The probability simplex is the set of all probability distributions on a finite set and is the most fundamental object in the finite probability theory. In this paper we give a characterization of statistical models on finite sets which are statistically equivalent to probability simplexes in terms of α-families including exponential families and mixture families. The subject has a close relation to some fundamental aspects of information geometry such as α-connections and autoparallelity.

We prove that a tree model is an exponential family (e-family) of Markov kernels, if and only if it is an FSMX model. The notion of e-family of Markov kernels was first introduced by Nakagawa and Kanaya ('93) in the one-dimensional case. Then, Nagaoka ('05) gave its established form, and Hayashi & Watanabe ('16) discussed it. A tree model is the Markov model defined by a context tree. It is noted by Weinberger et al., ('95) that tree models are classified into two classes; FSMX models and non-FSMX models, depending on the shape of their context trees. The FSMX model is a tree model and a finite state machine. We further show that, for Markov models, the e-family of Markov kernels is equivalent to the asymptotic e-family, which was introduced by Takeuchi & Barron ('98). Note that Takeuchi & Kawabata ('07) proved that non-FSMX tree models are not asymptotic e-families for the binary alphabet case. This paper enhances their result and reveals the information geometrical properties of tree models.

It is well known that the relative entropy (Kullback-Leibler divergence) is represented in the form of Bregman divergence on exponential families and mixture families for some coordinate systems. We give a characterization of the class of statistical manifolds (smooth manifolds of probability mass functions on finite sample spaces) having coordinate systems for which the relative entropy is a Bregman divergence.

Wide-Angle Fovea Vision Sensor (WAFVS) system was designed and developed being inspired from advantages of the human eye's functions. This system is characterized by its space-variant data acquisition property, i.e., the WAFVS captures a 120-degree wide-angle input image in which its resolution (or magnification) changes like the human visual acuity. As well-known, the human visual acuity is the highest at its central field of view (FOV) and decreases rapidly towards its peripheral FOV. Thus, using the WAFVS, we can observe a target in detail by its central field of view while observing the whole of environment by its wide field of view. In addition, by controlling a view direction of the WAFVS, this WAFVS system gets visual information from the environment more in detail by smaller data amount. Hence, the WAFVS achieves a better performance of data transmission and data storage. One of severe problems in remote control of rovers, UAVs, and satellites is of a pay-load. In this point of view, the authors think that the WAFVS is suitable for the planetary exploring rover because it was originally developed for multi-purpose use of a single vision sensor. This paper describes the multi-purpose use of the WAFVS system, i.e., the following tasks: (1) observing the environment displayed to the operator for the remote navigation of the rover, (2) recording images of important scenes by changing a view direction of the WAFVS, and (3) monitoring if the instruments on the rover work well or not. Moreover, this paper experiments and discusses on how to display images to the operator when an eye-tracking device is applied as a target coordinate input device. Accuracy index, i.e., a measurement error of a target, is defined in order to evaluate performance of a combination among the vision sensor, the coordinate input device and the image display method.

There exists a well-known visual illusion with respect to color propagation. That is, a human subject confuses a color in the subject's peripheral field of view (FOV) as another color in the central FOV (with a shape of circular disk) spreads into the peripheral FOV or as a color in the peripheral FOV erodes another color in the central FOV (also with a shape of circular disk) when he/she keeps gazing at a specific color visual stimulus in his/her central FOV for more than several seconds. In this paper, the authors experiment this illusion using multiple naive subjects in conditions of the visual stimuli as the central or peripheral colors and the disk size change. This paper has proposed a rate of propagation as a criterion and has analyzed and discussed the illusion using it.

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

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

In the previous work in Proc. ISIT2003 and Proc. ISITA2004, we have investigated some relationships between sufficient statistic and weakly universal lossless source coding, and proposed asymptotically sufficient statistic method to evaluate the pointwise redundancy of source codes. This method is an attempt to understand the universality of general lossless source codes from a simple and unified viewpoint. In this paper, we present a new theorem which enables our method to show the pointwise strong universality of lossless source codes. As an example of the theorem, we prove the pointwise strong universality of the original Lynch-Davisson code and conditional Lynch-Davisson code for the class of stationary memoryless and Markov sources, respectively. Moreover, it is shown that this method can be applied to the class of finite state sources. We prove that a blockwise Lynch-Davisson code is pointwise strongly universal for this class. From the viewpoint of our method, all of these algorithms can be seen as examples of a two-step source code using a kind of asymptotically sufficient statistic. The result of this paper gives a unified viewpoint for the universality of context-based algorithms and block-based algorithms, which are typical two types of universal lossless source coding algorithms

The capacity of a classical-quantum channel (or, in other words, the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. A capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of Verdu-Han (1994) which are based on the so-called information-spectrum method. The general results are applied to the stationary memoryless case with or without cost constraint on inputs, whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated.

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.

A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown. The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto (1973), except that more careful treatment is necessary here due to the noncommutativity of operators.

We explore some basic properties of coding theory of a general quantum communication channel and its operational capacity, including: 1) adaptive measurement with feedback code; 2) reconsideration of single-letterized capacity formula; and 3) pseudoclassicality of a channel.

A new type of sufficient condition is provided for a probability distribution on the nonnegative integers to be given an optimal D-ary prefix code by a Huffman-type algorithm. In the justification of our algorithm, we introduce two new (essentially one) concepts as the definition of the "optimality" of a prefix D-ary code, which are shown to be equivalent to that defined in the traditional way. These new concepts of the optimality are meaningful even for the case where the Shannon entropy H(P) diverges.

A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold. It is important to study the geometry of the neural manifold, rather than the behavior of a single network, in order to know the capabilities and limitations of neural networks of a fixed topology. Using the new theory of information geometry, a natural invariant Riemannian metric and a dual pair of affine connections on the Boltzmann neural network manifold are established. The meaning of geometrical structures is elucidated from the stochastic and the statistical point of view. This leads to a natural modification of the Boltzmann machine learning rule.

This paper elucidates the correspondence between the Schur-Cohn (SC) test and the Routh-Hurwitz (RH) test by showing that the latter is obtained as a limit of the former. The argument is developed in a stochastic framework, where stochastic interpretations of the tests are used. The interpretation of the SC test can be derived from its equivalency to the Levinson-Durbin algorithm, while that of the RH test is newly presented here.