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Sergio Verdu - One of the best experts on this subject based on the ideXlab platform.

  • Arimoto–Rényi Conditional Entropy and Bayesian $M$ -Ary Hypothesis Testing
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$ -ary hypothesis testing in terms of the Arimoto–Renyi Conditional Entropy of an arbitrary order $\alpha $ . The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ( $\alpha =1$ ) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano’s inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano’s inequality, allowing $M$ to be infinite, a lower bound on the Arimoto–Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto–Renyi Conditional Entropy for both positive and negative $\alpha $ . Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto–Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random-coding ensemble.

  • arimoto renyi Conditional Entropy and bayesian m ary hypothesis testing
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$ -ary hypothesis testing in terms of the Arimoto–Renyi Conditional Entropy of an arbitrary order $\alpha $ . The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ( $\alpha =1$ ) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano’s inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano’s inequality, allowing $M$ to be infinite, a lower bound on the Arimoto–Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto–Renyi Conditional Entropy for both positive and negative $\alpha $ . Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto–Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random-coding ensemble.

  • arimoto renyi Conditional Entropy and bayesian hypothesis testing
    International Symposium on Information Theory, 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy.

  • Arimoto-R\'enyi Conditional Entropy and Bayesian $M$-ary Hypothesis Testing
    arXiv: Information Theory, 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ($\alpha=1$) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing $M$ to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy for both positive and negative $\alpha$. Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto-Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random coding ensemble.

  • ISIT - Arimoto-Rényi Conditional Entropy and Bayesian hypothesis testing
    2017 IEEE International Symposium on Information Theory (ISIT), 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy.

Mark M Wilde - One of the best experts on this subject based on the ideXlab platform.

  • optimal uniform continuity bound for Conditional Entropy of classical quantum states
    Quantum Information Processing, 2020
    Co-Authors: Mark M Wilde
    Abstract:

    In this short note, I show how a recent result of Alhejji and Smith (A tight uniform continuity bound for equivocation, 2019. arXiv:1909.00787v1) regarding an optimal uniform continuity bound for classical Conditional Entropy leads to an optimal uniform continuity bound for quantum Conditional Entropy of classical–quantum states. The bound is optimal in the sense that there always exists a pair of classical–quantum states saturating the bound, and so, no further improvements are possible. An immediate application is a uniform continuity bound for the entanglement of formation that improves upon the one previously given by Winter (Commun Math Phys 347(1):291–313, 2016. arXiv:1507.07775). Two intriguing open questions are raised regarding other possible uniform continuity bounds for Conditional Entropy: one about quantum–classical states and another about fully quantum bipartite states.

  • Optimal uniform continuity bound for Conditional Entropy of classical--quantum states
    Quantum Information Processing, 2020
    Co-Authors: Mark M Wilde
    Abstract:

    In this short note, I show how a recent result of Alhejji and Smith [arXiv:1909.00787] regarding an optimal uniform continuity bound for classical Conditional Entropy leads to an optimal uniform continuity bound for quantum Conditional Entropy of classical--quantum states. The bound is optimal in the sense that there always exists a pair of classical--quantum states saturating the bound, and so no further improvements are possible. An immediate application is a uniform continuity bound for entanglement of formation that improves upon the one previously given by Winter in [arXiv:1507.07775]. Two intriguing open questions are raised regarding other possible uniform continuity bounds for Conditional Entropy, one about quantum--classical states and another about fully quantum bipartite states.

Igal Sason - One of the best experts on this subject based on the ideXlab platform.

  • Arimoto–Rényi Conditional Entropy and Bayesian $M$ -Ary Hypothesis Testing
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$ -ary hypothesis testing in terms of the Arimoto–Renyi Conditional Entropy of an arbitrary order $\alpha $ . The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ( $\alpha =1$ ) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano’s inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano’s inequality, allowing $M$ to be infinite, a lower bound on the Arimoto–Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto–Renyi Conditional Entropy for both positive and negative $\alpha $ . Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto–Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random-coding ensemble.

  • arimoto renyi Conditional Entropy and bayesian m ary hypothesis testing
    IEEE Transactions on Information Theory, 2018
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$ -ary hypothesis testing in terms of the Arimoto–Renyi Conditional Entropy of an arbitrary order $\alpha $ . The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ( $\alpha =1$ ) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano’s inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano’s inequality, allowing $M$ to be infinite, a lower bound on the Arimoto–Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto–Renyi Conditional Entropy for both positive and negative $\alpha $ . Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto–Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random-coding ensemble.

