The Experts below are selected from a list of 37524 Experts worldwide ranked by ideXlab platform
Marco Dorigo - One of the best experts on this subject based on the ideXlab platform.
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solving the homogeneous probabilistic traveling salesman problem by the aco metaheuristic
Lecture Notes in Computer Science, 2002Co-Authors: Leonora Bianchi, Luca Maria Gambardella, Marco DorigoAbstract:The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem in which each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a Random Subset of customers in the same order as they appear in the a priori tour.We propose an ant based a priori tour construction heuristic, the probabilistic Ant Colony System (pACS), which is derived from ACS, a similar heuristic previously designed for the TSP problem. We show that pACS finds better solutions than other tour construction heuristics for a wide range of homogeneous customer probabilities. We also show that for high customers probabilities ACS solutions are better than pACS solutions.
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an ant colony optimization approach to the probabilistic traveling salesman problem
Parallel Problem Solving from Nature, 2002Co-Authors: Leonora Bianchi, Luca Maria Gambardella, Marco DorigoAbstract:The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem where each customer has a given probability of requiring a visit. The goal is to find an a priori tour of minimal expected length over all customers, with the strategy of visiting a Random Subset of customers in the same order as they appear in the a priori tour.We address the question of whether and in which context an a priori tour found by a TSP heuristic can also be a good solution for the PTSP. We answer this question by testing the relative performance of two ant colony optimization algorithms, Ant Colony System (ACS) introduced by Dorigo and Gambardella for the TSP, and a variant of it (pACS) which aims to minimize the PTSP objective function.We show in which probability configuration of customers pACS and ACS are promising algorithms for the PTSP.
Peter Richtarik - One of the best experts on this subject based on the ideXlab platform.
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sdna stochastic dual newton ascent for empirical risk minimization
International Conference on Machine Learning, 2016Co-Authors: Peter Richtarik, Martin Takac, Olivier FercoqAbstract:We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a Random Subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all local curvature information contained in the examples, which leads to striking improvements in both theory and practice -- sometimes by orders of magnitude. In the special case when an L2-regularizer is used in the primal, the dual problem is a concave quadratic maximization problem plus a separable term. In this regime, SDNA in each step solves a proximal subproblem involving a Random principal submatrix of the Hessian of the quadratic function; whence the name of the method.
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quartz Randomized dual coordinate ascent with arbitrary sampling
Neural Information Processing Systems, 2015Co-Authors: Peter Richtarik, Tong ZhangAbstract:We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and updates a Random Subset of the dual variables, chosen according to an arbitrary distribution. In contrast to typical analysis, we directly bound the decrease of the primal-dual error (in expectation), without the need to first analyze the dual error. Depending on the choice of the sampling, we obtain efficient serial and mini-batch variants of the method. In the serial case, our bounds match the best known bounds for SDCA (both with uniform and importance sampling). With standard mini-batching, our bounds predict initial data-independent speedup as well as additional data-driven speedup which depends on spectral and sparsity properties of the data.
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sdna stochastic dual newton ascent for empirical risk minimization
arXiv: Learning, 2015Co-Authors: Peter Richtarik, Martin Takac, Olivier FercoqAbstract:We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a Random Subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all curvature information contained in the examples, which leads to striking improvements in both theory and practice - sometimes by orders of magnitude. In the special case when an L2-regularizer is used in the primal, the dual problem is a concave quadratic maximization problem plus a separable term. In this regime, SDNA in each step solves a proximal subproblem involving a Random principal submatrix of the Hessian of the quadratic function; whence the name of the method. If, in addition, the loss functions are quadratic, our method can be interpreted as a novel variant of the recently introduced Iterative Hessian Sketch.
Gongguo Tang - One of the best experts on this subject based on the ideXlab platform.
