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ニューラルネットワーク
のアルゴリズム
4/18/2018
カムエラ ラウ (Kamuela Lau)
1
自己紹介
• ロンウイットに12月に入社
• 米国ハワイ州出身
• Williams College(ウィリアムズ大学)
• 東北復興支援・ボランティア活動
• ツイッター:@kamu_lau
2
ランキング学習
Lucene/Solr/ES
クエリ1
文書a1
文書b1
:
ランキング1
クエリ2
文書a2
文書b2
:
ランキング2
クエリn
文書an
文書bn
:
ランキングn
・・・ ランキング学習
モデル
クエリx
文書ax
文書bx
:
ランキング?
クエリx
文書ax
文書bx
:
ランキング
推定値
教師データ作成
リランキング特徴抽出
特徴抽出
:LTR4Lが提供
3
損失関数
• 結果を期待(ラベル)と比較
• 二重誤差(Square Error)
• 交差エントロピー誤差
C =
X
i
P0
i log Pi
<latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit>
4
C =
X
i
(yi xi)2
<latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit>
精度評価指標
• 損失ではランク全体の精度が見えな
い
• アルゴリズムの性能を評価するもの
• 例:NDCG、MAP、MRR など
DCG@k =
kX
j=1
G(yj)⌘(j)
G(yj) = 2yj
1
⌘(j) =
1
log(j + 1)<latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">AAACxnichVHLahRBFD1pX3F8ZNSN4KZwyDCDOFQFQRECgxGSZR5OEkgnTXWnZuyZftFdPTI2Da79AReuFETEz3ChP+AinyDiKmI2Lrzd0yIa1Nt01alzz7l1q8qOPDfRnB/MGCdOnjp9ZvZs7dz5Cxfn6pcubyZhGjuq54ReGG/bMlGeG6iedrWntqNYSd/21JY9WiryW2MVJ24YPNCTSO36chC4fdeRmiirLpv3l5a7I7bIzCT1rWy4KPK9EVtuTaxh21RatoZtZpq15pQh3cJeRihnN5koEz9FVKEfSycTeWZ64aA1ZDeYaOc1q97gHV4GOw5EBRqoYjWsv4aJfYRwkMKHQgBN2INEQt8OBDgi4naRERcTcsu8Qo4aeVNSKVJIYkc0Dmi1U7EBrYuaSel2aBeP/picDPP8I3/DD/kH/pZ/4t//WisraxS9TGi2p14VWXNPr24c/dfl06zx8Jfrnz1r9HGn7NWl3qOSKU7hTP3jx88ON+6uz2dN/pJ/pv5f8AP+jk4QjL86r9bU+nMUDyD+vO7jYHOhI3hHrN1qdO9VTzGLa7iOFt33bXSxglX0aN/3+IJvODJWjMBIjUdTqTFTea7gtzCe/ACZvak3</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit>
NDCG@k =
1
Zk
DCG@k
<latexit sha1_base64="RM1su2ggM3jSrptwET0LfvClXms=">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</latexit><latexit sha1_base64="RM1su2ggM3jSrptwET0LfvClXms=">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</latexit><latexit sha1_base64="RM1su2ggM3jSrptwET0LfvClXms=">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</latexit><latexit sha1_base64="RM1su2ggM3jSrptwET0LfvClXms=">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</latexit>
文書
期待の星
の数
実際の星
の数
期待のラ
ンク
実際のラ
ンク
NDCG
A 3 3 1 1 1
B 3 2 2 3 0.919720789
C 2 2 3 2 0.959453515
D 2 1 4 5 0.953887566
E 1 1 5 4 0.958112357
F 1 1 6 6 0.959110289
文書
期待の星
の数
実際の星
の数
期待のラ
ンク
実際のラ
ンク
NDCG
A 3 3 1 1 1
B 3 2 2 2 1
C 2 2 3 3 1
D 2 1 4 4 1
E 1 1 5 5 1
F 1 1 6 6 1
5
パーセプトロンとPRank
パーセプトロン(Perceptron)
• パーセプトロンは、生き物の神経メカニズムを単純に
モデルしたもの
• 複数の信号を受け取り、ひとつの信号を出力
出力
入力
PRank
• 入力層のノード数は文書の特徴量
• 出力ノード1個
• ランキング順位数と同じ数のしきい値を用意
• 出力を初めて超えるしきい値の番号が予測値(クラス)
• 符号に基づいて重みを更新
6
PRank
xd
w
Abstract
ument is used to produce the equations used in the Learning-
sentation.
ons
~xd = x1 . . . xn
~! = !1 !2 . . . !n
(1)
~! · ~x =
0
B
B
B
B
B
B
@
!1
!2
.
.
.
!n
1
C
C
C
C
C
C
A
x1 x2 . . . xn (2)
𝝉 = クラスの符号の数
= i番目のしきい値(符号のみ)bi
~! = ~! + (⌧ ⇥ ~x)
bi = bi 1
~b = b1 . . . bm
~! = !1 . . . !n
~xd = x1 . . . xn
~! = 0 . . . 0
~b = 0 . . . 1
重みとしきい値の初期値
7
PRank 重みの更新
b1 b2 b3 b4 b5
w
x
w
x
8
PRank NDCG
MQ2007 Fold1
9
PRank の利点と欠点
• 単純パーセプトロンはシン
プルで学習ができる
• 不安定な評価と損失
• 線形非分離な問題を解けな
い
モデル
10
OAP-BPM
• 複数のPRank
• bernoulli number という確率で
文書の特徴を各PRankに入力
• PRank に文書の特徴を入力し
た場合、OAP を以下の式で重
みを更新
PRank1
PRank2
PRank3
OAP
文書
b
b
b
~W = ~W +
~wi
N
~W<latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit>
11
OAP-BPM NDCG
MQ2007 Fold1
12
ニューラルネットワークと
多層パーセプトロン
• 複数のノードの層で構造
• 各ノードは相前後する層の全てのノードにリ
ンク
• リンクは重み付き
• 隠れ層と出力層の入力信号はwx+b
• 一つか複数の入力
• 一つの出力
• 活性化関数
• g(x) = 出力
入力層
隠れ層 1
隠れ層 2
出力層
13
多層パーセプトロンの
アルゴリズム
共通点
• フォーワードプロパゲーション
• 最急降下法・確率的勾配降下法とバックプロパゲーションで損失を
最小化
異なる点
• ネットワークの構造
• 損失関数
• 重みの更新手法・頻度
14
最急降下法と
確率的勾配降下法
• 最急降下法(Gradient Descent; Batch Gradient Descent)
• 関数の勾配ベクトルと逆の傾きへ向かうと、極小値に近づく
• エポック(全データ)ごとに重みを更新→ 時間がかかる
• 確率的勾配降下法(Stochastic Gradient Descent, SGD)
• 勾配ベクトルをデータの一部(mini-batch)で近似
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-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
-1
1
2
3
4
15
バックプロパゲーション
隠れ層 2
出力層
(oi = A(Ii))<latexit sha1_base64="e/bqynqxifSovS9ZB3kQYM9PG/Q=">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</latexit><latexit sha1_base64="e/bqynqxifSovS9ZB3kQYM9PG/Q=">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</latexit><latexit sha1_base64="e/bqynqxifSovS9ZB3kQYM9PG/Q=">AAACcXichVHLSsNAFD2N7/qqulHchBalIpQbERRB8LHRnVVbBR8liaMOpklI0oIWf8AfUHClICJ+hht/wEU/QVxWcOPC2zQgKuodZubMmXvunJkxXEv6AVE1pjQ1t7S2tXfEO7u6e3oTff153yl5psiZjuV4m4buC0vaIhfIwBKbrif0omGJDeNosb6/URaeLx17PTh2xU5RP7DlvjT1gKndtFOQ6qw6n14uyLGxQiJFGQpD/Qm0CKQQxYqTuMU29uDARAlFCNgIGFvQ4XPbggaCy9wOKsx5jGS4L3CKOGtLnCU4Q2f2iMcDXm1FrM3rek0/VJt8isXdY6WKEXqiO6rRI93TM73/WqsS1qh7OebZaGiFW+g9G1x7+1dV5DnA4afqT88B9jEdepXs3Q2Z+i3Mhr58cl5bm1kdqYzSNb2w/yuq0gPfwC6/mjdZsXqJOH+A9v25f4L8REajjJadTM0tRF/RjmEkkeb3nsIclrCCHJ/r4QJXuI7VlCFFVZKNVCUWaQbwJZTxD1Ysjao=</latexit><latexit sha1_base64="e/bqynqxifSovS9ZB3kQYM9PG/Q=">AAACcXichVHLSsNAFD2N7/qqulHchBalIpQbERRB8LHRnVVbBR8liaMOpklI0oIWf8AfUHClICJ+hht/wEU/QVxWcOPC2zQgKuodZubMmXvunJkxXEv6AVE1pjQ1t7S2tXfEO7u6e3oTff153yl5psiZjuV4m4buC0vaIhfIwBKbrif0omGJDeNosb6/URaeLx17PTh2xU5RP7DlvjT1gKndtFOQ6qw6n14uyLGxQiJFGQpD/Qm0CKQQxYqTuMU29uDARAlFCNgIGFvQ4XPbggaCy9wOKsx5jGS4L3CKOGtLnCU4Q2f2iMcDXm1FrM3rek0/VJt8isXdY6WKEXqiO6rRI93TM73/WqsS1qh7OebZaGiFW+g9G1x7+1dV5DnA4afqT88B9jEdepXs3Q2Z+i3Mhr58cl5bm1kdqYzSNb2w/yuq0gPfwC6/mjdZsXqJOH+A9v25f4L8REajjJadTM0tRF/RjmEkkeb3nsIclrCCHJ/r4QJXuI7VlCFFVZKNVCUWaQbwJZTxD1Ysjao=</latexit>
ノード j
ノード i
重み i, j
Ii =
X
j
Iij =
X
j
oj!ij
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ターゲット(正解)を入力
