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random algorithms for convex minimization problems

MATHEMATICAL PROGRAMMING 2011年第2期129卷 225-253页

作者： Nedic, Angelia Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

This paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems, where the constraint set is specified as the intersection of possibly infinitely many constraint sets. Each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function. The proposed algorithms are applicable to the situation where the whole constraint set of the problem is not known in advance, but it is rather learned in time through observations. Also, the algorithms are of interest for constrained optimization problems where the constraints are known but the number of constraints is either large or not finite. We analyze the proposed algorithm for the case when the objective function is differentiable with Lipschitz gradients and the case when the objective function is not necessarily differentiable. The behavior of the algorithm is investigated both for diminishing and non-diminishing stepsize values. The almost sure convergence to an optimal solution is established for diminishing stepsize. For non-diminishing stepsize, the error bounds are established for the expected distances of the weighted averages of the iterates from the constraint set, as well as for the expected sub-optimality of the function values along the weighted averages.

关键词： Convex minimization Gradient algorithms Subgradient algorithms random algorithms Error bounds

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Impact of random weights on nonlinear system identification using convolutional neural networks

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INFORMATION SCIENCES 2019年 477卷 1-14页

作者： Yu, Wen Pacheco, Mario Natl Polytech Inst CINVESTAV IPN Dept Control Automat Av IPN 2508 Mexico City 07360 DF Mexico

randomized algorithms have been successfully applied in modeling dynamic system. How do random weights affect system identification and why do they sometimes work well? In this paper, we use the convolutional neural network (CNN) as an identification model to answer these questions. Since the convolution operation is an important property of the dynamic system and in the frequency domain it becomes the product, the CNN model is analyzed in the frequency domain. We first modify the CNN model, so that it can model both the input and the output series. Then we analyze the impact of the random weights of CNN in the frequency domain. We prove the existence of optimal weights and analyze the modeling accuracy under optimal weights and random weights. Through theoretical analysis, we propose a two-step training method and compare it with the random weight algorithm. The proposed CNN model with random weights is validated with three benchmark problems. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Convolutional neural network random algorithms Frequency domain Deep learning

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A random least-trimmed-squares identification algorithm

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AUTOMATICA 2003年第9期39卷 1651-1659页

作者： Bai, EW Univ Iowa Dept Elect & Comp Engn Iowa City IA 52242 USA

The Least-trimmed-squares (LTS) estimator is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. In this paper, we propose a random LTS algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval. Moreover, if the number of data points goes to infinite, the algorithm becomes a deterministic one that converges to the true LTS in some probability sense. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： least squares least trimmed squares random algorithms system identification parameter estimation

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An Interpretable Constructive Algorithm for Incremental random Weight Neural Networks and Its Application

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2024年第12期20卷 13622-13632页

作者： Nan, Jing Dai, Wei Yuan, Guan Zhou, Ping China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Jiangsu Peoples R China Singapore Univ Technol & Design Engn Prod Dev Pillar Singapore 487372 Singapore China Univ Min & Technol Sch Informat & Control Engn Sch Comp Sci & Technol Digitizat MineEngn Res CtrMinist Educ Xuzhou 221116 Jiangsu Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China Minist Educ Key Lab Coal Proc & Efficient Utilizat Xuzhou 221116 Jiangsu Peoples R China

In this article, we aim to offer an interpretable learning paradigm for incremental random weight neural networks (IRWNNs). IRWNNs have become a hot research direction of neural network algorithms due to their ease of deployment and fast learning speed. However, existing IRWNNs have difficulty explaining how hidden nodes (parameters) affect the convergence of network residuals. To address this gap, this article proposes an interpretable construction algorithm (ICA). Specifically, we first conduct a spatial geometric analysis of the network construction process and establish the spatial geometric relationship between the network residuals and hidden parameters to visualize the influence of hidden parameters on the convergence of the network residuals. Second, based on the spatial geometric relationship and node pool strategy, an interpretable control strategy with spatial geometry information is established to obtain hidden parameters conducive to the convergence of network residuals. In addition, to facilitate ICA to handle complex tasks of big data, this article proposes a lightweight ICA with low complexity, namely ICA+. Finally, it is proved theoretically that the ICA and ICA+ proposed in this article have universal approximation properties. The experimental results on two real-world datasets and seven benchmark datasets demonstrate the advantages of the proposed ICA and ICA+ in terms of fast learning, good generalization, and compactness of network structure.

关键词： Data modeling interpretable constructive algorithm neural networks (NNs) random algorithms spatial geometric information

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random generation of tournaments and asymmetric graphs with given out-degrees

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1996年第2期95卷 411-419页

作者： Charon, I Germa, A Hudry, O ECOLE NATL SUPER TELECOMMUN BRETAGNE F-75634 PARIS 13FRANCE

In this paper, we first present a polynomial algorithm which computes a random tournament with given out-degrees;any tournament having these out-degrees has a nonzero probability to be computed. Then we give a necessary and sufficient condition for a sequence of numbers to be the out-degrees (or similarly the in-degrees) of an asymmetric graph. Lastly, using the above algorithm and this characterization, we design a second polynomial algorithm to compute a random asymmetric graph with given out-degrees, and any asymmetric graph with these out-degrees has a nonzero probability to be found.

关键词： graph theory random algorithms tournaments asymmetric graphs out-degrees

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A random Algorithm for Designing the System Matrix in Compressive Spectral Imaging by Homogenizing its Structure

A Random Algorithm for Designing the System Matrix in Compre...

