The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Banyak mesin pembelajaran yang mempunyai struktur hierarki atau pembolehubah tersembunyi kini digunakan dalam sains maklumat, kecerdasan buatan dan bioinformatik. Walau bagaimanapun, beberapa mesin pembelajaran yang digunakan dalam bidang tersebut bukanlah model statistik biasa tetapi tunggal, justeru prestasi generalisasi mereka masih tidak diketahui. Untuk mengatasi masalah ini, dalam kertas sebelumnya, kami telah membuktikan persamaan baru dalam pembelajaran statistik, yang mana kami boleh menganggarkan kerugian generalisasi Bayes daripada kehilangan latihan Bayes dan varians fungsi, dengan syarat taburan sebenar adalah satu ketunggalan yang terkandung dalam a mesin pembelajaran. Dalam kertas ini, kami membuktikan bahawa persamaan yang sama berlaku walaupun taburan benar tidak terkandung dalam model parametrik. Kami juga membuktikan bahawa, persamaan yang dicadangkan dalam kes biasa adalah bersamaan secara asimtotik dengan kriteria maklumat Takeuchi. Oleh itu, persamaan yang dicadangkan sentiasa terpakai tanpa sebarang syarat pada taburan benar yang tidak diketahui.
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Salinan
Sumio WATANABE, "Equations of States in Statistical Learning for an Unrealizable and Regular Case" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 3, pp. 617-626, March 2010, doi: 10.1587/transfun.E93.A.617.
Abstract: Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but singular statistical models, hence their generalization performance is still left unknown. To overcome these problems, in the previous papers, we proved new equations in statistical learning, by which we can estimate the Bayes generalization loss from the Bayes training loss and the functional variance, on the condition that the true distribution is a singularity contained in a learning machine. In this paper, we prove that the same equations hold even if a true distribution is not contained in a parametric model. Also we prove that, the proposed equations in a regular case are asymptotically equivalent to the Takeuchi information criterion. Therefore, the proposed equations are always applicable without any condition on the unknown true distribution.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.617/_p
Salinan
@ARTICLE{e93-a_3_617,
author={Sumio WATANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Equations of States in Statistical Learning for an Unrealizable and Regular Case},
year={2010},
volume={E93-A},
number={3},
pages={617-626},
abstract={Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but singular statistical models, hence their generalization performance is still left unknown. To overcome these problems, in the previous papers, we proved new equations in statistical learning, by which we can estimate the Bayes generalization loss from the Bayes training loss and the functional variance, on the condition that the true distribution is a singularity contained in a learning machine. In this paper, we prove that the same equations hold even if a true distribution is not contained in a parametric model. Also we prove that, the proposed equations in a regular case are asymptotically equivalent to the Takeuchi information criterion. Therefore, the proposed equations are always applicable without any condition on the unknown true distribution.},
keywords={},
doi={10.1587/transfun.E93.A.617},
ISSN={1745-1337},
month={March},}
Salinan
TY - JOUR
TI - Equations of States in Statistical Learning for an Unrealizable and Regular Case
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 617
EP - 626
AU - Sumio WATANABE
PY - 2010
DO - 10.1587/transfun.E93.A.617
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2010
AB - Many learning machines that have hierarchical structure or hidden variables are now being used in information science, artificial intelligence, and bioinformatics. However, several learning machines used in such fields are not regular but singular statistical models, hence their generalization performance is still left unknown. To overcome these problems, in the previous papers, we proved new equations in statistical learning, by which we can estimate the Bayes generalization loss from the Bayes training loss and the functional variance, on the condition that the true distribution is a singularity contained in a learning machine. In this paper, we prove that the same equations hold even if a true distribution is not contained in a parametric model. Also we prove that, the proposed equations in a regular case are asymptotically equivalent to the Takeuchi information criterion. Therefore, the proposed equations are always applicable without any condition on the unknown true distribution.
ER -