  • arimoto renyi Conditional Entropy and bayesian hypothesis testing
    International Symposium on Information Theory, 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy.

  • Arimoto-R\'enyi Conditional Entropy and Bayesian $M$-ary Hypothesis Testing
    arXiv: Information Theory, 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy ($\alpha=1$) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing $M$ to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy for both positive and negative $\alpha$. Furthermore, we give upper bounds on the minimum error probability as functions of the Renyi divergence. In the setup of discrete memoryless channels, we analyze the exponentially vanishing decay of the Arimoto-Renyi Conditional Entropy of the transmitted codeword given the channel output when averaged over a random coding ensemble.

  • ISIT - Arimoto-Rényi Conditional Entropy and Bayesian hypothesis testing
    2017 IEEE International Symposium on Information Theory (ISIT), 2017
    Co-Authors: Igal Sason, Sergio Verdu
    Abstract:

    This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Renyi Conditional Entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon Conditional Entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing M to be infinite, a lower bound on the Arimoto-Renyi Conditional Entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi Conditional Entropy.

Jie Yang - One of the best experts on this subject based on the ideXlab platform.

  • ACCV (1) - Visual saliency based on Conditional Entropy
    Computer Vision – ACCV 2009, 2010
    Co-Authors: Yue Zhou, Junchi Yan, Zhibin Niu, Jie Yang
    Abstract:

    By the guidance of attention, human visual system is able to locate objects of interest in complex scene. In this paper, we propose a novel visual saliency detection method - the Conditional saliency for both image and video. Inspired by biological vision, the definition of visual saliency follows a strictly local approach. Given the surrounding area, the saliency is defined as the minimum uncertainty of the local region, namely the minimum Conditional Entropy, when the perceptional distortion is considered. To simplify the problem, we approximate the Conditional Entropy by the lossy coding length of multivariate Gaussian data. The final saliency map is accumulated by pixels and further segmented to detect the proto-objects. Experiments are conducted on both image and video. And the results indicate a robust and reliable feature invariance saliency.

  • visual saliency based on Conditional Entropy
    Asian Conference on Computer Vision, 2009
    Co-Authors: Yue Zhou, Junchi Yan, Zhibin Niu, Jie Yang
    Abstract:

    By the guidance of attention, human visual system is able to locate objects of interest in complex scene. In this paper, we propose a novel visual saliency detection method - the Conditional saliency for both image and video. Inspired by biological vision, the definition of visual saliency follows a strictly local approach. Given the surrounding area, the saliency is defined as the minimum uncertainty of the local region, namely the minimum Conditional Entropy, when the perceptional distortion is considered. To simplify the problem, we approximate the Conditional Entropy by the lossy coding length of multivariate Gaussian data. The final saliency map is accumulated by pixels and further segmented to detect the proto-objects. Experiments are conducted on both image and video. And the results indicate a robust and reliable feature invariance saliency.

Lev B. Levitin - One of the best experts on this subject based on the ideXlab platform.

  • QCQC - Quantum Generalization of Conditional Entropy and Information
    Quantum Computing and Quantum Communications, 1999
    Co-Authors: Lev B. Levitin
    Abstract:

    The concepts of Conditional Entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum one is that the Entropy and information in quantum systems. The fundamental difference between the classical case and the quantum one is that the Entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and "superdense coding" are described and explained in terms of the generalized Conditional Entropy and information.

  • Conditional Entropy and Information in Quantum Systems
    Chaos Solitons & Fractals, 1999
    Co-Authors: Lev B. Levitin
    Abstract:

    Abstract The concepts of Conditional Entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum systems. The fundamental difference between the classical case and the quantum one is that the Entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and superdense coding are described and explained in terms of the generalized Conditional Entropy and information.

  • Quantum generalization of Conditional Entropy and information
    Lecture Notes in Computer Science, 1999
    Co-Authors: Lev B. Levitin
    Abstract:

    The concepts of Conditional Entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum one is that the Entropy and information in quantum systems.The fundamental difference between the classical case and the quantum one is that the Entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and superdense coding are described and explained in terms of the generalized Conditional Entropy and information.

  • Conditional Entropy and information in quantum systems
    Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 1
    Co-Authors: Lev B. Levitin
    Abstract:

    The concepts of Conditional Entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities.