Details of a Researcher - Kobayashi, Kei

Papers - Kobayashi, Kei

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Representing Hierarchical Structured Data Using Cone Embedding

Takehara D., Kobayashi K.

Mathematics (Mathematics) 11 ( 10 ) 2023.05

Extracting hierarchical structure in graph data is becoming an important problem in fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods in non-Euclidean spaces, such as Poincaré embedding and Lorentz embedding, and it is now possible to learn efficient embedding by taking advantage of the structure of these spaces. In this study, we propose embedding into another type of metric space called a metric cone by learning an only one-dimensional coordinate variable added to the original vector space or a pre-trained embedding space. This allows for the extraction of hierarchical information while maintaining the properties of the pre-trained embedding. The metric cone is a one-dimensional extension of the original metric space and has the advantage that the curvature of the space can be easily adjusted by a parameter even when the coordinates of the original space are fixed. Through an extensive empirical evaluation we have corroborated the effectiveness of the proposed cone embedding model. In the case of randomly generated trees, cone embedding demonstrated superior performance in extracting hierarchical structures compared to existing techniques, particularly in high-dimensional settings. For WordNet embeddings, cone embedding exhibited a noteworthy correlation between the extracted hierarchical structures and human evaluation outcomes.

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Entropy-regularized optimal transport on multivariate normal and q-normal distributions

Tong, Q., Kobayashi, K.

Entropy (Entropy) 23 ( 2 ) 302 - 20 2021

Research paper (scientific journal), Accepted

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.

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語彙サイズの異なる大学生の英語心内辞書

折田充, 村里泰昭, 小林景, 吉井誠, Richard Lavin, 相澤一美, 神本忠光

熊本大学英語英文学 63.64 207 - 222 2021

Research paper (bulletin of university, research institution), Accepted

Empirical geodesic graphs and CAT(k) metrics for data analysis

Kei Kobayashi, Henry P. Wynn

Statistics and Computing (Spriger) 30 ( 1 ) 1 - 18 2020

Research paper (scientific journal), Joint Work, Accepted, ISSN 1573-1375

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated along the path. The geodesic, then, is the shortest such path and defines a geodesic metric. Such metrics are transformed in a number of ways to produce parametrised families of geodesic metric spaces, empirical versions of which allow computation of intrinsic means and associated measures of dispersion. These reveal properties of the data, based on geometry, such as those that are difficult to see from the raw Euclidean distances. Examples of application include clustering and classification. For certain parameter ranges, the spaces become CAT(0) spaces and the intrinsic means are unique. In one case, a minimal spanning tree of a graph based on the data becomes CAT(0). In another, a so-called “metric cone” construction allows extension to CAT(k) spaces. It is shown how to empirically tune the parameters of the metrics, making it possible to apply them to a number of real cases.

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心内辞書内の単語の結びつき方―英単語学習プログラムへの取り組み前

折田充, 村里泰昭, 小林景, 神本忠光, 相澤一美, Richard S. Lavin, 吉井誠

KASELE BULLETIN 468 9 - 18 2020

Research paper (bulletin of university, research institution), Accepted

英語心内辞書における名詞クラスターの構造化

折田充, 村里泰昭, 小林景, 神本忠光, 吉井誠, Richar, S. Lavin, 相澤一美

KASELE BULLETIN 46 1 - 10 2018

Research paper (scientific journal), Joint Work, Accepted

Are the Once Acquired Cluster Structure Retained?: The Effect of Autonomous Vocabulary E-learning to Promote Restructuring of the L2 English Mental Lexicon

ORITA Mitsuru, MURASATO Yasuaki, KOBAYASHI Kei, KAMIMOTO Tadamitsu, YOSHI Makoto, Richard Lavin, AIZAWA Kazumi

KASELE BULLETIN ４５ 1 - 8 2017.07

Research paper (scientific journal), Accepted

多様体学習とデータ空間の幾何学

小林景

RIMS Kokyuroku 2057 1 - 10 2017

英語心内辞書の変容を目指した単語学習プログラムの効果

折田充, 村里泰昭, 小林景, 相澤一美, 神本忠光, 吉井誠, Richar, S. Lavin

KASELE BULLETIN 44 1 - 10 2016.07

Research paper (bulletin of university, research institution), Joint Work, Accepted

Flattening the Density Gradient for Eliminating Spatial Centrality to Reduce Hubness

Hara, K, Suzuki, I, Kobayashi, K, Fukumizu, K, Radovanovic, M

30th AAAI Conference on Artificial Intelligence (AAAI) (AAAI Press) 1659 - 1665 2016

Spatial centrality, whereby samples closer to the center of a dataset tend to be closer to all other samples, is regarded as one source of hubness. Hubness is well known to degrade k-nearest-neighbor (k-NN) classification. Spatial centrality can be removed by centering, i.e., shifting the origin to the global center of the dataset, in cases where inner product similarity is used. However, when Euclidean distance is used, centering has no effect on spatial centrality because the distance between the samples is the same before and after centering. As described in this paper, we propose a solution for the hubness problem when Euclidean distance is considered. We provide a theoretical explanation to demonstrate how the solution eliminates spatial centrality and reduces hubness. We then present some discussion of the reason the proposed solution works, from a viewpoint of density gradient, which is regarded as the origin of spatial centrality and hubness. We demonstrate that the solution corresponds to flattening the density gradient. Using real-world datasets, we demonstrate that the proposed method improves k-NN classification performance and outperforms an existing hub-reduction method.

