作者:
Oishi, YKimura, HUniv Tokyo
Grad Sch Informat Sci & Technol Dept Math Informat Bunkyo Ku Tokyo 1130033 Japan
The randomized algorithm of Calafiore and Polyak, which consists of random sampling and subgradient descent, is analyzed in the case that it is used to solve parameter-dependent linear matrix inequalities. This paper ...
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ISBN:
(纸本)0780370619
The randomized algorithm of Calafiore and Polyak, which consists of random sampling and subgradient descent, is analyzed in the case that it is used to solve parameter-dependent linear matrix inequalities. This paper shows that the expected time to achieve a solution is infinite if this algorithm is used in its original form. However, it is also shown that the algorithm can be improved so that its expected achievement time becomes finite. An explicit upper bound of the expected achievement time is given in a special case. A numerical example is provided.
For data analysis, a partial singular value decomposition (SVD) of the sparse matrix representing the data is a powerful tool. However, computing the SVD of a large matrix can take a significant amount of time even on...
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ISBN:
(纸本)9781450337236
For data analysis, a partial singular value decomposition (SVD) of the sparse matrix representing the data is a powerful tool. However, computing the SVD of a large matrix can take a significant amount of time even on a current high-performance supercomputer. Hence, there is a growing interest in a novel algorithm that can quickly compute the SVD for efficiently processing massive amounts of data that are being generated from many modern applications. To respond to this demand, in this paper, we study randomized algorithms that update the SVD as changes are made to the data, which is often more efficient than recomputing the SVD from scratch. Furthermore, in some applications, recomputing the SVD may not be possible because the original data, for which the SVD has been already computed, is no longer available. Our experimental results with the data sets for the Latent Semantic Indexing and population clustering demonstrate that these randomized algorithms can obtain the desired accuracy of the SVD with a small number of data accesses, and compared to the state-of-the-art updating algorithm, they often require much lower computational and communication costs. Our performance results on a hybrid CPU/GPU cluster show that these randomized algorithms can obtain significant speedups over the state-of-the-art updating algorithm.
In the majority problem, we are given n balls coloured black or white and we are allowed to query whether two balls have the same colour or not. The goal is to find a ball of majority colour in the minimum number of q...
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Competitive analysis is concerned with comparing the performance of on-line algorithms with that of optimal off-line algorithms. In some cases randomization can lead to algorithms with improved performance ratios on w...
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Competitive analysis is concerned with comparing the performance of on-line algorithms with that of optimal off-line algorithms. In some cases randomization can lead to algorithms with improved performance ratios on worst-case sequences. In this paper we present new ramdomized on-line algorithms for snoopy caching and the spin-block problem. These algorithms achieve competitive ratios approaching e/(e - 1) almost-equal-to 1.58 against an oblivious adversary. These ratios are optimal and are a surprising improvement over the best possible ratio in the deterministic case, which is 2. We also consider the situation when the request sequences for these problems are generated according to an unknown probability distribution. In this case we show that deterministic algorithms that adapt to the observed request statistics also have competitive factors approaching e/(e - 1). Finally, we obtain randomized algorithms for the 2-server problem on a class of isosceles triangles. These algorithms are optimal against an oblivious adversary and have competitive ratios that approach e/(e - 1). This compares with the ratio of 3/2 that can be achieved on an equilateral triangle.
作者:
Oishi, YKimura, HUniv Tokyo
Grad Sch Informat Sci & Technol Dept Math Informat Bunkyo Ku Tokyo 1138656 Japan Univ Tokyo
Grad Sch Frontier Sci Dept Complex Sci & Engn Bunkyo Ku Tokyo 1130033 Japan
randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak a...
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randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided. (C) 2003 Elsevier Ltd. All rights reserved.
In this paper a few "difficult" problems related to simultaneous stabilization of three plants (equivalent to a certain problem related to unit interpolation in H.) have been addressed through the framework ...
