arXiv subjects
Publications and source records attributed to Hideitsu Hino.
Based on information and para-contact metric geometries, in this paper a class of dynamical systems is formulated for describing time-development of expectation variables. Here such systems for expectation variables are exactly derived from continuous-time master equations describing nonequilibrium processes.
Bayesian optimization is an effective method to efficiently optimize unknown objective functions with high evaluation costs. Traditional Bayesian optimization algorithms select one point per iteration for single objective function, whereas in recent years, Bayesian optimization for multi-objective optimization or multi-point search per iteration have been proposed. However, Bayesian optimization that can deal with them at the same time in non-heuristic way is not known at present. We propose a Bayesian optimization algorithm that can deal with multi-objective optimization and multi-point search at the same time. First, we define an acquisition function that considers both multi-objective and multi-point search problems. It is difficult to analytically maximize the acquisition function as the computational cost is prohibitive even when approximate calculations such as sampling approximation are performed; therefore, we propose an accurate and computationally efficient method for estimating gradient of the acquisition function, and develop an algorithm for Bayesian optimization with multi-objective and multi-point search. It is shown via numerical experiments that the performance of the proposed method is comparable or superior to those of heuristic methods.
In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of a set of appropriately chosen Markov kernels. To geometrize such dynamical systems for expectation variables, information geometry is used for expressing equilibrium states, and contact geometry is used for nonequilibrium states. Here time-developments of the expectation variables are identified with contact Hamiltonian vector fields on a contact manifold. Also, it is shown that the convergence rate of this dynamical system is exponential. Duality emphasized in information geometry is also addressed throughout.
Analyses of volcanic ash are typically performed either by qualitatively classifying ash particles by eye or by quantitatively parameterizing its shape and texture. While complex shapes can be classified through qualitative analyses, the results are subjective due to the difficulty of categorizing complex shapes into a single class. Although quantitative analyses are objective, selection of shape parameters is required. Here, we applied a convolutional neural network (CNN) for the classification of volcanic ash. First, we defined four basal particle shapes (blocky, vesicular, elongated, rounded) generated by different eruption mechanisms (e.g., brittle fragmentation), and then trained the CNN using particles composed of only one basal shape. The CNN could recognize the basal shapes with over 90% accuracy. Using the trained network, we classified ash particles composed of multiple basal shapes based on the output of the network, which can be interpreted as a mixing ratio of the four basal shapes. Clustering of samples by the averaged probabilities and the intensity is consistent with the eruption type. The mixing ratio output by the CNN can be used to quantitatively classify complex shapes in nature without categorizing forcibly and without the need for shape parameters, which may lead to a new taxonomy.
Geochemically discriminating between magmatism in different tectonic settings remains a fundamental part of understanding the processes of magma generation within the Earth's mantle. Here, we present an approach where machine-learning (ML) methods are used for quantitative tectonic discrimination and feature selection using global geochemical datasets containing data for volcanic rocks generated in eight different tectonic settings. This study uses support vector machine, random forest, and sparse multinomial regression (SMR) approaches. All these ML methods with data for 20 elements and 5 isotopic ratios allowed the successful geochemical discrimination between igneous rocks formed in eight different tectonic settings with a discriminant ratio better than 83% for all settings barring oceanic plateaus and back-arc basins. SMR is a particularly powerful and interpretable ML method because it quantitatively identifies geochemical signatures that characterize the tectonic settings of interest and the characteristics of each sample as a probability of the membership of the sample for each setting. We also present the most representative basalt composition for each tectonic setting. The new data provide reference points for future geochemical discussions. Our results indicate that at least 17 elements and isotopic ratios are required to characterize each tectonic setting, suggesting that geochemical tectonic discrimination cannot be achieved using only a small number of elemental compositions and/or isotopic ratios. The results show that volcanic rocks formed in different tectonic settings have unique geochemical signatures, indicating that both volcanic rock geochemistry and magma generation processes are closely connected to the tectonic setting.
