The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
H Nagaoka - One of the best experts on this subject based on the ideXlab platform.
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An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
IEEE Transactions on Information Theory, 2007Co-Authors: H Nagaoka, Masahito HayashiAbstract:The information-spectrum analysis made by Han for classical Hypothesis Testing for simple hypotheses is extended to a unifying framework including both classical and quantum Hypothesis Testing. The results are also applied to fixed-length source coding when loosening the normalizing condition for probability distributions and for quantum states. We establish general formulas for several quantities relating to the asymptotic optimality of tests/codes in terms of classical and quantum information spectra
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Making Good Codes for Classical-Quantum Channel Coding via Quantum Hypothesis Testing
IEEE Transactions on Information Theory, 2007Co-Authors: Tomohiro Ogawa, H NagaokaAbstract:In this correspondence, we give an alternative proof of the direct part of the classical-quantum channel coding theorem (the Holevo-Schumacher-Westmoreland (HSW) theorem), using ideas of quantum Hypothesis Testing. In order to show the existence of good codes, we invoke a limit theorem, relevant to the quantum Stein's lemma, in quantum Hypothesis Testing as the law of large numbers used in the classical case. We also apply a greedy construction of good codes using a packing procedure of noncommutative operators. Consequently we derive an upper bound on the coding error probability, which is used to give an alternative proof of the HSW theorem. This approach elucidates how the Holevo information applies to the classical-quantum channel coding problems
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an information spectrum approach to classical and quantum Hypothesis Testing for simple hypotheses
arXiv: Quantum Physics, 2002Co-Authors: H Nagaoka, Masahito HayashiAbstract:The information-spectrum analysis made by Han for classical Hypothesis Testing for simple hypotheses is extended to a unifying framework including both classical and quantum Hypothesis Testing as well as fixed-length source coding, whereby general formulas for several quantities concerning the asymptotic optimality of tests/codes are established in terms of classical and quantum information spectrum. Generality of theorems and simplicity of proofs are fully pursued, and as byproducts some improvements on the original classical results are also obtained.
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A new proof of the channel coding theorem via Hypothesis Testing in quantum information theory
Proceedings IEEE International Symposium on Information Theory, 2002Co-Authors: H NagaokaAbstract:A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum Hypothesis Testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error probability, which is similar to Feinstein's lemma in classical channel coding. The upper bound is used to show the proof of the direct part along with a variant of Hiai-Petz's theorem in Hypothesis Testing.
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Strong converse and Stein's lemma in quantum Hypothesis Testing
IEEE Transactions on Information Theory, 2000Co-Authors: Tomohiro Ogawa, H NagaokaAbstract:The Hypothesis Testing problem for two quantum states is treated. We show a new inequality between the errors of the first kind and the second kind, which complements the result of Hiai and Petz (1991) to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy, which yields the strong converse in quantum Hypothesis Testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi (1989) in classical Hypothesis Testing.
Masahito Hayashi - One of the best experts on this subject based on the ideXlab platform.
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role of Hypothesis Testing in quantum information
arXiv: Quantum Physics, 2017Co-Authors: Masahito HayashiAbstract:Recently, it is well recognized that Hypothesis Testing has deep relations with other topics in quantum information theory as well as in classical information theory. These relations enable us to derive precise evaluation in the finite-length setting. However, such usefulness of Hypothesis Testing is not limited to information theoretical topics. For example, it can be used for verification of entangled state and quantum computer as well as guaranteeing the security of keys generated via quantum key distribution. In this talk, we overview these kinds of applications of Hypothesis Testing.
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quantum Hypothesis Testing for quantum gaussian states quantum analogues of chi square t and f tests
arXiv: Quantum Physics, 2011Co-Authors: Wataru Kumagai, Masahito HayashiAbstract:We treat quantum counterparts of Testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum Hypothesis Testing problems concerning quantum Gaussian states families, and contain disturbance parameters, which have group symmetry. Quantum Hunt-Stein Theorem removes a part of these disturbance parameters, but other types of difficulty still remain. In order to remove them, combining quantum Hunt-Stein theorem and other reduction methods, we establish a general reduction theorem that reduces a complicated quantum Hypothesis Testing problem to a fundamental quantum Hypothesis Testing problem. Using these methods, we derive quantum counterparts of chi-square, t and F tests as optimal tests in the respective settings.
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An Information-Spectrum Approach to Classical and Quantum Hypothesis Testing for Simple Hypotheses
IEEE Transactions on Information Theory, 2007Co-Authors: H Nagaoka, Masahito HayashiAbstract:The information-spectrum analysis made by Han for classical Hypothesis Testing for simple hypotheses is extended to a unifying framework including both classical and quantum Hypothesis Testing. The results are also applied to fixed-length source coding when loosening the normalizing condition for probability distributions and for quantum states. We establish general formulas for several quantities relating to the asymptotic optimality of tests/codes in terms of classical and quantum information spectra
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an information spectrum approach to classical and quantum Hypothesis Testing for simple hypotheses
arXiv: Quantum Physics, 2002Co-Authors: H Nagaoka, Masahito HayashiAbstract:The information-spectrum analysis made by Han for classical Hypothesis Testing for simple hypotheses is extended to a unifying framework including both classical and quantum Hypothesis Testing as well as fixed-length source coding, whereby general formulas for several quantities concerning the asymptotic optimality of tests/codes are established in terms of classical and quantum information spectrum. Generality of theorems and simplicity of proofs are fully pursued, and as byproducts some improvements on the original classical results are also obtained.