発話思考データ分析から見るL2心内辞書構造

折田充, 小林景, 神本忠光, 菅本強司

大学教育年報 19 23 - 37 2016

Accepted

Reducing hubness: A cause of vulnerability in recommender systems

Hara K., Suzuki I., Kobayashi K., Fukumizu K.

SIGIR 2015 - Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR 2015 - Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval) 815 - 818 2015.08

It is known that memory-based collaborative filtering systems are vulnerable to shilling attacks. In this paper, we demonstrate that hubness, which occurs in high dimensional data, is exploited by the attacks. Hence we explore methods for reducing hubness in user-response data to make these systems robust against attacks. Using the MovieLens dataset, we empirically show that the two methods for reducing hubness by transforming a similarity matrix|(i) centering and (ii) conversion to a commute time kernel|can thwart attacks without degrading the recommendation performance.

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Localized centering: Reducing hubness in large-sample data

Hara K., Suzuki I., Shimbo M., Kobayashi K., Fukumizu K., Radovanovic M.

Proceedings of the National Conference on Artificial Intelligence (Proceedings of the National Conference on Artificial Intelligence) 4 2645 - 2651 2015.06

Hubness has been recently identified as a problematic phenomenon occurring in high-dimensional space. In this paper, we address a different type of hubness that occurs when the number of samples is large. We investigate the difference between the hubness in highdimensional data and the one in large-sample data. One finding is that centering, which is known to reduce the former, does not work for the latter. We then propose a new hub-reduction method, called localized centering. It is an extension of centering, yet works effectively for both types of hubness. Using real-world datasets consisting of a large number of documents, we demonstrate that the proposed method improves the accuracy of knearest neighbor classification.

Reducing Hubness for Kernel Regression

Hara, K, Suzuki, I, Kobayashi, K, Fukumizu, K, Radovanovic, M

SISAP2015 (Springer) 9371 339 - 344 2015

ISSN 03029743

In this paper, we point out that hubness—some samples in a high-dimensional dataset emerge as hubs that are similar to many other samples—influences the performance of kernel regression. Because the dimension of feature spaces induced by kernels is usually very high, hubness occurs, giving rise to the problem of multicollinearity, which is known as a cause of instability of regression results. We propose hubnessreduced kernels for kernel regression as an extension of a previous approach for kNN classification that reduces spatial centrality to eliminate hubness.

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Statistical analysis via the curvature of data space

Kei Kobayashi, Orita Mitsuru, Henry P. Wynn

BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING (MAXENT 2014) (AMER INST PHYSICS) 1641 ( 97 (2015) ) 97 - 104 2015

Accepted, ISSN 0094-243X

It has been known that the curvature of data spaces plays a role in data analysis. For example, the Frechet mean (intrinsic mean) always exists uniquely for a probability measure on a non-positively curved metric space. In this paper, we use the curvature of data spaces in a novel manner. A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. The population version defines distance by the amount of probability mass accumulated on travelling between two points and geodesic metric arises from the shortest path version. Such metrics are then transformed in a number of ways to produce families of geodesic metric spaces. Empirical versions of the geodesics allow computation of intrinsic means and associated measures of dispersion. A version of the empirical geodesic is introduced based on some metric graphs computed from the sample points. For certain parameter ranges the spaces become CAT(0) spaces and the intrinsic means are unique. In the graph case a minimal spanning tree obtained as a limiting case is CAT(0). In other cases the aggregate squared distance from a test point provides local minima which yield information about clusters. This is particularly relevant for metrics based on so-called metric cones which allow extensions to CAT(.) spaces. We show how our methods work by using some actual data. This paper is a summary of a longer version [5]. See it for proof of theorems and details.

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Computational algebraic methods in efficient estimation

Kobayashi, Kei The, Institute of, Statistical Mathematics, Wynn, Henry London School of Economics

Geometric Theory of Information (Signals and Communication Technology) (Springer-Verlag) 119 - 140 2014.05

Accepted

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Asymptotically efficient estimators for algebraic statistical manifolds

Kobayashi K., Wynn H.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)) 8085 LNCS 721 - 728 2013.10

ISSN 03029743

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficiency estimators can be constructed, such as bias corrected Maximum Likelihood Estimators and more general estimators, but for which the estimating equations are purely algebraic. In addition it is shown how Gröbner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such are homotopy methods. © 2013 Springer-Verlag.

