The Experts below are selected from a list of 519189 Experts worldwide ranked by ideXlab platform
Hiroshi Nakagawa - One of the best experts on this subject based on the ideXlab platform.
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copeland dueling bandit problem regret lower bound Optimal Algorithm and computationally efficient Algorithm
International Conference on Machine Learning, 2016Co-Authors: Junpei Komiyama, Junya Honda, Hiroshi NakagawaAbstract:We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. The hardness of recommending Copeland winners, the arms that beat the greatest number of other arms, is characterized by deriving an asymptotic regret bound. We propose Copeland Winners Relative Minimum Empirical Divergence (CW-RMED) and derive an asymptotically Optimal regret bound for it. However, it is not known whether the Algorithm can be efficiently computed or not. To address this issue, we devise an efficient version (ECW-RMED) and derive its asymptotic regret bound. Experimental comparisons of dueling bandit Algorithms show that ECW-RMED significantly outperforms existing ones.
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regret lower bound and Optimal Algorithm in finite stochastic partial monitoring
arXiv: Machine Learning, 2015Co-Authors: Junpei Komiyama, Junya Honda, Hiroshi NakagawaAbstract:Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner suffers a loss and receives a feedback signal. The goal of the learner is to minimize the total loss. In this paper, we study partial monitoring with finite actions and stochastic outcomes. We derive a logarithmic distribution-dependent regret lower bound that defines the hardness of the problem. Inspired by the DMED Algorithm (Honda and Takemura, 2010) for the multi-armed bandit problem, we propose PM-DMED, an Algorithm that minimizes the distribution-dependent regret. PM-DMED significantly outperforms state-of-the-art Algorithms in numerical experiments. To show the Optimality of PM-DMED with respect to the regret bound, we slightly modify the Algorithm by introducing a hinge function (PM-DMED-Hinge). Then, we derive an asymptotically Optimal regret upper bound of PM-DMED-Hinge that matches the lower bound.
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regret lower bound and Optimal Algorithm in dueling bandit problem
Conference on Learning Theory, 2015Co-Authors: Junpei Komiyama, Junya Honda, Hisashi Kashima, Hiroshi NakagawaAbstract:We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An Algorithm that is inspired by the Deterministic Minimum Empirical Divergence Algorithm (Honda and Takemura, 2010) is proposed, and its regret is analyzed. The proposed Algorithm is found to be the first one with a regret upper bound that matches the lower bound. Experimental comparisons of dueling bandit Algorithms show that the proposed Algorithm significantly outperforms existing ones.
Michael I Jordan - One of the best experts on this subject based on the ideXlab platform.
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spectral methods meet em a provably Optimal Algorithm for crowdsourcing
Neural Information Processing Systems, 2014Co-Authors: Yuchen Zhang, Xi Chen, Dengyong Zhou, Michael I JordanAbstract:The Dawid-Skene estimator has been widely used for inferring the true labels from the noisy labels provided by non-expert crowdsourcing workers. However, since the estimator maximizes a non-convex log-likelihood function, it is hard to theoretically justify its performance. In this paper, we propose a two-stage efficient Algorithm for multi-class crowd labeling problems. The first stage uses the spectral method to obtain an initial estimate of parameters. Then the second stage refines the estimation by optimizing the objective function of the Dawid-Skene estimator via the EM Algorithm. We show that our Algorithm achieves the Optimal convergence rate up to a logarithmic factor. We conduct extensive experiments on synthetic and real datasets. Experimental results demonstrate that the proposed Algorithm is comparable to the most accurate empirical approach, while outperforming several other recently proposed methods.
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spectral methods meet em a provably Optimal Algorithm for crowdsourcing
arXiv: Machine Learning, 2014Co-Authors: Yuchen Zhang, Xi Chen, Dengyong Zhou, Michael I JordanAbstract:Crowdsourcing is a popular paradigm for effectively collecting labels at low cost. The Dawid-Skene estimator has been widely used for inferring the true labels from the noisy labels provided by non-expert crowdsourcing workers. However, since the estimator maximizes a non-convex log-likelihood function, it is hard to theoretically justify its performance. In this paper, we propose a two-stage efficient Algorithm for multi-class crowd labeling problems. The first stage uses the spectral method to obtain an initial estimate of parameters. Then the second stage refines the estimation by optimizing the objective function of the Dawid-Skene estimator via the EM Algorithm. We show that our Algorithm achieves the Optimal convergence rate up to a logarithmic factor. We conduct extensive experiments on synthetic and real datasets. Experimental results demonstrate that the proposed Algorithm is comparable to the most accurate empirical approach, while outperforming several other recently proposed methods.
