{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1571417127445952768.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"NAID","@value":"110003233111"}}],"dc:title":[{"@language":"ja","@value":"階層型ニューラルネットワークの混合モデルによるベイズ最適な予測について"},{"@language":"en","@value":"On Bayes Optimal Prediction based on Mixture Model of Multilayer Neural Networks"}],"dc:language":"ja","description":[{"type":"abstract","notation":[{"@language":"ja","@value":"確率モデルの学習問題において, 学習データと同じ母集団のデータ(未学習データ)の出力を精度高く予測することが重要であり, モデル選択は一つの解決方法となっている. しかし, 目的を未学習データの出力の予測と考えた場合, 必ずしもモデルを一つに限定する必要はなく, このとき要求されるのは, 精度の高い予測を行うことである. このような予測を考慮した確率モデルを構築する方法として, ベイズ決定理論に基づいた学習理論が広く研究されている. 本稿ではまず, 候補である複数のNNモデル全ての混合モデルを用いて予測することがベイズ最適であることを示す. しかし, このベイズ最適をNNモデルに対して厳密に計算しようとすると, パラメータ空間上の複雑な積分操作が必要になり, 計算不可能になってしまう. そこで, ラプラスの方法を用いて, この積分操作を排除し, 漸近近似的に事後予測分布を計算することによるベイス最適なNNモデルの予測法を提案する."},{"@language":"en","@value":"In learning of the probabilistic models, it is important to predict accurately for the output of future observation. On prediction of the future observation, it is not necessary to select a particular model from the model class. The objective here is to predict the output of the future observations accurately. On the other hand, a lot of researches of the prediction methods based on Bayes decision theory for the probabilistic models have been reported. These Bayesian methods are efficient to the prediction with accuracy. In this paper, we, at first, show that the prediction using the mixture model of all neural network models in the model class is bayes optimal. However, this mixture model is difficult to calculate strictly for neural network models, since the complex integration on the parameter space is cannot be calculated for the general priors. We, therefore, propose the new prediction method with asymptotic Bayes optimality, based on Laplacian method which calculates the asymptotic posterior predictive distribution and then removes the integration, apply this method to the multilayer neural network models and verify the efficiency of the proposal through the simulation experiments."}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1581417127445952768","@type":"Researcher","foaf:name":[{"@language":"ja","@value":"俵 信彦"},{"@language":"en","@value":"TAWARA Nobuhiko"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"武蔵工業大学"},{"@language":"en","@value":"Musashi Institute of Technology"}]},{"@id":"https://cir.nii.ac.jp/crid/1581417127445952769","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000004894660"}],"foaf:name":[{"@language":"ja","@value":"橋川 弘紀"},{"@language":"en","@value":"HASHIKAWA Hiroki"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"武蔵工業大学"},{"@language":"en","@value":"Musashi Institute of Technology"}]},{"@id":"https://cir.nii.ac.jp/crid/1420564276162643328","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"40287967"},{"@type":"NRID","@value":"1000040287967"},{"@type":"CINII_AUTHOR_ID","@value":"DA17030822"},{"@type":"URI","@value":"https://ci.nii.ac.jp/author/DA17030822#entity"},{"@type":"URI","@value":"https://viaf.org/viaf/NII%7CDA17030822"},{"@type":"NRID","@value":"9000283890079"},{"@type":"NRID","@value":"9000287204803"},{"@type":"NRID","@value":"9000412357934"},{"@type":"NRID","@value":"9000404678515"},{"@type":"NRID","@value":"9000380426663"},{"@type":"NRID","@value":"9000409339125"},{"@type":"NRID","@value":"9000273029654"},{"@type":"NRID","@value":"9000258447298"},{"@type":"NRID","@value":"9000259859382"},{"@type":"NRID","@value":"9000411224085"},{"@type":"NRID","@value":"9000404232252"},{"@type":"NRID","@value":"9000404232985"},{"@type