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New Branching Filters With Explicit Negative Dependence

IEEE ACCESS 2020年 8卷 157306-157321页

作者： Kouritzin, Michael A. Mackay, Anne Vellone-Scott, Nicolas Univ Alberta Dept Math & Stat Sci Edmonton AB T6G 2G1 Canada Univ Quebec Montreal Dept Math Montreal PQ H2X 3Y7 Canada

Particle filters are used to solve nonlinear filtering problems. We focus on the sampling step of a particle filter and present new algorithms that introduce explicit negative dependence between the number of particles reassigned at each location, with the goal of improving the performance of the filtering algorithm. We review partial and complete sampling in the context of both interacting and branching filters, that is, when the number of particles stays constant through all steps and when it does not. In particular, we use the quick simulation field algorithm to reproduce the variance structure induced by the minimal variance filter and create a new filtering algorithm. A numerical example is used to assess the performance of the new algorithms.

关键词： Random variables Sampling methods Monte Carlo methods approximation algorithms Atmospheric measurements Particle measurements Licenses Nonlinear filtering sequential Monte Carlo Bernoulli sampling interacting filters branching filters

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A Novel Value Iteration Scheme With Adjustable Convergence Rate

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第10期34卷 7430-7442页

作者： Ha, Mingming Wang, Ding Liu, Derong Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intellige Beijing Peoples R China Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

In this article, a novel value iteration scheme is developed with convergence and stability discussions. A relaxation factor is introduced to adjust the convergence rate of the value function sequence. The convergence conditions with respect to the relaxation factor are given. The stability of the closed-loop system using the control policies generated by the present VI algorithm is investigated. Moreover, an integrated VI approach is developed to accelerate and guarantee the convergence by combining the advantages of the present and traditional value iterations. Also, a relaxation function is designed to adaptively make the developed value iteration scheme possess fast convergence property. Finally, the theoretical results and the effectiveness of the present algorithm are validated by numerical examples.

关键词： Convergence Iterative algorithms Stability criteria Heuristic algorithms approximation algorithms Optimal control Numerical stability Adaptive dynamic programming (ADP) admissible control policy convergence rate discrete-time nonlinear systems reinforcement learning (RL) value iteration

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Unfolding WMMSE Using Graph Neural Networks for Efficient Power Allocation

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2021年第9期20卷 6004-6017页

作者： Chowdhury, Arindam Verma, Gunjan Rao, Chirag Swami, Ananthram Segarra, Santiago Rice Univ Dept Elect & Comp Engn ECE Houston TX 77005 USA US Army CCDC Army Res Lab Adelphi MD 20783 USA

We study the problem of optimal power allocation in a single-hop ad hoc wireless network. In solving this problem, we depart from classical purely model-based approaches and propose a hybrid method that retains key modeling elements in conjunction with data-driven components. More precisely, we put forth a neural network architecture inspired by the algorithmic unfolding of the iterative weighted minimum mean squared error (WMMSE) method, that we denote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE are parameterized using graph neural networks (GNNs), where the time-varying underlying graphs are given by the fading interference coefficients in the wireless network. These GNNs are trained through a gradient descent approach based on multiple instances of the power allocation problem. We show that the proposed architecture is permutation equivariant, thus facilitating generalizability across network topologies. Comprehensive numerical experiments illustrate the performance attained by UWMMSE along with its robustness to hyper-parameter selection and generalizability to unseen scenarios such as different network densities and network sizes.

关键词： Resource management Wireless networks Interference Computer architecture approximation algorithms Transmitters Receivers WMMSE power allocation graph neural networks deep learning algorithm unfolding

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On the adaptivity gap of stochastic orienteering

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MATHEMATICAL PROGRAMMING 2015年第1-2期154卷 145-172页

作者： Bansal, Nikhil Nagarajan, Viswanath Eindhoven Univ Technol Dept Math & Comp Sci NL-5600 MB Eindhoven Netherlands Univ Michigan Ind & Operat Engn Dept Ann Arbor MI 48109 USA

The input to the stochastic orienteering problem (Gupta et al. in SODA, pp 1522-1538, 2012) consists of a budget B and metric (V, d) where each vertex has a job with a deterministic reward and a random processing time (drawn from a known distribution). The processing times are independent across vertices. The goal is to obtain a non-anticipatory policy (originating from a given root vertex) to run jobs at different vertices, that maximizes expected reward, subject to the total distance traveled plus processing times being at most B. An adaptive policy can choose the next vertex to visit based on observed random instantiations. Whereas, a non-adaptive policy is just given by a fixed ordering of vertices. The adaptivity gap is the worst-case ratio of the optimal adaptive and non-adaptive rewards. We prove an lower bound on the adaptivity gap of stochastic orienteering. This provides a negative answer to the O(1)-adaptivity gap conjectured by Gupta et al. (2012), and comes close to the upper bound. This result holds even on a line metric. We also show an upper bound on the adaptivity gap for the correlated stochastic orienteering problem, where the reward of each job is random and possibly correlated to its processing time. Using this, we obtain an improved quasi-polynomial time -approximation algorithm for correlated stochastic orienteering.