Plasticity is one of the most important properties of the nervous system, which enables animals to adjust their behavior to the ever-changing external environment. Changes in synaptic efficacy between neurons constitute one of the major mechanisms of plasticity. Therefore, estimation of neural connections is crucial for investigating information processing in the brain. Although many analysis methods have been proposed for this purpose, most of them suffer from one or all the following mathematical difficulties: (1) only partially observed neural activity is available; (2) correlations can include both direct and indirect pseudo-interactions; and (3) biological evidence that a neuron typically has only one type of connection (excitatory or inhibitory) should be considered. To overcome these difficulties, a novel probabilistic framework for estimating neural connections from partially observed spikes is proposed in this paper. First, based on the property of a sum of random variables, the proposed method estimates the influence of unobserved neurons on observed neurons and extracts only the correlations among observed neurons. Second, the relationship between pseudo-correlations and target connections is modeled by neural propagation in a multiplicative manner. Third, a novel information-theoretic framework is proposed for estimating neuron types. The proposed method was validated using spike data generated by artificial neural networks. In addition, it was applied to multi-unit data recorded from the CA1 area of a rat's hippocampus. The results confirmed that our estimates are consistent with previous reports. These findings indicate that the proposed method is useful for extracting crucial interactions in neural signals as well as in other multi-probed point process data.
We developed a method to classify volcanic ash samples by introducing statistically determined grain types. Using more than 10,000 numbers of automatically measured grain data (parameters of grain shape and transparency) and the cluster analysis, we made grain types without human eyes. By components of the grain type in each samples, we classified samples from types of basaltic monogenetic volcanoes: 1) Funabara scoria cone, Izu Peninsula, Japan (magmatic eruption origin); 2) Nippana tuff ring, Miyakejima, Japan (phreatomagmatic eruption origin); and 3) rootless cones in Myvatn, Iceland (rootless eruption origin). We tested two cases; using grain shape parameters only, and both of grain shape parameters and transparency values. It is found that the sample classification is more consistent with their eruption style in the case of using both parameters of grain shape and transparency. By sampling several layers of an outcrop, this procedure can be used to interpret changes in eruption/fragmentation style during a volcanic event. Furthermore, this procedure might be applicable to other aims such as sedimentology and planetary science.
A large number of image super resolution algorithms based on the sparse coding are proposed, and some algorithms realize the multi-frame super resolution. In multi-frame super resolution based on the sparse coding, both accurate image registration and sparse coding are required. Previous study on multi-frame super resolution based on sparse coding firstly apply block matching for image registration, followed by sparse coding to enhance the image resolution. In this paper, these two problems are solved by optimizing a single objective function. The results of numerical experiments support the effectiveness of the proposed approch.
An image super-resolution method from multiple observation of low-resolution images is proposed. The method is based on sub-pixel accuracy block matching for estimating relative displacements of observed images, and sparse signal representation for estimating the corresponding high-resolution image. Relative displacements of small patches of observed low-resolution images are accurately estimated by a computationally efficient block matching method. Since the estimated displacements are also regarded as a warping component of image degradation process, the matching results are directly utilized to generate low-resolution dictionary for sparse image representation. The matching scores of the block matching are used to select a subset of low-resolution patches for reconstructing a high-resolution patch, that is, an adaptive selection of informative low-resolution images is realized. When there is only one low-resolution image, the proposed method works as a single-frame super-resolution method. The proposed method is shown to perform comparable or superior to conventional single- and multi-frame super-resolution methods through experiments using various real-world datasets.
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for other methods the spectral information can be used to estimate the excess risk. An important question remains on how close the sample eigenvalues/eigenvectors are to the population values. In this paper, we improve earlier results on concentration bounds for eigenvalues of general kernel matrices. For distance and inner product kernel functions, e.g. radial basis functions, we provide new concentration bounds, which are characterized by the eigenvalues of the sample covariance matrix. Meanwhile, the obstacles for sharper bounds are accounted for and partially addressed. As a case study, we derive a concentration inequality for sample kernel target-alignment.
On thinking of a Grover-type quantum search algorithm for an ordered tuple of multi-qubit states, a gradient system associated with the negative von-Neumann entropy is studied on the space of regular relative-configurations of multi-qubit states (SR${}^2$CMQ). The SR${}^2$CMQ emerges, through a geometric procedure, from the space of ordered tuples of multi-qubit states for the quantum search. The aim of this paper is to give a brief report on the integrability of the gradient dynamical system together with quantum information geometry of the underlying space, SR${}^2$CMQ, of that system.