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Asymptotically efficient estimators for algebraic statistical manifolds

Kei Kobayashi, Henry P. Wynn

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Springer-Verlag) 8085 721 - 728 2013

Accepted, ISSN 0302-9743

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Upper Bounds on Total Variation Distance by DeRobertis Separation

Kobayashi, Kei The, Institute of, Statistical Mathematics

Proceedings of the Institute of Statistical Mathematics (統計数理研究所) 59-2 ( 2 ) 321 - 328 2011.12

Accepted, ISSN 0912-6112

Bayesian shrinkage prediction for the regression problem

Kei Kobayashi, Fumiyasu Komaki

JOURNAL OF MULTIVARIATE ANALYSIS (ELSEVIER INC) 99 ( 9 ) 1888 - 1905 2008.10

Accepted, ISSN 0047259X

We consider Bayesian shrinkage predictions for the Normal regression problem under the frequentist Kullback-Leibler risk function.
Firstly, we consider the multivariate Normal model with an unknown mean and a known covariance. While the unknown mean is fixed, the covariance of future samples can be different from that of training samples. We show that the Bayesian predictive distribution based on the uniform prior is dominated by that based on a class of priors if the prior distributions for the covariance, and future covariance matrices are rotation invariant.
Then, we consider a class of priors for the mean parameters depending on the future covariance matrix. With such a prior, we can construct a Bayesian predictive distribution dominating that based on the uniform prior.
Lastly, applying this result to the prediction of response variables in the Normal linear regression model, we show that there exists a Bayesian predictive distribution dominating that based on the uniform prior. Minimaxity of these Bayesian predictions follows from these results. (C) 2008 Elsevier Inc. All rights reserved.

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Parallel matching for ranking all teams in a tournament

Kei Kobayashi, Hideki Kawasaki, Akimichi Takemura

ADVANCES IN APPLIED PROBABILITY (APPLIED PROBABILITY TRUST) 38 ( 3 ) 804 - 826 2006.09

Accepted, ISSN 00018678

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Information criteria for support vector machines

Kei Kobayashi, Fumiyasu Komaki

IEEE TRANSACTIONS ON NEURAL NETWORKS (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC) 17 ( 3 ) 571 - 577 2006.05

Accepted, ISSN 10459227

This paper presents kernel regularization information criterion (KRIC), which is a new criterion for tuning regularization parameters in kernel logistic regression (KLR) and support vector machines (SVMs). The main idea of the KRIC is based on the regularization information criterion (RIC). We derive an eigenvalue equation to calculate the KRIC and solve the problem. The computational cost for parameter tuning by the KRIC is reduced drastically by using the Nystrom approximation. The test error rate of SVMs or KLR with the regularization parameter tuned by the KRIC is comparable with the one by the cross validation or evaluation of the evidence. The computational cost of the KRIC is significantly lower than the one of the other criteria.

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Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

Kei Kobayashi, Kokichi Sugihara

Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) (Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)) 85 ( 6 ) 21 - 31 2002.06

Accepted, ISSN 10420967

A multiplicatively weighted crystal growth Voronoi diagram is a type of planar segmentation diagram that can result when crystals grow at different speeds from several points. In this paper, we first define a multiplicatively weighted crystal growth Voronoi diagram, discuss its properties, and find the analytic solution for the simple case. The approximate solution method for the complex case is constructed by using a difference method for partial differential equations called the fast marching method. Then the multiplicatively weighted crystal growth Voronoi diagram is used to construct a technique for optimum path planning of competing mobile robots. © 2002 Scripta Technica, Electron. Comm. Jpn.

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Crystal Voronoi diagram and its applications

Kei Kobayashi, Kokichi Sugihara

Future Generation Computer Systems (Future Generation Computer Systems) 18 ( 5 ) 681 - 692 2002.04

Accepted, ISSN 0167739X

This paper studies the multiplicatively weighted crystal-growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. The analytic equation describing the boundary curve is given for a simple case. For the general case, an approximation algorithm is proposed. This algorithm is based on a finite-difference method, called a fast marching method, for solving a special type of a partial differential equation. The proposed algorithm is applied to the planning of a collision-free path for a robot avoiding enemy attacks. © 2002 Elsevier Science B.V. All rights reserved.

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Crystal Voronoi Diagram and Its Applications to Collision-Free Paths

Kei KOBAYASHI, Kokichi Sugihara

Computational Science ICCS2001 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)) 2073 738 - 747 2001

Accepted, ISSN 03029743

This paper studies the multiplicatively weighted crystal- growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. An approximation algorithm is proposed. This algorithm is based on a finite difference method, called a fast marching method, for solving a special type of a partial differential equation. The proposed algorithm is applied to the planning of a collision-free path for a robot avoiding enemy attacks. © 2001 Springer-Verlag Berlin Heidelberg.

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乗法重みつき結晶成長ボロノイ図の近似構成法とその応用

小林景, 杉原厚吉

電子情報通信学会論文誌A J83-A ( 12 ) 1495 - 1504 2000

Accepted

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