David P Woodruff - One of the best experts on this subject based on the ideXlab platform.
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an Optimal Algorithm for e 1 heavy hitters in insertion streams and related problems
ACM Transactions on Algorithms, 2019Co-Authors: Arnab Bhattacharyya, David P WoodruffAbstract:We give the first Optimal bounds for returning the e1-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of m items in { 1, 2, … , n} and parameters 0 < e < p l 1, let fi denote the frequency of item i, i.e., the number of times item i occurs in the stream. With arbitrarily large constant probability, our Algorithm returns all items i for which fi g p m, returns no items j for which fj l (p −e)m, and returns approximations f˜i with vf˜i − fiv l e m for each item i that it returns. Our Algorithm uses O(e−1 log p −1 + p −1 log n + log log m) bits of space, processes each stream update in O(1) worst-case time, and can report its output in time linear in the output size. We also prove a lower bound, which implies that our Algorithm is Optimal up to a constant factor in its space complexity. A modification of our Algorithm can be used to estimate the maximum frequency up to an additive e m error in the above amount of space, resolving Question 3 in the IITK 2006 Workshop on Algorithms for Data Streams for the case of e1-heavy hitters. We also introduce several variants of the heavy hitters and maximum frequency problems, inspired by rank aggregation and voting schemes, and show how our techniques can be applied in such settings. Unlike the traditional heavy hitters problem, some of these variants look at comparisons between items rather than numerical values to determine the frequency of an item.
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an Optimal Algorithm for l1 heavy hitters in insertion streams and related problems
Symposium on Principles of Database Systems, 2016Co-Authors: Arnab Bhattacharyya, David P WoodruffAbstract:We give the first Optimal bounds for returning the l1-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of m items in {1, 2, ..., n} and parameters 0
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a simple message Optimal Algorithm for random sampling from a distributed stream
IEEE Transactions on Knowledge and Data Engineering, 2016Co-Authors: Yungyu Chung, Srikanta Tirthapura, David P WoodruffAbstract:We present a simple, message-Optimal Algorithm for maintaining a random sample from a large data stream whose input elements are distributed across multiple sites that communicate via a central coordinator. At any point in time, the set of elements held by the coordinator represent a uniform random sample from the set of all the elements observed so far. When compared with prior work, our Algorithms asymptotically improve the total number of messages sent in the system. We present a matching lower bound, showing that our protocol sends the Optimal number of messages up to a constant factor with large probability. We also consider the important case when the distribution of elements across different sites is non-uniform, and show that for such inputs, our Algorithm significantly outperforms prior solutions.
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an Optimal Algorithm for l1 heavy hitters in insertion streams and related problems
arXiv: Data Structures and Algorithms, 2016Co-Authors: Arnab Bhattacharyya, David P WoodruffAbstract:We give the first Optimal bounds for returning the $\ell_1$-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of $m$ items in $\{1, 2, \dots, n\}$ and parameters $0 < \epsilon < \phi \leq 1$, let $f_i$ denote the frequency of item $i$, i.e., the number of times item $i$ occurs in the stream. With arbitrarily large constant probability, our Algorithm returns all items $i$ for which $f_i \geq \phi m$, returns no items $j$ for which $f_j \leq (\phi -\epsilon)m$, and returns approximations $\tilde{f}_i$ with $|\tilde{f}_i - f_i| \leq \epsilon m$ for each item $i$ that it returns. Our Algorithm uses $O(\epsilon^{-1} \log\phi^{-1} + \phi^{-1} \log n + \log \log m)$ bits of space, processes each stream update in $O(1)$ worst-case time, and can report its output in time linear in the output size. We also prove a lower bound, which implies that our Algorithm is Optimal up to a constant factor in its space complexity. A modification of our Algorithm can be used to estimate the maximum frequency up to an additive $\epsilon m$ error in the above amount of space, resolving Question 3 in the IITK 2006 Workshop on Algorithms for Data Streams for the case of $\ell_1$-heavy hitters. We also introduce several variants of the heavy hitters and maximum frequency problems, inspired by rank aggregation and voting schemes, and show how our techniques can be applied in such settings. Unlike the traditional heavy hitters problem, some of these variants look at comparisons between items rather than numerical values to determine the frequency of an item.
