9. Linear-Chain CRF(2)
• Forward-backward Score を計算
→ Edge の期待値を計算
(Normalization factor: Forward score で )
a
a'
b
b'
[BOS] [EOS]
3
0.5
3
4
2
4
2
1
F:3
F:0.5
F:10
F:14
F:34=Z B :1
B :2
B :1
B :10
B :8
F:1 B :34=Z
(3×4×1)/34
9
11. 計算量の問題:素性数 (1)
• 例えば、 3 次の場合 :
– ある feature function : f (X, yi-3, yi-2, yi-1, yi)
• X について条件を設定
( ex: 大文字で始まる)
• X についての条件がなければ、純粋な遷移素性
(transition feature)
– すべてのラベルの組み合わせについて素性関数
を生成
11
12. 計算量の問題:素性数 (2)
• ラベル L:[L1, L2] 、 f(xi) を x に関する関数とすると
f1(X, yi-3, yi-2, yi-1, yi)=1 if yi-3 = L1 and yi-2 = L1 and yi-1 = L1 and yi =
L1 and f(xi)
f2(X, yi-3, yi-2, yi-1, yi)=1 if yi-3 = L2 and yi-2 = L1 and yi-1 = L1 and yi = L1
and f(xi)
f1(X, yi-3, yi-2, yi-1, yi)=1 if yi-3 = L1 and yi-2 = L2 and yi-1 = L1 and yi = L1
and f(xi)
f2(X, yi-3, yi-2, yi-1, yi)=1 if yi-3 = L2 and yi-2 = L2 and yi-1 = L1 and yi = L1
and f(xi)
… ( 2^4 通り)→次数に対して指数的に増加
12
18. Feature function の生成(例)
• f(X) = UC(xi) = 1 if xi begins with upper case
• 訓練データ :
... nonexective/JJ director/NN Nov./NNP ...
... chairman/NN of/IN Consolidated/NNP ...
... that/WDT makes/VBZ Kent/NNP ...
↓
f1(X, Y) = 1 if UC(xi) and yi = NNP
f2(X, Y) = 1 if UC(xi) and yi = NNP and yi-1 = NN
f3(X, Y) = 1 if UC(xi) and yi = NNP and yi-1 = IN
...
18