Run time distributions or time-to-target plots display on the ordinate axis the probability that an algorithm will find a solution at least as good as a given target value within a given running time, shown on the abs...
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Run time distributions or time-to-target plots display on the ordinate axis the probability that an algorithm will find a solution at least as good as a given target value within a given running time, shown on the abscissa axis. Given a pair of different randomized algorithms and , we describe a numerical method that gives the probability that finds a solution at least as good as a given target value in a smaller computation time than , for the case where the runtimes of each of the two algorithms follow any runtime distribution. An illustrative example of a numerical application is also reported. We describe the perl program tttplots-compare, developed to compare time-to-target plots or general runtime distribution for measured CPU times of any two randomized heuristics. A listing of the perl program is given, and the program can also be downloaded from http://***/similar to celso/compare-tttplots..
This work is an attempt to establish a probabilistic framework for the assessment and design of observer-based fault detection systems. The fundament of our study is randomized algorithms methods which are successfull...
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This work is an attempt to establish a probabilistic framework for the assessment and design of observer-based fault detection systems. The fundament of our study is randomized algorithms methods which are successfully applied to deal with uncertainty issues in robust control. For our purpose, probabilistic parameter models for faults and model uncertainties are first introduced. The main focus of our work is on the development of randomized algorithms for the assessment of false alarm rate, fault detection rate and mean time to detection as well as for the design of observer-based fault detection systems. To illustrate the potential applications of the proposed algorithms and methods, benchmark study on a real three-tank system is included. (C) 2019 Elsevier Ltd. All rights reserved.
algorithms and dynamics over networks often involve randomization and randomization can induce oscillating dynamics that fail to converge in a deterministic sense. Under assumptions of independence across time and lin...
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algorithms and dynamics over networks often involve randomization and randomization can induce oscillating dynamics that fail to converge in a deterministic sense. Under assumptions of independence across time and linearity of the updates, we show that the oscillations are ergodic if the expected dynamics is stable. We apply this result to three problems of network systems, namely, the estimation from relative measurements, the PageRank computation, and the dynamics of opinions in social networks. In these applications, the randomized dynamics is the asynchronous counterpart of a deterministic (stable) synchronous one. By ergodicity, the deterministic limit can be recovered via a time-averaging operation, which can be performed locally by each node of the network.
The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of...
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The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of their lack of sensitivity to outlying data points. The basic measure of the robustness of an estimator is its breakdown point, that is, the fraction (up to 50%) of outlying data points that can corrupt the estimator, One problem with robust estimators is that achieving high breakdown points (near 50%) has proved to be computationally demanding. In this paper we present the best known theoretical algorithm and a practical subquadratic algorithm for computing a 50% breakdown point line estimator, the Siegel or repeated median line estimator. We first present an O(n log n) randomized expected-time algorithm, where la is the number of given points. This algorithm relies, however, on sophisticated data structures. We also present a very simple O(n log(2) n) randomized algorithm for this problem, which uses no complex data structures. We provide empirical evidence that, for many realistic input distributions, the running time of this second algorithm is actually O (n log n) expected time.
In the field of Computer Science and Engineering, the algorithms course is considered very important for not only it forms the basis for several concepts but also, its in-depth understanding can help one solve many ne...
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ISBN:
(纸本)9781479968763
In the field of Computer Science and Engineering, the algorithms course is considered very important for not only it forms the basis for several concepts but also, its in-depth understanding can help one solve many new and challenging problems in an efficient manner. Whether a student pursues his career in academia or industry, depth of his understanding in algorithms is certainly tested during competitive exams directly or indirectly. In this paper, we discuss a case study of using an innovative approach based on randomized algorithms and some statistics in teaching algorithms to engineering students, with aim to provide students a better individual learning experience. The approach has wider applicability but here it is practiced in relation to sorting algorithms. In this paper, we also discuss the student's feedback that we collected after completion of the course. It was observed that students were very appreciative of this novel approach used, and the majority of students found that it helped them in getting more clarity and deeper understanding of sorting algorithms.
Feature selection is a crucial problem in efficient machine learning,and it also greatly contributes to the explainability of machine-driven ***,like decision trees and Least Absolute Shrinkage and Selection Operator(...
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Feature selection is a crucial problem in efficient machine learning,and it also greatly contributes to the explainability of machine-driven ***,like decision trees and Least Absolute Shrinkage and Selection Operator(LASSO),can select features during ***,these embedded approaches can only be applied to a small subset of machine learning *** based methods can select features independently from machine learning models but they often suffer from a high computational *** enhance their efficiency,many randomized algorithms have been *** this paper,we propose automatic breadth searching and attention searching adjustment approaches to further speedup randomized wrapper based feature *** conduct theoretical computational complexity analysis and further explain our algorithms’generic *** conduct experiments on both synthetic and real datasets with different machine learning base *** show that,compared with existing approaches,our proposed techniques can locate a more meaningful set of features with a high efficiency.
In this paper, we present an introduction to Monte Carlo and Las Vegas randomized algorithms for systems and control. Specific applications of these algorithms include stability analysis, Lyapunov functions, and distr...
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In this paper, we present an introduction to Monte Carlo and Las Vegas randomized algorithms for systems and control. Specific applications of these algorithms include stability analysis, Lyapunov functions, and distributed consensus problems.
randomized algorithms are analyzed as if unlimited amounts of perfect randomness were available, while pseudorandom number generation is usually studied from the perspective of cryptographic security or for the statis...
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randomized algorithms are analyzed as if unlimited amounts of perfect randomness were available, while pseudorandom number generation is usually studied from the perspective of cryptographic security or for the statistical properties of the numbers generated. Bach proposed studying the interaction between pseudorandom number generators and randomized algorithms. This paper follows Bach's lead;the authors assume that a (small) random seed is available to start up a simple pseudorandom number generator that is then used for the randomized algorithm. randomized algorithms are studied for (1) sorting, (2) selection, and (3) oblivious routing in networks.
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theo...
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In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular values of sub-Gaussian matrices, we make a probabilistic analysis for the error bounds for the randomized algorithm. We demonstrate the effectiveness of proposed algorithms via several numerical examples. (C) 2021 Elsevier B.V. All rights reserved.
In this paper we show how randomized algorithms can be applied to the design of a robust controller. The design objective consists on the problem of finding a controller such that guarantees a proper behavior in front...
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In this paper we show how randomized algorithms can be applied to the design of a robust controller. The design objective consists on the problem of finding a controller such that guarantees a proper behavior in front of uncertainties, taking into account the worst possible situation (robust solution). A randomized algorithm that provides a probabilistic solution is proposed. The proposed strategy is applied to the control of the hot water production system installed at the University Hospital “Virgen del Rocio” (Seville, Spain).
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