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an Optimal Algorithm for the distinct elements problem
Symposium on Principles of Database Systems, 2010Co-Authors: Daniel M Kane, Jelani Nelson, David P WoodruffAbstract:We give the first Optimal Algorithm for estimating the number of distinct elements in a data stream, closing a long line of theoretical research on this problem begun by Flajolet and Martin in their seminal paper in FOCS 1983. This problem has applications to query optimization, Internet routing, network topology, and data mining. For a stream of indices in {1,...,n}, our Algorithm computes a (1 ± e)-approximation using an Optimal O(1/e-2 + log(n)) bits of space with 2/3 success probability, where 0
Junpei Komiyama - One of the best experts on this subject based on the ideXlab platform.
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copeland dueling bandit problem regret lower bound Optimal Algorithm and computationally efficient Algorithm
International Conference on Machine Learning, 2016Co-Authors: Junpei Komiyama, Junya Honda, Hiroshi NakagawaAbstract:We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. The hardness of recommending Copeland winners, the arms that beat the greatest number of other arms, is characterized by deriving an asymptotic regret bound. We propose Copeland Winners Relative Minimum Empirical Divergence (CW-RMED) and derive an asymptotically Optimal regret bound for it. However, it is not known whether the Algorithm can be efficiently computed or not. To address this issue, we devise an efficient version (ECW-RMED) and derive its asymptotic regret bound. Experimental comparisons of dueling bandit Algorithms show that ECW-RMED significantly outperforms existing ones.
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regret lower bound and Optimal Algorithm in finite stochastic partial monitoring
arXiv: Machine Learning, 2015Co-Authors: Junpei Komiyama, Junya Honda, Hiroshi NakagawaAbstract:Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner suffers a loss and receives a feedback signal. The goal of the learner is to minimize the total loss. In this paper, we study partial monitoring with finite actions and stochastic outcomes. We derive a logarithmic distribution-dependent regret lower bound that defines the hardness of the problem. Inspired by the DMED Algorithm (Honda and Takemura, 2010) for the multi-armed bandit problem, we propose PM-DMED, an Algorithm that minimizes the distribution-dependent regret. PM-DMED significantly outperforms state-of-the-art Algorithms in numerical experiments. To show the Optimality of PM-DMED with respect to the regret bound, we slightly modify the Algorithm by introducing a hinge function (PM-DMED-Hinge). Then, we derive an asymptotically Optimal regret upper bound of PM-DMED-Hinge that matches the lower bound.
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regret lower bound and Optimal Algorithm in dueling bandit problem
Conference on Learning Theory, 2015Co-Authors: Junpei Komiyama, Junya Honda, Hisashi Kashima, Hiroshi NakagawaAbstract:We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An Algorithm that is inspired by the Deterministic Minimum Empirical Divergence Algorithm (Honda and Takemura, 2010) is proposed, and its regret is analyzed. The proposed Algorithm is found to be the first one with a regret upper bound that matches the lower bound. Experimental comparisons of dueling bandit Algorithms show that the proposed Algorithm significantly outperforms existing ones.
David Haussler - One of the best experts on this subject based on the ideXlab platform.
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calculation of the learning curve of bayes Optimal classification Algorithm for learning a perceptron with noise
Conference on Learning Theory, 1991Co-Authors: M Opper, David HausslerAbstract:The learning curve of Bayes Optimal classification Algorithm when learning a perceptron from noisy random training examples is calculated exactly in the limit of large training sample size and large instance space dimension using methods of statistical mechanics. It is shown that under certain assumptions, in this “thermodynamic” limit, the probability of misclassification of Bayes Optimal Algorithm is less than that of a canonical stochastic learning Algorithm, by a factor approaching 2 as the ratio of number of training examples to instance space dimension grows. Exact asymptotic learning curves for both Algorithms are derived for particular distributions. In addition, it is shown that the learning performance of Bayes Optimal Algorithm can be approximated by certain learning Algorithms that use a neural net with a layer of hidden units to learn a perceptron.
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generalization performance of bayes Optimal classification Algorithm for learning a perceptron
Physical Review Letters, 1991Co-Authors: M Opper, David HausslerAbstract:The generalization error of the Bayes Optimal classification Algorithm when learning a perceptron from noise-free random training examples is calculated exactly using methods of statistical mechanics. It is shown that if an assumption of replica symmetry is made, then, in the thermodynamic limit, the error of the Bayes Optimal Algorithm is less than the error of a canonical stochastic learning Algorithm, by a factor approaching \ensuremath{\surd}2 as the ratio of the number of training examples to perceptron weights grows. In addition, it is shown that approximations to the generalization error of the Bayes Optimal Algorithm can be achieved by learning Algorithms that use a two-layer neutral net to learn a perceptron.
