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Kernel Bayes' Rule
A nonparametric kernel-based method for realizing Bayes’ rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes’ ru...
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A kernel method for realizing Bayes’ rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The poste...
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We state a quantum version of Bayes’s rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle ...
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Sparked by a remarkable result due to Hemaspaandra et al. [1], the voting rule attributed to Charles Dodgson (aka Lewis Carroll) has become one of the most studied voting rules in computational social choice. However, the computer science literature often neglects that Dodgson’s rule has some serious shortcomings as a choice procedure. This short note contains four examples revealing Dodgson’s ...
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ژورنال
عنوان ژورنال: Cogent Mathematics & Statistics
سال: 2018
ISSN: 2574-2558
DOI: 10.1080/23311835.2018.1447220