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分枝限定法でモデル選択の計算量を低減する

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Joe Suzuki
Joe Suzuki

2018 行動計量学会

Data & Analytics
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大阪大学 鈴木讓 行動計量学会第46回大会 2018年9月6日 分枝限定法で モデル選択の計算量を低減する
ロードマップ 1. BNの構造学習 2. BNの構造学習の計算を分枝限定法で削減 (既存) 3. Gaussian BNの場合の分枝限定法の適用方法 (提案) 4. 実験 5. 結論と課題
ベイジアンネットワーク (BN) 分布の因数分解を、有向非巡回グラフで表現したもの マルコフ同値
P=3変数の場合、11種類のBN
それぞれに事前確率をかけたものを比較 データから、事後確率最大のBNを見出す
確率のようなもの
条件付きスコアを求める
各構造のスコアを比較する Xが先頭の構造だけで16個 Yが先頭、Zが先頭の場合も比較 各構造の事前確率は、等しいとする
(別の)条件付きスコアを求める
各構造のスコアを(別の方法で)比較する 全部で6個 p変数の場合、pの階乗個の比較 最短経路問題でとける
のすべてを計算しないで、 を計算して、 最適な構造を見出したい 計算量を低減する
動的計画法の適用 (Silander-Myllymaki, 2006)
分枝限定法の適用 (Suzuki, ICML-96) の計算を削除できる 最適な構造が見出される ことは、保証される
事後確率最大でも、情報量基準最小でもよい この条件が成立すると、それ以上深い探索は不要 (Suzuki, ICML-96, UAI-17) ➖(尤度)は、非負
Gaussian BN (今回の検討事項) 多変量正規分布をあらわすBN 依存している 変数の個数 分枝限定法の カットルール の構成 ー（尤度）は、負になりうる
提案するカットルール (残り)すべての変数に依存するとき、 尤度が最大になる
実験1 : 人工データ 分岐限定法を使用しないときとくらべ、 1/20から1/10の計算量1/10から1/5の時間
実験2: 実データ (Hitters, BeastCancer)
まとめ Gaussian BNの構造学習の計算量の削減 • 計算ノード数で1/10-1/20, 計算時間で1/5-1/10に削減 (変数が20-25程度の場合) • 連続BNで、はじめて分枝限定法を適用 • 一般性があるので、波及効果が大きい 今後の課題 Nを固定したときの計算量がpの多項式になることの証明 (離散BNでは証明が完成してる) (来週からの国際会議で発表)

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分枝限定法でモデル選択の計算量を低減する