elkamchouchi-Elshenawy-Shaban cryptosystem extends RSA with Gaussian integers for enhanced security, while the Logistic Map introduces complexity through chaotic behavior, and XOR operations ensure data confidentiality. Developed with Python and Laravel, the application includes functionalities for login, registration, key generation, encryption, decryption, and key management. Testing confirmed the method's effectiveness, with decrypted images matching the originals. Results showed encryption and decryption times for the Elkamchouchi-Elshenawy-Shaban algorithm increase with key size, while Logistic Map and XOR operations remain unaffected, achieving processing times under one second per cycle. This application provides a secure and efficient solution for protecting image data, leveraging hybrid cryptosystems to ensure safe transmission.

关键词： Data privacy Image matching Image communication approximation algorithms Public key cryptography Encryption Complexity theory Computer security Logistics Testing

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A Decoupled Channel Estimation Method for Beyond Diagonal RIS

A Decoupled Channel Estimation Method for Beyond Diagonal RI...

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Asilomar Conference on Signals, Systems & Computers

作者： Bruno Sokal Fazal-E-Asim André L. F. de Almeida Hongyu Li Bruno Clerckx Federal University of Ceara Fortaleza Brazil Imperial College London London U.K.

ISBN: (数字)9798350354058

ISBN: (纸本)9798350354065

Beyond diagonal reconfigurable intelligent surface (BD- RIS) is a new architecture for RIS where elements are interconnected to provide more wave manipulation flexibility than traditional single-connected RIS, enhancing data rate and coverage. However, channel estimation for BD- RIS is challenging due to the more complex multiple-connection structure involving their scattering elements. To address this issue, this paper proposes a decoupled channel estimation method for BD- RIS that yields separate estimates of the involved channels to enhance the accuracy of the overall combined channel by capitalizing on its Kronecker structure. Starting from a least squares estimate of the combined channel and by properly reshaping the resulting filtered signal, the proposed algorithm resorts to a Khatri-Rao Factorization (KRF) method that teases out the individual channels based on simple rank-one matrix approximation steps. Numerical results show that the proposed decoupled channel estimation yields more accurate channel estimates than the classical least squares scheme.

关键词： Training Computers Accuracy Channel estimation Scattering Estimation Computer architecture Reconfigurable intelligent surfaces Filtering algorithms approximation algorithms

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Efficient Simulations for Pricing Barrier Options under Stochastic Volatility Model

Efficient Simulations for Pricing Barrier Options under Stoc...

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International Conference on Optimization and Applications (ICOA)

作者： Abdelghani Benjouad Mohammed Kaicer Department of Economics FSJES Moulay Ismail University Meknes Morocco Department of Mathematics Faculty of Sciences Ibn Tofail University Kenitra Morocco

ISBN: (数字)9798350387353

ISBN: (纸本)9798350387360

In this work, a numerical method is proposed to evaluate barrier options. We use a classical and recently proposed numerical techniques for derivative pricing with applications to barrier options under stochastic volatility model. Monte-Carlo simulations are used which refer to a set of methods for generating synthetic time series of the volatility and stock price of equities, from which option price can be derived. We present our numerical results; we find that these schemes are intended to have faster convergence.

关键词： Monte Carlo methods Time series analysis Stochastic processes Pricing approximation algorithms Numerical models Standards Optimization Convergence

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State-Space Piece-Wise Affine System Identification with Online Deterministic Annealing

State-Space Piece-Wise Affine System Identification with Onl...

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European Control Conference (ECC)

作者： Christos N. Mavridis Aris Kanellopoulos John S. Baras Karl Henrik Johansson Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Department of Electrical and Computer Engineering and the Institute for Systems Research University of Maryland College Park USA

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

We propose an online identification scheme for discrete-time piece-wise affine state-space models based on a system of adaptive algorithms running in two timescales. A stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale, estimating the partition of the augmented state-input space that defines the switching signal. At the same time, an adaptive identification algorithm, running at a higher timescale, updates the parameters of the local models based on the estimate of the switching signal. Identifiability conditions for the switched system are discussed and convergence results are given based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for piece-wise affine systems, the proposed approach progressively estimates the number of modes needed and is appropriate for online system identification using sequential data acquisition. This progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off, desired in practical applications. Experimental results validate the efficacy of the proposed methodology.

