報告書番号

R01002

タイトル（和文）

Survey of Model Selection Criteria for Large Margin Classifiers

タイトル（英文）

Survey of Model Selection Criteria for Large Margin Classifiers

概要 （図表や脚注は「報告書全文」に掲載しております）

最近、サポートベクターマシンを代表とするラージマージン分類手法が、手書き文字認識などの様々な実問題に対して、従来手法の分類能力より優れた結果を生み出している。このラージマージン分類手法を実問題に適用していくためには、実問題に適用した際のラージマージン分類手法の能力を、正確に評価できる基準(モデル選択基準)が必要となる。ラージマージン分類手法に最も能力を発揮させる最適なモデルを選択する基準について調査し、現状の主流となっているモデル選択基準として、「一つ抜き法」による評価とモデルの最低能力による評価があることが分かった。また、現在提案されている各種モデル選択基準の中では、サポートベクターマシンに対して「一つ抜き法」を近似するspan boundが、計算量の少なさ、評価精度の面から最も有効であることを確認した。

概要 （英文）

The problem of model selection for Large Margin Classifiers, which are Support Vector Machines and Boosting Methods and etc, is important for acquiring higher levels of generalization capability. In this paper, especially, we consider the estimate of eneralization performance for a Support Vector Machine and AdaBoost. This paper shows some results of our survey for model selection criteria of a Support Vector Machine and AdaBoost. In our survey, there are two streams in the research of modelselection criteria for Large Margin Classifiers. The two streams are as follows: (1)The first stream is that the generalization bounds of Large Margin Classifiers are used as the model selection criteria. (2)The Second stream is that the approximations of leave-one-out cross validation are applied as the model selection criteria.The generalization bounds for a Support Vector Machine and AdaBoost are very interesting from the statistical point of view. But, these bounds are not sufficient from the applicational point of view. There is sometimes a big gap between the generalization bounds and the true generalization performance. Because the generalization bounds show the upper bound of the true generalization performance. The approximations of leave-one-out cross validation for a Support Vector Machine are very interesting from the statistical and the applicational points of view. Especially, span bound proposed by Chapelle and Vapnik is very useful for estimating the generalization performance via the approximation of leave-one-out cross validation. There is a small gap between span boundand the true generalization performance. Large Margin concept is also applied to regression problems. In the regression case, there are not any model selection criteria for Large Margin concept. And it is nonsense for the regression based on Large Margin concept to use the traditional model selection criteria such as AIC, TIC, NIC and NNIC. Because the traditional model criteria can not deal with high dimensional space. Finally, we will need to develop a new criterion for AdaBoost and regressions based on Large Margin concept from statistical and applicational points of view in the near future.

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