关键词： approximation algorithms Stochastic Vehicle routing

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Variational Learning algorithms for Channel Estimation in RIS-Assisted mmWave Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第1期72卷 222-238页

作者： Nakul, Milind Rajoriya, Anupama Budhiraja, Rohit Georgia Inst Technol Atlanta GA 30332 USA Indian Inst Technol Kanpur IIT Kanpur Dept Elect Engn Kanpur 208016 India

We consider the problem of estimating channel in reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) systems. We propose two variational expectation maximization (VEM) based channel estimation algorithms, which exploit the angular domain sparsity of RIS-assisted mmWave channel. To fully capture this sparsity, both within and across UEs, we construct a novel column-wise coupled Gaussian prior. The first proposed structured-mean-field-based VEM (SMF-VEM) algorithm uses the proposed prior, and calculates the posterior distribution of the unknown channel by assuming that it belongs to a set of multivariate distributions. This algorithm inverts a high-dimensional matrix in its posterior update, and consequently does not scale well for a large number of RIS elements and base station antennas, which are commonly used in practical systems. The second proposed fast mean field-based VEM (FMF-VEM) algorithm reduces complexity by assuming a fully-factorized posterior. It also bounds the variational objective to remove the residue coupling between the channel and phase matrices. Using extensive numerical investigations for a practical RIS mmWave system, and by using multiple metrics, we show that the proposed i) SMF- and FMF-VEM algorithms outperform several of their state-of-the-art counterparts;and ii) FMF-VEM has a much lower time complexity than SMF-VEM.

关键词： Channel estimation approximation algorithms Millimeter wave communication Sparse matrices Matching pursuit algorithms Bayes methods Signal processing algorithms Variational inference expectation maximization sparse Bayesian learning (SBL)

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Approximating low-congestion routing and column-restricted packing problems

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INFORMATION PROCESSING LETTERS 2000年第1-2期74卷 19-25页

作者： Baveja, A Srinivasan, A Rutgers State Univ Sch Business Camden NJ 08102 USA Bell Labs Lucent Technol Murray Hill NJ 07974 USA Natl Univ Singapore Sch Comp Singapore 119260 Singapore

We contribute to a body of research asserting that the fractional and integral optima of column-sparse integer programs are "nearby". This yields improved approximation algorithms for some generalizations of the knapsack problem, with applications to low-congestion routing in networks, file replication in distributed databases, and other packing problems. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： algorithms approximation algorithms packing integer programming routing

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Constrained Nonnegative Matrix Factorization for Blind Hyperspectral Unmixing Incorporating Endmember Independence

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2021年 14卷 11853-11869页

作者： Ekanayake, E. M. M. B. Weerasooriya, H. M. H. K. Ranasinghe, D. Y. L. Herath, S. Rathnayake, B. Godaliyadda, G. M. R., I Ekanayake, M. P. B. Herath, H. M. V. R. Monash Univ Dept Elect & Comp Syst Engn Clayton Vic 3800 Australia Off Res & Innovat Serv Technol Campus Padukka 10500 CO Sri Lanka Univ Peradeniya Dept Elect & Elect Engn Peradeniya 20400 KY Sri Lanka Rensselaer Polytech Inst Dept Elect Comp & Syst Engn Troy NY 12180 USA

Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmembers weighted by fractional abundances. The endmembers of a hyperspectral image (HSI) are more likely to be generated by independent sources and be mixed in a macroscopic degree before arriving at the sensor element of the imaging spectrometer as mixed spectra. Over the past few decades, many attempts have focused on imposing auxiliary regularizes on the conventional nonnegative matrix factorization (NMF) framework in order to effectively unmix these mixed spectra. As a promising step toward finding an optimum regularizer to extract endmembers, this article presents a novel blind HU algorithm, referred to as kurtosis-based smooth nonnegative matrix factorization (KbSNMF) which incorporates a novel regularizer based on the statistical independence of the probability density functions of endmember spectra. Imposing this regularizer on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. Experiments conducted on diverse synthetic HSI datasets (with numerous numbers of endmembers, spectral bands, pixels, and noise levels) and three standard real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm compared to several state-of-the-art NMF-based HU baselines. The proposed algorithm exhibits superior performance especially in terms of extracting endmember spectra from hyperspectral data;therefore, it could uplift the performance of recent deep learning HU methods which utilize the endmember spectra as supervisory input data for abundance extraction.