关键词： Switched systems Annealing Stochastic processes Switches approximation algorithms Real-time systems System identification

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On the Hardness and approximation of the Densest $K$-Subgraph Problem in Parameterized Metric Graphs

SSRN

引用

SSRN 2022年

作者： Chang, Shih-Chia Chen, Li-Hsuan Hsieh, Sun-Yuan Hung, Ling-Ju Kao, Shih-Shun Klasing, Ralf Department of Business Administration National Taipei University of Business Taipei City100026 Taiwan ProBrand Technology Inc. Taoyuan City330 Taiwan Department of Computer Science and Information Engineering National Cheng Kung University Tainan701401 Taiwan Department of Creative Technologies Product Design National Taipei University of Business Taoyuan City324022 Taiwan CNRS LaBRI Université de Bordeaux 351 Cours de la Libération Talence33405 cedex France

A complete weighted graph $G= (V, E, w)$ is called $\Delta_{\beta}$-metric, for some $\beta \geq 1/2$, if $G$ satisfies the $\beta$-triangle inequality, {\em i.e.,} $w(u,v) \leq \beta \cdot (w(u,x) + w(x,v))$ for all vertices $u,v,x\in V$. Given a $\Delta_{\beta}$-metric graph $G=(V, E, w)$, the {\sc $\Delta_{\beta}$-Weighted Densest $k$-Subgraph} ($\Delta_{\beta}$-WD$k$S) problem is to find an induced subgraph $G[C]$ with exactly $k$ vertices such that the total edge weight of $G[C]$ is maximized. For $\beta = 1$, this problem, $\Delta$-WD$k$S, is known NP-hard and admits a $\fracapproximationapproximation$-approximation algorithms. In this paper, we show that for any $\beta > 1/2$, $\Delta_{\beta}$-WD$k$S is NP-hard. We prove that $\Delta_{\beta}$-WD$k$S can be approximated to within a factor $(\fracapproximation{2\beta}+\frac{2\beta-1}{2\beta \cdot (2k-3)})$ for any $\beta > \fracapproximationapproximation$. Moreover, we show how to modify any $\alpha$-approximation algorithm for $\Delta$-WD$k$S to obtain a $\delta_{\alpha,\beta}$-approximationalgorithm for $\Delta_{\beta}$-WD$k$S for every $\fracapproximationapproximation 1$. © 2022, The Authors. All rights reserved.

关键词： approximation algorithms

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Reconfigurable Intelligent Surface Aided Rate-Splitting Multiple Access for Multi-User Downlink Transmission

Reconfigurable Intelligent Surface Aided Rate-Splitting Mult...

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IEEE International Conference on Communications Workshops, ICC

作者： Yue Li Yujie Zhang Xiao Chen Baolong Li Jianfeng Shi School of Electronic and Information Engineering Nanjing University of Information Science and Technology Nanjing China School of Intelligent Engineering Nanjing Institute of Railway Technology Nanjing China School of Artificial Intelligence Nanjing University of Information Science and Technology Nanjing China

ISBN: (数字)9798350304053

ISBN: (纸本)9798350304060

This paper examines the resource allocation problem in a wireless communication system utilizing rate-splitting multiple access (RSMA) assisted by the reconfigurable intelligent surface (RIS). We aim to jointly optimize user rate allocation, base station (BS) beamforming vectors, and RIS phase shift matrix to maximize the sum-rate of all users while satisfying quality of service requirements, power constraints, and constraints related to RIS reflecting elements. Firstly, closed-form expressions for the optimal user rate allocation scheme are derived, and the weighted minimum mean square error (WMMSE) method is employed to design BS beamforming vectors and nearly optimal solutions for ideal RIS phase shifts. Secondly, an alternative solution is proposed for the near-optimal design of non-ideal RIS phase shifts, utilizing successive convex approximation (SCA) and penalty methods. Ultimately, the simulation results confirm that the proposed algorithm surpasses benchmark algorithms in its rate performance. Additionally, compared to RIS-assisted non-orthogonal multiple access (NOMA) and RIS-assisted space division multiple access (SDMA), RIS-assisted RSMA can achieve rate performance improvements of 24.4% and 10.2%. respectively.

关键词： Wireless communication NOMA Array signal processing Simulation Conferences Reconfigurable intelligent surfaces approximation algorithms

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Sparse Array Design for ISAC in the Presence of Beam-Squint

Sparse Array Design for ISAC in the Presence of Beam-Squint

引用

International Conference on Communications, Signal Processing, and their Applications (ICCSPA)

作者： Ahmet M. Elbir Asmaa Abdallah Abdulkadir Celik Ahmed M. Eltawil King Abdullah University of Science and Technology Saudi Arabia

ISBN: (数字)9798350384819

ISBN: (纸本)9798350384826

This paper presents an efficient approach for joint antenna selection and hybrid beamforming for integrated sensing and communications (ISAC) in the presence of beamsquint. We proposed a manifold optimization-based technique that incorporates beam-squint compensation for hybrid beamformer design. To reduce computational and memory costs for antenna selection, we propose novel algorithms leveraging grouped subarrays, wherein the entire array is divided into non-overlapping groups. Numerical simulations show that the proposed approach exhibits up to 95% lower complexity for large antenna arrays while maintaining satisfactory communications with approximately 6% loss in the achievable rate.

关键词： Manifolds Costs Array signal processing Signal processing algorithms Integrated sensing and communication Numerical simulation approximation algorithms Complexity theory Antenna arrays

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