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vandermonde factorization of hankel matrix for complex exponential signal recovery application in fast nmr spectroscopy
IEEE Transactions on Signal Processing, 2018Co-Authors: Jiaxi Ying, Gongguo Tang, Zhong Chen, Xiaobo QuAbstract:Many signals are modeled as a superposition of exponential functions in spectroscopy of chemistry, biology, and medical imaging. This paper studies the problem of recovering exponential signals from a Random Subset of samples. We exploit the Vandermonde structure of the Hankel matrix formed by the exponential signal and formulate signal recovery as Hankel matrix completion with Vandermonde factorization (HVaF). A numerical algorithm is developed to solve the proposed model and its sequence convergence is analyzed theoretically. Experiments on synthetic data demonstrate that HVaF succeeds over a wider regime than the state-of-the-art nuclear-norm-minimization-based Hankel matrix completion method, while it has a less restriction on frequency separation than the state-of-the-art atomic norm minimization and fast iterative hard thresholding methods. The effectiveness of HVaF is further validated on biological magnetic resonance spectroscopy data.
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compressed sensing off the grid
IEEE Transactions on Information Theory, 2013Co-Authors: Gongguo Tang, Badri Narayan Bhaskar, Parikshit Shah, Benjamin RechtAbstract:This paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a Random Subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a grid, but can assume any values in the normalized frequency domain [0, 1]. An atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies, which is then reformulated as an exact semidefinite program. Even with this continuous dictionary, it is shown that O(slog s log n) Random samples are sufficient to guarantee exact frequency localization with high probability, provided the frequencies are well separated. Extensive numerical experiments are performed to illustrate the effectiveness of the proposed method.
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Compressed sensing off the grid
IEEE Transactions on Information Theory, 2013Co-Authors: Gongguo Tang, Badri Narayan Bhaskar, Parikshit Shah, Benjamin RechtAbstract:We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a Random Subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a grid, but can assume any values in the normalized frequency domain [0,1]. We propose an atomic norm minimization approach to exactly recover the unobserved samples. We reformulate this atomic norm minimization as an exact semidefinite program. Even with this continuous dictionary, we show that most sampling sets of size O(s log s log n) are sufficient to guarantee the exact frequency estimation with high probability, provided the frequencies are well separated. Numerical experiments are performed to illustrate the effectiveness of the proposed method.
Wei Cui - One of the best experts on this subject based on the ideXlab platform.
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spectrally sparse signal recovery via hankel matrix completion with prior information
IEEE Transactions on Signal Processing, 2021Co-Authors: Xu Zhang, Yulong Liu, Wei CuiAbstract:This article studies the problem of reconstructing spectrally sparse signals from a small Random Subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of spectrally sparse signals in the lifting domain and the similarity between the signals and their prior information, we propose a convex method to recover the undersampled spectrally sparse signals. The proposed approach integrates the inner product of the desired signal and its prior information in the lift domain into vanilla Hankel matrix completion, which maximizes the correlation between the signals and their prior information. Theoretical analysis indicates that when the prior information is reliable, the proposed method has a better performance than vanilla Hankel matrix completion, which reduces the number of measurements by a logarithmic factor. We also develop an ADMM algorithm to solve the corresponding optimization problem. Numerical results are provided to verify the performance of proposed method and corresponding algorithm.
Xiaobo Qu - One of the best experts on this subject based on the ideXlab platform.
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vandermonde factorization of hankel matrix for complex exponential signal recovery application in fast nmr spectroscopy
IEEE Transactions on Signal Processing, 2018Co-Authors: Jiaxi Ying, Gongguo Tang, Zhong Chen, Xiaobo QuAbstract:Many signals are modeled as a superposition of exponential functions in spectroscopy of chemistry, biology, and medical imaging. This paper studies the problem of recovering exponential signals from a Random Subset of samples. We exploit the Vandermonde structure of the Hankel matrix formed by the exponential signal and formulate signal recovery as Hankel matrix completion with Vandermonde factorization (HVaF). A numerical algorithm is developed to solve the proposed model and its sequence convergence is analyzed theoretically. Experiments on synthetic data demonstrate that HVaF succeeds over a wider regime than the state-of-the-art nuclear-norm-minimization-based Hankel matrix completion method, while it has a less restriction on frequency separation than the state-of-the-art atomic norm minimization and fast iterative hard thresholding methods. The effectiveness of HVaF is further validated on biological magnetic resonance spectroscopy data.
