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Kameo Matusita

Bio: Kameo Matusita is an academic researcher. The author has contributed to research in topics: Decision rule & Decision tree. The author has an hindex of 9, co-authored 16 publications receiving 469 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the authors formulate the problem as making decision whether the random variable under consideration has F0=N(0, 1) or some F with d(F, Fo)>~ (>0), where ~ is a constant which is to be predetermined from the actual situation of the problem.
Abstract: Distance between distribution functions of ten becomes a useful and convenient concept in statistics. In a class of distributions, distance can be defined in various ways. We, therefore, have to choose an adequate distance for a particular problem. Fur the r , to t r ea t the problem efficiently, we are required, or at least i t is ve ry desirable, to control all errors tha t may be committed in making decision or inference. For this purpose we have to formulate, or reformulate if necessary, the problem suitably. A proper formulation of the problem is very important for ge t t ing command over possible errors. For instance, suppose tha t we wan t to know whether or not the random variable under consideration can be considered to have mean zero, when it is given that the random variable has the Gaussian dist r ibut ion N(O, 1). In this case, if we take the problem as the one inquiring jus t whether or not the mean of the random variable is zero, we can not control possible errors. For we can find a distribution which has mean not equal to 0, bu t which is as near to the distribution N(0, 1) as desired, and this makes it impossible to control all possible errors in inference or decision making based on a finite number of observations. In terms of hypothesis testing, we can not make the first and second kinds of errors simultaneously as small as desired (i.e., while we can make the first kind of error smaller than any given (positive) value, this is not the case wi th the second kind of error). One way to avoid such inconvenience is to formulate the problem as follows. That is, introducing an adequate distance d ( . , . ) i n the space of distributions concerned, we set the problem as making decision whether the random variable under consideration has F0=N(0 , 1) or some F with d(F, Fo)>~ (>0) , where ~ is a constant which is to be predetermined from the actual situation of the problem. For the problem thus formulated we can control the errors (see Matusi ta [1], Matusita, Akaike [2]). So far, the author has t rea ted various problems with the same idea, the idea of controlling possible errors (see Matusi ta [1], [3], [5], [7], [8],

51 citations


Cited by
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Book
01 Jan 1996
TL;DR: The Bayes Error and Vapnik-Chervonenkis theory are applied as guide for empirical classifier selection on the basis of explicit specification and explicit enforcement of the maximum likelihood principle.
Abstract: Preface * Introduction * The Bayes Error * Inequalities and alternatedistance measures * Linear discrimination * Nearest neighbor rules *Consistency * Slow rates of convergence Error estimation * The regularhistogram rule * Kernel rules Consistency of the k-nearest neighborrule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-Chervonenkis theory * Lower bounds for empirical classifier selection* The maximum likelihood principle * Parametric classification *Generalized linear discrimination * Complexity regularization *Condensed and edited nearest neighbor rules * Tree classifiers * Data-dependent partitioning * Splitting the data * The resubstitutionestimate * Deleted estimates of the error probability * Automatickernel rules * Automatic nearest neighbor rules * Hypercubes anddiscrete spaces * Epsilon entropy and totally bounded sets * Uniformlaws of large numbers * Neural networks * Other error estimates *Feature extraction * Appendix * Notation * References * Index

3,598 citations

Journal ArticleDOI
TL;DR: In this article, three general methods for obtaining measures of diversity within a population and dissimilarity between populations are discussed, one is based on an intrinsic notion of diversity between individuals and others make use of the concepts of entropy and discrimination.

1,462 citations

Journal ArticleDOI
TL;DR: In this article, concrete decision rules are given for the problem of goodness of fit and for two samples with a risk smaller than any pre-assigned value, and for estimation.
Abstract: Concrete decision rules are given for the problem of goodness of fit and the problem of two samples with a risk smaller than any preassigned value. The problem of estimation is also treated.

314 citations

Journal ArticleDOI
TL;DR: A [phi]-entropy functional is defined on the probability space and its Hessian along a direction of the tangent space of the parameter space is taken as the metric, and the distance between two probability distributions is computed as the geodesic distance induced by the metric.

287 citations

Posted Content
TL;DR: This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.
Abstract: This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in quantum cryptography and quantum computation theory. The results reported include the following. An exact expression for the quantum fidelity between two mixed states is derived. The optimal measurement that gives rise to it is studied in detail. Several upper and lower bounds on the quantum mutual information are derived via similar techniques and compared to each other. Of note is a simple derivation of the important upper bound first proved by Holevo and an explicit expression for another (tighter) upper bound that appears implicitly in the same derivation. Several upper and lower bounds to the quan- tum Kullback relative information are derived. The measures developed are also applied to ferreting out the extent to which quantum systems must be disturbed by information gathering measurements. This is tackled in two ways. The first is in setting up a general formalism for describing the tradeoff between inference and disturbance. The main point of this is that it gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures. The second result on this theme is a theorem that prohibits "broadcasting" an unknown (mixed) quantum state. That is to say, there is no way to replicate an unknown quantum state onto two separate quantum systems when each system is considered without regard to the other. This includes the possibility of correlation or quantum entanglement between the systems. This result is a significant extension and generalization of the standard "no-cloning" theorem for pure states.

264 citations