16
NNRank
• ポイントワイズ
• 出力層のノード数はクラス(分
類)の数
• 出力活性化関数:Sigmoid
• ネットワークは直接文書を分類
• しきい値が初めて出力を超える
ノードの番号が予測の星の数
入力層
隠れ層 1
出力層
しきい値:
0.5
0.9
0.7
0.4
2
0.9
0.4
0.7
1
0.4
0.6
0.7
0星の数
17
NNRank
• 損失関数:二重誤差
• 文書ごとに重みを更新:
• 特徴を入力、
forwardProp()
• ネットワークの出力により
分類
• ラベルと違えば、ラベルを
出力層に入力、backProp()
• 重みを更新
入力層
隠れ層 1
出力層
0.9
0.7
0.4
2星の数
文書A:
ラベル 3
1
1
1
ターゲットで
backProp
~t3 = 1 1 1
~t2 = 1 1 0
~t1 = 1 0 0
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ターゲット
18
NNRank NDCG
MQ2008 Fold1
19
RankNet
• Microsoft が開発
• Bing で使われている
• 様々なアルゴリズムのベース
• ペアワイズ
• 入力次元:文書1個の特徴量
• 出力ノード1個
• 出力活性化関数:Sigmoid
入力層
隠れ層
出力層
20
RankNet
• 交差エントロピー誤差
• バックプロパゲーションに
は2つの文書が必要
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P
0
ij =
8
><
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0 yi < yj
1
2 yi = yj
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Cij ⌘ P
0
ij log Pij (1 P
0
ij) log(1 Pij)<latexit sha1_base64="hirN6fBf7bqTWKsLcaEiJRZ7crE=">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</latexit><latexit sha1_base64="hirN6fBf7bqTWKsLcaEiJRZ7crE=">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</latexit><latexit sha1_base64="hirN6fBf7bqTWKsLcaEiJRZ7crE=">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</latexit><latexit sha1_base64="hirN6fBf7bqTWKsLcaEiJRZ7crE=">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</latexit>
+<latexit sha1_base64="nWKFGGgHjKaMtrKfOp8RR1jmLL0=">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</latexit><latexit sha1_base64="nWKFGGgHjKaMtrKfOp8RR1jmLL0=">AAACbXichVHLSsNAFD2Nr1pfVREERcTiY1VuRFBcibpwadVqsRVJ4lRD0yQkaUst/oBrwYUoKIiIn+HGH3DhJ4gLFxXcuPA2DYgW9Q4zc+bMPXfOzKi2obse0VNIampuaW0Lt0c6Oru6e6K9fZuuVXA0kdQsw3JSquIKQzdF0tM9Q6RsRyh51RBbam6ptr9VFI6rW+aGV7bFTl7ZN/WsrikeU9uZZatkKo5jlXajMYqTH6ONQA5ADEGsWtEbZLAHCxoKyEPAhMfYgAKXWxoyCDZzO6gw5zDS/X2BI0RYW+AswRkKszke93mVDliT17Warq/W+BSDu8PKUYzTI91SlR7ojp7p49daFb9GzUuZZ7WuFfZuz/Hg+vu/qjzPHg6+VH969pDFnO9VZ++2z9RuodX1xcPT6vr82nhlgq7ohf1f0hPd8w3M4pt2nRBrZ4jwB8g/n7sRbE7HZYrLiZnYwmLwFWEMYQxT/N6zWMAKVpHkc02c4BwXoVdpQBqWRuqpUijQ9ONbSJOfpv2N+Q==</latexit><latexit sha1_base64="nWKFGGgHjKaMtrKfOp8RR1jmLL0=">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</latexit><latexit sha1_base64="nWKFGGgHjKaMtrKfOp8RR1jmLL0=">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</latexit>
Pij ⌘
eoij
1 + eoij
<latexit sha1_base64="NmPt3JK7GyvoF++XemdbvcFtL8o=">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</latexit><latexit sha1_base64="NmPt3JK7GyvoF++XemdbvcFtL8o=">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</latexit><latexit sha1_base64="NmPt3JK7GyvoF++XemdbvcFtL8o=">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</latexit><latexit sha1_base64="NmPt3JK7GyvoF++XemdbvcFtL8o=">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</latexit>
