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2009.05.25

貪欲な変数選択による最適化

最適化問題において、最適化対象の変数を最初は空に初期化して、関数値にもっとも効きそうな変数から順に最適化対象にGreedyに加えていく方法は変数の数が非常に多い場合(全ての部分文字列に特徴が対応するなど、そもそも列挙できないくらい多い場合など)に有効です。

詳細な中身は違いますが、grafting, column generation, cutting planeとかがこの枠組みに当てはまルと思います。

ここでのポイントは「効きそうな変数」を効率的に求めることができたら、圧倒的に速く最適化できるようになることです。別分野でデータマイニングの手法だとか、上限/下限だとかデータ構造とか何か技を持っている人は、ぜひチャレンジしてみてください。

で、私もやってます。という宣伝

・特徴(変数)が文書中の全ての部分文字列に対応する場合
"Text Categorization with All Substring Features", SDM 2009, D. Okanohara, J. Tsujii [poster(ppt)]

・特徴が基本素性の全ての組み合わせの場合
"Learning Combination Features with L1 Regularization", NAACL HLT 2009, D. Okanohara T. Tsujii. to appear

あといくつかできそうなのですが、実装が追い付かない。

とりあえず上の二つは今のライブラリに組み込む形などで公開したいとおもいます

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