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International Workshop on Engineering Applications (WEA)

作者： Noriega, Camilo Mejia, Yuri Arguello, Henry Univ Ind Santander Escuela Ingn Sistemas & Informat Bucaramanga Colombia Univ Ind Santander Escuela Ingn Elect Elect & Telecomun Bucaramanga Colombia

ISBN: (纸本)9781509002283

Compressive spectral imaging systems (CSI) use a focal plane array (FPA) to measure two-dimensional (2D) coded projections of a three-dimensional (3D) spatio-spectral scene. A reconstruction algorithm based on compressive sensing theory exploits the projections to retrieve the underlying 3D scene. Compressive sensing relies on two principles: sparsity and incoherence. Higher incoherence drives to better reconstructed images quality. The Colored Coded Aperture Spectral Imager (C-CASSI) is a CSI system where the coded projections are produced by optical elements named coded apertures. The C-CASSI system can be modeled as a linear transformation. The transformation matrix represents the physical effects of the coded aperture and the prism on the scene. The transformation matrix is also called the system representative matrix. The colored coded apertures modulate spatially and spectrally the light from the scene. The reconstruction image quality is highly dependent on the colored coded apertures design. An algorithm that randomly designs the coded apertures maintains the incoherence between the sensing matrix and the representation base. However, a coded aperture designed completely random, may cause the voxel information be sensed more than once, or not be sensed. This paper presents a random algorithm for colored coded apertures design by homogenizing defined parameters of the C-CASSI system representative matrix. Homogenization parameters guarantee that a voxel information would be sensed at least once. The homogenization is achieved leveling the selected parameters of the matrix, like the average of unblocking elements per column and the average of unblocking elements per row. Simulations show improvement up to 3.10 dB in the PSNR reconstructed images by using the colored coded apertures designs compared with traditional coded apertures.

关键词： Colored coded apertures C-CASSI spectral images random algorithms

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Verification of the Miller-Rabin probabilistic primality test

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JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING 2003年第1-2期56卷 3-21页

作者： Hurd, J Univ Cambridge Comp Lab Cambridge CB2 3QG England

Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the Miller-Rabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation satisfies the stronger property of guaranteed termination. Completing the proof of correctness requires a significant body of group theory and computational number theory to be formalized in the theorem prover. Once verified, the primality test can either be executed in the logic (using rewriting) and used to prove the compositeness of numbers, or manually extracted to standard ML and used to find highly probable primes. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： formal verification random algorithms primality test

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Hypothesis group testing for disjoint pairs

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2008年第1期15卷 7-16页

作者： Bishop, Morgan A. Macula, Anthony J. Renz, Thomas E. Ufimtsev, Vladimir V. SUNY Coll Geneseo Dept Math Geneseo NY 14454 USA JEANSEE Geneseo NY USA USAF Res Lab IFTC Rome Res Site Rome NY 13441 USA

Classical group testing (CGT) is a widely applicable biotechnical technique used to identify a small number of distinguished objects from a population when the presence of any one of these distinguished objects among a group of others produces an observable result. This paper discusses a variant of CGT called group testing for disjoint pairs (GTAP). The difference between the two is that in GTDP, the distinguished items are pairs from, not individual objects in, the population. There are several biological examples of when this abstract model applies. One biological example is DNA hybridization. The presence of pairs of hybridized DNA strands can be detected in a pool of DNA strands. Another situation is the detection of binding interactions between prey and bait proteins. This paper gives a random pooling method, similar in spirit to hypothesis testing, which identifies pairs of objects from a population that collectively have an observable function. This method is simply to apply, achieves good results, is amenable to automation and can be easily modified to compensate for testing errors.

关键词： group testing complexes nonadaptive pooling random algorithms

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On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage

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AUTOMATICA 2006年第2期42卷 251-260页

作者： Gupta, V Chung, TH Hassibi, B Murray, RM CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA

In this note we consider the following problem. Suppose a set of sensors is jointly trying to estimate a process. One sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors. What is the sensor schedule that results in the minimum error covariance? We describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable. The problem described above comes up in many domains out of which we discuss two. In the sensor selection problem, there are multiple sensors that cannot operate simultaneously (e.g., sonars in the same frequency band). Thus measurements need to be scheduled. In the sensor coverage problem, a geographical area needs to be covered by mobile sensors each with limited range. Thus from every position, the sensors obtain a different view-point of the area and the sensors need to optimize their trajectories. The algorithm is applied to these problems and illustrated through simple examples. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： sensor selection sensor location selection distributed sensor networks Riccati-like equation random algorithms

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Voting method for the detection of subpixel flow field

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PATTERN RECOGNITION LETTERS 2003年第1-3期24卷 197-214页

作者： Imiya, A Iwawaki, K Natl Inst Informat Chiyoda Ku Tokyo 1018430 Japan Chiba Univ Inst Media & Informat Technol Media Technol Div Inage Ku Chiba 2638522 Japan Chiba Univ Sch Sci & Technol Inage Ku Chiba 2638522 Japan

In this paper, we show that the randomized sampling and voting process detects optical flow. Using an appropriate number of images from a sequence of images, our method detects subpixel motion in this sequence. We use the accumulator space for the unification of these flow vectors which are computed from different time intervals. Numerical examples for the test image sequences show the performance of our method. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： Hough transform subpixel analysis model fitting random algorithms optical flow

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