":"NRID","@value":"9000404295784"},{"@type":"NRID","@value":"9000413376658"},{"@type":"NRID","@value":"9000411250565"},{"@type":"NRID","@value":"9000402794222"},{"@type":"NRID","@value":"9000403546326"},{"@type":"NRID","@value":"9000380426506"},{"@type":"NRID","@value":"9000405645781"},{"@type":"NRID","@value":"9000404239821"},{"@type":"NRID","@value":"9000404249234"},{"@type":"NRID","@value":"9000404239781"},{"@type":"NRID","@value":"9000403599345"},{"@type":"NRID","@value":"9000283890096"},{"@type":"NRID","@value":"9000356478023"},{"@type":"NRID","@value":"9000414938682"},{"@type":"NRID","@value":"9000411547159"},{"@type":"NRID","@value":"9000404267305"},{"@type":"NRID","@value":"9000404262368"},{"@type":"NRID","@value":"9000412357878"},{"@type":"NRID","@value":"9000412357958"},{"@type":"NRID","@value":"9000409336461"},{"@type":"NRID","@value":"9000415351937"},{"@type":"NRID","@value":"9000403320632"},{"@type":"NRID","@value":"9000258447337"},{"@type":"NRID","@value":"9000411222398"},{"@type":"NRID","@value":"9000004826843"},{"@type":"NRID","@value":"9000283890219"},{"@type":"NRID","@value":"9000414938686"},{"@type":"NRID","@value":"9000414092585"},{"@type":"NRID","@value":"9000404262366"},{"@type":"NRID","@value":"9000402794673"},{"@type":"NRID","@value":"9000415428845"},{"@type":"NRID","@value":"9000283890482"},{"@type":"NRID","@value":"9000309576883"},{"@type":"NRID","@value":"9000404296304"},{"@type":"NRID","@value":"9000378076975"},{"@type":"NRID","@value":"9000378076978"},{"@type":"NRID","@value":"9000392053847"},{"@type":"NRID","@value":"9000403546082"},{"@type":"NRID","@value":"9000380426277"},{"@type":"NRID","@value":"9000409337544"},{"@type":"NRID","@value":"9000314077227"},{"@type":"NRID","@value":"9000309568072"},{"@type":"NRID","@value":"9000258728164"},{"@type":"NRID","@value":"9000245921441"},{"@type":"NRID","@value":"9000404232261"},{"@type":"NRID","@value":"9000363220420"},{"@type":"NRID","@value":"9000412357950"},{"@type":"NRID","@value":"9000409325222"},{"@type":"NRID","@value":"9000411224144"},{"@type":"NRID","@value":"9000360548409"},{"@type":"NRID","@value":"9000362196559"},{"@type":"NRID","@value":"9000265556888"},{"@type":"NRID","@value":"9000016265112"},{"@type":"NRID","@value":"9000404296299"},{"@type":"NRID","@value":"9000402447628"},{"@type":"NRID","@value":"9000409339180"},{"@type":"NRID","@value":"9000258447255"},{"@type":"NRID","@value":"9000345211043"},{"@type":"NRID","@value":"9000404303079"},{"@type":"NRID","@value":"9000402795400"},{"@type":"NRID","@value":"9000273011852"},{"@type":"NRID","@value":"9000259859394"},{"@type":"NRID","@value":"9000315683205"},{"@type":"NRID","@value":"9000408615897"},{"@type":"NRID","@value":"9000412543973"},{"@type":"NRID","@value":"9000402794954"},{"@type":"NRID","@value":"9000398133834"},{"@type":"NRID","@value":"9000398304011"},{"@type":"NRID","@value":"9000409336749"},{"@type":"NRID","@value":"9000258447147"},{"@type":"NRID","@value":"9000411222410"},{"@type":"NRID","@value":"9000335557042"},{"@type":"NRID","@value":"9000265556898"},{"@type":"NRID","@value":"9000045781909"},{"@type":"NRID","@value":"9000004789705"},{"@type":"NRID","@value":"9000404232256"},{"@type":"NRID","@value":"9000404232968"},{"@type":"NRID","@value":"9000283890537"},{"@type":"NRID","@value":"9000404295861"},{"@type":"NRID","@value":"9000287218755"},{"@type":"NRID","@value":"9000404262358"},{"@type":"NRID","@value":"9000402795690"},{"@type":"NRID","@value":"9000392053499"},{"@type":"NRID","@value":"9000409336858"},{"@type":"NRID","@value":"9000314077260"},{"@type":"NRID","@value":"9000411224080"},{"@type":"NRID","