Yuval Kochman - One of the best experts on this subject based on the ideXlab platform.
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on the reliability function of distributed Hypothesis Testing under optimal detection
International Symposium on Information Theory, 2018Co-Authors: Nir Weinberger, Yuval KochmanAbstract:The distributed Hypothesis-Testing problem with full side-information is studied. The trade-off (reliability function) between the type 1 and type 2 error exponents under limited rate is studied in the following way. First, the problem of determining the reliability function of distributed Hypothesis-Testing is reduced to the problem of determining the reliability function of channel-detection codes (in analogy to a similar result which connects the reliability of distributed compression and ordinary channel codes). Second, a random-coding bound based on an hierarchical ensemble, as well as an expurgated bound, are derived for the reliability of channel-detection codes. The resulting bounds are the first to be derived for quantization-and-binning schemes under optimal detection.
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On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection
arXiv: Information Theory, 2018Co-Authors: Nir Weinberger, Yuval KochmanAbstract:The distributed Hypothesis-Testing problem with full side-information is studied. The trade-off (reliability function) between the type 1 and type 2 error exponents under limited rate is studied in the following way. First, the problem of determining the reliability function of distributed Hypothesis-Testing is reduced to the problem of determining the reliability function of channel-detection codes (in analogy to a similar result which connects the reliability of distributed compression and ordinary channel codes). Second, a single-letter random-coding bound based on an hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for the optimal detection rule. We believe that the resulting bounds are ensemble-tight, and hence optimal within the class of quantization-and-binning schemes.
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On Binary Distributed Hypothesis Testing
arXiv: Information Theory, 2017Co-Authors: Eli Haim, Yuval KochmanAbstract:We consider the problem of distributed binary Hypothesis Testing of two sequences that are generated by an i.i.d. doubly-binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different levels of correlation between the two source components, i.e., the crossover probability between the two. The terminals communicate with a decision function via rate-limited noiseless links. We analyze the tradeoff between the exponential decay of the two error probabilities associated with the Hypothesis test and the communication rates. We first consider the side-information setting where one encoder is allowed to send the full sequence. For this setting, previous work exploits the fact that a decoding error of the source does not necessarily lead to an erroneous decision upon the Hypothesis. We provide improved achievability results by carrying out a tighter analysis of the effect of binning error; the results are also more complete as they cover the full exponent tradeoff and all possible correlations. We then turn to the setting of symmetric rates for which we utilize Korner-Marton coding to generalize the results, with little degradation with respect to the performance with a one-sided constraint (side-information setting).
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on composite binary Hypothesis Testing with training data
Allerton Conference on Communication Control and Computing, 2017Co-Authors: Michael Bell, Yuval KochmanAbstract:Motivated by an outlier detection problem, we consider the problem of Testing between a known i.i.d. distribution over a finite alphabet, and a composite Hypothesis consisting of all other i.i.d. distributions over the same alphabet. We wish to quantify the loss with respect to simple Hypothesis Testing, and further to find how much of it can be re-gained using a training sequence that is known to come from the unknown distribution. To that end, we present new optimality criteria, universal minimax with and without a training sequence. We show that under our criteria, the acceptance region of the optimal tests takes the simple form of a “sphere of types”, where the center is shifted to be “antipodal” to the type of the training sequence (if such a sequence is present). Further, noting that universality has no cost in the exponential sense, we turn to the second-order regime of fixed error probabilities, where we define a figure of merit that we call resolution tradeoff. In this regime we solve Gaussian Hypothesis Testing problems, that are asymptotically equivalent to the original ones, in order to derive the resolution tradeoffs with and without training sequence.
Torrin M Liddell - One of the best experts on this subject based on the ideXlab platform.
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the bayesian new statistics Hypothesis Testing estimation meta analysis and power analysis from a bayesian perspective
Psychonomic Bulletin & Review, 2018Co-Authors: John K Kruschke, Torrin M LiddellAbstract:In the practice of data analysis, there is a conceptual distinction between Hypothesis Testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from Hypothesis Testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to Hypothesis Testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.
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the bayesian new statistics Hypothesis Testing estimation meta analysis and power analysis from a bayesian perspective
2016Co-Authors: John K Kruschke, Torrin M LiddellAbstract:In the practice of data analysis, there is a conceptual distinction between Hypothesis Testing, on the one hand, and estimation with quantified uncertainty, on the other hand. Among frequentists in psychology a shift of emphasis from Hypothesis Testing to estimation has been dubbed “the New Statistics” (Cumming, 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to Hypothesis Testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, random control trials, and planning (e.g., power analysis).
John K Kruschke - One of the best experts on this subject based on the ideXlab platform.
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the bayesian new statistics Hypothesis Testing estimation meta analysis and power analysis from a bayesian perspective
Psychonomic Bulletin & Review, 2018Co-Authors: John K Kruschke, Torrin M LiddellAbstract:In the practice of data analysis, there is a conceptual distinction between Hypothesis Testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from Hypothesis Testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to Hypothesis Testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.
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the bayesian new statistics Hypothesis Testing estimation meta analysis and power analysis from a bayesian perspective
2016Co-Authors: John K Kruschke, Torrin M LiddellAbstract:In the practice of data analysis, there is a conceptual distinction between Hypothesis Testing, on the one hand, and estimation with quantified uncertainty, on the other hand. Among frequentists in psychology a shift of emphasis from Hypothesis Testing to estimation has been dubbed “the New Statistics” (Cumming, 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to Hypothesis Testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, random control trials, and planning (e.g., power analysis).