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In this paper a few "difficult" problems related to simultaneous stabilization of three plants (equivalent to a certain problem related to unit interpolation in H.) have been addressed through the framework of randomized algorithms. These problems which were proposed by Blondel (Simultaneous Stabilization of Linear Systems, Springer, Berlin, 1994) and Blondel and Gevers (Math. Control Signals Systems 6 (1994) 135) concern the existence of a controller. (C) 2002 Elsevier Science Ltd. All rights reserved.
This paper considers a family of randomized on-line algorithms, Algorithm R(m), where 1 less-than-or-equal-to m less-than-or-equal-to n - 1 and n is the number of input points, for the on-line Steiner tree and on-line...
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This paper considers a family of randomized on-line algorithms, Algorithm R(m), where 1 less-than-or-equal-to m less-than-or-equal-to n - 1 and n is the number of input points, for the on-line Steiner tree and on-line spanning tree problems on Euclidean space. Our main result is that if m is a fixed constant, the competitive ratios of Algorithm R(m) for the on-line Steiner tree and spanning tree problems are THETA(n). We also show that the competitive ratio of Algorithm R(n - 1), which is deterministic greedy algorithm, for the on-line spanning tree problem is the same as that for the on-line Steiner tree problem, which is O(log n).
In this paper we study a probabilistic approach which is an alternative to the classical worst-case algorithms for robustness analysis and design of uncertain control systems. That is, we aim to estimate the probabili...
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In this paper we study a probabilistic approach which is an alternative to the classical worst-case algorithms for robustness analysis and design of uncertain control systems. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted to a box I! attains a given level of performance gamma. Since this probability depends on the underlying distribution, we address the following question: What is a "reasonable" distribution so that the estimated probability makes sense? To answer this question, we define two worst-case criteria and prove that the uniform distribution is optimal in both cases. In the second part of the paper we turn our attention to a subsequent problem. That is, we estimate the sizes of both the so-called "good" and "bad" sets via sampling. Roughly speaking, the good set contains the parameters q is an element of Q with a performance level better than or equal to gamma while the bad set is the set of parameters q is an element of Q with a performance level worse than gamma. We give bounds on the minimum sample size to attain a good estimate of these sets in a certain probabilistic sense.
In this paper, we first study a generalized canonical correlation analysis (CCA)-based fault detection (FD) method aiming at maximizing the fault detectability under an acceptable false alarm rate. More specifically, ...
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In this paper, we first study a generalized canonical correlation analysis (CCA)-based fault detection (FD) method aiming at maximizing the fault detectability under an acceptable false alarm rate. More specifically, two residual signals are generated for detecting of faults in input and output subspaces, respectively. The minimum covariances of the two residual signals are achieved by taking the correlation between input and output into account. Considering the limited application scope of the generalized CCA due to the Gaussian assumption on the process noises, an FD technique combining the generalized CCA with the threshold-setting based on the randomized algorithm is proposed and applied to the simulated traction drive control system of high-speed trains. The achieved results show that the proposed method is able to improve the detection performance significantly in comparison with the standard generalized CCA-based FD method.
randomized algorithms are a useful tool for analyzing the performance of complex uncertain systems. Their implementation requires the generation of a large number N of random samples representing the uncertainty scena...
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randomized algorithms are a useful tool for analyzing the performance of complex uncertain systems. Their implementation requires the generation of a large number N of random samples representing the uncertainty scenarios, and the corresponding evaluation of system performance. When N is very large and/or performance evaluation is costly or time consuming, it can be necessary to distribute the computational burden of such algorithms among many cooperating computing units. This paper studies distributed versions of randomized algorithms for expected value, probability and extrema estimation over a network of computing nodes with possibly time-varying communication links. Explicit a priori bounds are provided for the sample and communication complexity of these algorithms in terms of number of local samples, number of computing nodes and communication iterations. (C) 2008 Elsevier B.V. All rights reserved.
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