@value":"9000404942746"},{"@type":"NRID","@value":"9000329899686"},{"@type":"NRID","@value":"9000404295865"},{"@type":"NRID","@value":"9000403977705"},{"@type":"NRID","@value":"9000366505258"},{"@type":"NRID","@value":"9000314076703"},{"@type":"NRID","@value":"9000415128029"},{"@type":"NRID","@value":"9000304969621"},{"@type":"NRID","@value":"9000345261945"},{"@type":"NRID","@value":"9000347223714"},{"@type":"NRID","@value":"9000345211109"},{"@type":"NRID","@value":"9000412357912"},{"@type":"NRID","@value":"9000412357046"},{"@type":"NRID","@value":"9000403546330"},{"@type":"NRID","@value":"9000380426636"},{"@type":"NRID","@value":"9000409338502"},{"@type":"NRID","@value":"9000258447294"},{"@type":"NRID","@value":"9000283711090"},{"@type":"NRID","@value":"9000287218758"},{"@type":"NRID","@value":"9000380122219"},{"@type":"NRID","@value":"9000412357954"},{"@type":"NRID","@value":"9000412357078"},{"@type":"NRID","@value":"9000392054341"},{"@type":"NRID","@value":"9000411563174"},{"@type":"NRID","@value":"9000314077282"},{"@type":"NRID","@value":"9000241781114"},{"@type":"NRID","@value":"9000398034846"},{"@type":"NRID","@value":"9000303999630"},{"@type":"NRID","@value":"9000387931270"},{"@type":"NRID","@value":"9000411547155"},{"@type":"NRID","@value":"9000287216164"},{"@type":"NRID","@value":"9000399759326"},{"@type":"NRID","@value":"9000409336690"},{"@type":"NRID","@value":"9000411222391"},{"@type":"NRID","@value":"9000017664856"},{"@type":"NRID","@value":"9000415149116"},{"@type":"NRID","@value":"9000404247168"},{"@type":"NRID","@value":"9000283711049"},{"@type":"NRID","@value":"9000283890561"},{"@type":"NRID","@value":"9000283890025"},{"@type":"NRID","@value":"9000347160845"},{"@type":"NRID","@value":"9000412544129"},{"@type":"NRID","@value":"9000402794677"},{"@type":"NRID","@value":"9000409505591"},{"@type":"NRID","@value":"9000409337600"},{"@type":"NRID","@value":"9000273011862"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/masagoto"}],"foaf:name":[{"@language":"ja","@value":"後藤 正幸"},{"@language":"en","@value":"GOTOH Masayuki"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"早稲田大学"},{"@language":"en","@value":"Waseda University"}]}],"publication":{"publicationIdentifier":[{"@type":"NCID","@value":"AN10091178"}],"prism:publicationName":[{"@value":"電子情報通信学会技術研究報告. NC, ニューロコンピューティング"},{"@language":"en","@value":"IEICE technical report. Neurocomputing"}],"dc:publisher":[{"@value":"一般社団法人電子情報通信学会"},{"@language":"en","@value":"The Institute of Electronics, Information and Communication Engineers"}],"prism:publicationDate":"1996-03-18","prism:volume":"95","prism:number":"598","prism:startingPage":"41","prism:endingPage":"48"},"foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%A9%E3%83%AB%E3%83%8D%E3%83%83%E3%83%88%E3%83%AF%E3%83%BC%E3%82%AF","dc:title":"ニューラルネットワーク"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%83%99%E3%82%A4%E3%82%BA%E6%B1%BA%E5%AE%9A%E7%90%86%E8%AB%96","dc:title":"ベイズ決定理論"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%B7%B7%E5%90%88%E3%83%A2%E3%83%87%E3%83%AB","dc:title":"混合モデル"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%B1%8E%E5%8C%96%E8%83%BD%E5%8A%9B","dc:title":"汎化能力"},{"@id":"https://cir.nii.ac.jp/all?q=Neural%20Network","dc:title":"Neural Network"},{"@id":"https://cir.nii.ac.jp/all?q=Bayes%20Decision%20Theory","dc:title":"Bayes Decision Theory"},{"@id":"https://cir.nii.ac.jp/all?q=Mixture%20Model","dc:title":"Mixture Model"},{"@id":"https://cir.nii.ac.jp/all?q=Generalization","dc:title":"Generalization"}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050282812864595328","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"不確実性をもつ論理式の帰納推論に関する一考察"},{"@language":"en","@value":"Inductive