关键词： Matrix decomposition Hyperspectral imaging Data mining Feature extraction approximation algorithms Pragmatics Libraries Blind source separation constrained endmember independence Gaussianity hyperspectral unmixing (HU) kurtosis nonnegative matrix factorization (NMF)

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S-DIGing: A Stochastic Gradient Tracking Algorithm for Distributed Optimization

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2022年第1期6卷 53-65页

作者： Li, Huaqing Zheng, Lifeng Wang, Zheng Yan, Yu Feng, Liping Guo, Jing Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Xinzhou Teachers Univ Dept Comp Sci Xinzhou 034000 Peoples R China

In this article, we study convex optimization problems where agents of a network cooperatively minimize the global objective function which consists of multiple local objective functions. The intention of this work is to solve large-scale optimization problems where the local objective function is complicated, and numerous. Different from most of the existing works, the local objective function of each agent is presented as the average of finite instantaneous functions. Integrating the gradient tracking algorithm with stochastic averaging gradient technology, a distributed stochastic gradient tracking (termed as S-DIGing) algorithm is proposed. At each time instant, only one randomly selected gradient of an instantaneous function is computed, and applied to approximate the local batch gradient for each agent. Based on a novel primal-dual interpretation of the S-DIGing algorithm, it is shown that the S-DIGing algorithm linearly converges to the global optimal solution when step-size do not exceed an explicit upper bound, and the instantaneous functions are strongly convex with Lipschitz continuous gradients. Numerical experiments are presented to demonstrate the practicability of the S-DIGing algorithm, and correctness of the theoretical results.

关键词： Optimization Convergence Linear programming approximation algorithms Stochastic processes Machine learning algorithms Convex functions Distributed optimization gradient tracking stochastic averaging gradient multi-agent systems linear convergence

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A theoretical analysis of query selection for collaborative filtering

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MACHINE LEARNING 2003年第3期51卷 283-298页

作者： Dasgupta, S Lee, WS Long, PM Univ Calif San Diego Dept Comp Sci La Jolla CA 92093 USA Natl Univ Singapore Dept Comp Sci Singapore 117548 Singapore Natl Univ Singapore Singapore MIT Alliance Singapore 117548 Singapore Genome Inst Singapore Singapore Singapore

We consider the problem of determining which of a set of experts has tastes most similar to a given user by asking the user questions about his likes and dislikes. We describe a simple algorithm for generating queries for a theoretical model of this problem. We show that the algorithm requires at most opt(F)(ln(|F|/ opt(F)) + 1) + 1 queries to find the correct expert, where opt( F) is the optimal worst-case bound on the number of queries for learning arbitrary elements of the set of experts F. The algorithm runs in time polynomial in | F| and | X| (where X is the domain) and we prove that no polynomial-time algorithm can have a significantly better bound on the number of queries unless all problems in NP have n(O(log log n)) time algorithms. We also study a more general case where the user ratings come from a finite set Y and there is an integer-valued loss function l on Y that is used to measure the distance between the ratings. Assuming that the loss function is a metric and that there is an expert within a distance. from the user, we give a polynomial-time algorithm that is guaranteed to find such an expert after at most 2opt(F,eta) ln |F|/1+deg(F, eta) +2(eta+1)(1 + deg(F, eta)) queries, where deg(F, eta) is the largest number of experts in F that are within a distance 2eta of any f is an element of F.

关键词： collaborative filtering recommender systems membership queries approximation algorithms inapproximability

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SUBLINEAR TIME algorithms

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2011年第4期25卷 1562-1588页

作者： Rubinfeld, Ronitt Shapira, Asaf MIT Comp Sci Artificial Intelligence Lab Cambridge MA 02139 USA Tel Aviv Univ Blavatnik Sch Comp Sci Tel Aviv Israel Tel Aviv Univ Sch Math IL-69978 Tel Aviv Israel Georgia Inst Technol Sch Math & Comp Sci Atlanta GA 30332 USA

Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a very small portion of the input. We discuss the types of answers that one ca... 详细信息

关键词： sublinear time algorithms approximation algorithms randomized algorithms property testing

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