Inference for Uncertain Formulas from the Viewpoint of Information Theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855568899639808","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"A class of distortionless codes designed by Bayes decision theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137046433181952","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"Information-theoretic asymptotics of Bayes methods"}]},{"@id":"https://cir.nii.ac.jp/crid/1520009410164930432","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"ニューラルネットワークの汎化能力"},{"@language":"ja-Kana","@value":"ニューラル ネットワーク ノ ハンカ ノウリョク"}]},{"@id":"https://cir.nii.ac.jp/crid/1520009410169905024","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"ネットワーク学習アルゴリズムの最近の話題"},{"@language":"ja-Kana","@value":"ネットワーク ガクシュウ アルゴリズム ノ サイキン ノ ワダイ"}]},{"@id":"https://cir.nii.ac.jp/crid/1520009410308161664","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"階層型ニューラルネットワークにおける結合重みの非一意性とAIC"},{"@language":"ja-Kana","@value":"カイソウガタ ニューラル ネットワーク ニ オケル ケツゴウ オモミ ノ ヒ"}]},{"@id":"https://cir.nii.ac.jp/crid/1520853835196586880","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"情報量基準による3層ニューラルネットの隠れ層のユニット数の決定法"},{"@language":"ja-Kana","@value":"ジョウホウリョウ キジュン ニ ヨル 3ソウ ニューラル ネット ノ カクレソ"}]},{"@id":"https://cir.nii.ac.jp/crid/1570291225687762432","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1570291225687763968","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1570291225687801856","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Estimating the dimension of a model"}]},{"@id":"https://cir.nii.ac.jp/crid/1570572700664510592","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Precision, Complexity and Bayesian Model Determination"}]},{"@id":"https://cir.nii.ac.jp/crid/1570572700664512896","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"A Bayes Procedure for the Identification of Univariate Time Series Models"}]},{"@id":"https://cir.nii.ac.jp/crid/1570854177493495040","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"3層ニューラルネットワークにおける2階導関数を用いた学習アルゴリズムの高速化"},{"@language":"en","@value":"Speedup of Learning in 3-layer Neural Networks using Second-order Method"}]},{"@id":"https://cir.nii.ac.jp/crid/1571135650617894400","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1571417125594603776","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1571417125594642048","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"ベイズ決定理論に基づくデータ解析に関する一考察"}]},{"@id":"https://cir.nii.ac.jp/crid/1571980075548065536","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"共役勾配法によるBP学習について"}]},{"@id":"https://cir.nii.ac.jp/crid/1573105975454869632","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1573105975454870656","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1573668925408289152","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1573668925408330752","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"階層型ニューラルネットワークとその周辺"}]},{"@id":"https://cir.nii.ac.jp/crid/1573668927260607360","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"縮退したFisher情報行列を特つ系の学習について"},{"@language":"en","@value":"Learning in a system with a degenerate Fisher information matrix"}]},{"@id":"https://cir.nii.ac.jp/crid/1574231877212832256","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"情報量基準の変形によるニューラルネット最適化の一手法"},{"@language":"en","@value":"An Optimization Method of artificial Neural Networks based on a modified Information"}]}],"dataSourceIdentifier":[{"@type":"CIA","@value":"110003233111"}]}