C =
(
log(1 + eoij
) P
0
ij = 1
log(1 + eoji
) P
0
ij = 1
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@C
@oi
= (1 P
0
ij)
1
1 + eoij
=
@C
@oj<latexit sha1_base64="RVcb0ui1yd4OiFHKbJiVzWHMtno=">AAAC1HichVHPS9xAFH6bqtW11bW9CL0MXbRK2eVFBEtBEL14XH/sKrgaJumsHc1mQjK7oGlO4sWDVw+eKohI/4xe+g948E8Qjwoe2oMv2YC0Un0hM998731vvpmxfVeGGvEyZ7zo6u552duX73/1emCwMPSmFqpW4Iiqo1wVrNo8FK70RFVL7YpVPxC8abtixd6eS/IrbRGEUnnLescX602+6cmGdLgmyiqoeiPgTlT3eaAld9lc/ICVJWM2zcZMVmKVjehDbEVyKx5npY7GjCOTfWRiI1JpIk6KS0/224qtQhHLmAZ7DMwMFCGLiiqcQR2+gAIHWtAEAR5owi5wCOlbAxMQfOLWISIuICTTvIAY8qRtUZWgCk7sNo2btFrLWI/WSc8wVTu0i0t/QEoGI3iB53iDv/AHXuGf//aK0h6Jlx2a7Y5W+NbgwfDS3bOqJs0avj6onvSsoQGfUq+SvPspk5zC6ejbu0c3S58XR6JRPMFr8v8dL/EnncBr3zqnC2LxGPL0AOa/1/0Y1CbKJpbNhcnizGz2FL3wDt7DGN33FMzAPFSgSvtewO9cV67bqBnfjD1jv1Nq5DLNW/grjMN7cQ6yzA==</latexit><latexit sha1_base64="RVcb0ui1yd4OiFHKbJiVzWHMtno=">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</latexit><latexit sha1_base64="RVcb0ui1yd4OiFHKbJiVzWHMtno=">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</latexit><latexit sha1_base64="RVcb0ui1yd4OiFHKbJiVzWHMtno=">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</latexit>
21
RankNet 重みの更新
1. 文書i で forwardProp
2. 文書j で forwardProp
3. o を計算
4. で backProp
5. 文書i で forwardProp
6. で backProp
7. updateWeights**
(sj)<latexit sha1_base64="maLPbcvr7hn91Ka5EbwWb6KaxwU=">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</latexit><latexit sha1_base64="maLPbcvr7hn91Ka5EbwWb6KaxwU=">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</latexit><latexit sha1_base64="maLPbcvr7hn91Ka5EbwWb6KaxwU=">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</latexit><latexit sha1_base64="maLPbcvr7hn91Ka5EbwWb6KaxwU=">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</latexit>
(si)<latexit sha1_base64="BuKNss9ah39CwovrAeDrEjgdpXs=">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</latexit><latexit sha1_base64="BuKNss9ah39CwovrAeDrEjgdpXs=">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</latexit><latexit sha1_base64="BuKNss9ah39CwovrAeDrEjgdpXs=">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</latexit><latexit sha1_base64="BuKNss9ah39CwovrAeDrEjgdpXs=">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</latexit>
oij = si sj<latexit sha1_base64="mjLd3LeK4hEBPqhyMAoZMuRSh28=">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</latexit><latexit sha1_base64="mjLd3LeK4hEBPqhyMAoZMuRSh28=">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</latexit><latexit sha1_base64="mjLd3LeK4hEBPqhyMAoZMuRSh28=">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</latexit><latexit sha1_base64="mjLd3LeK4hEBPqhyMAoZMuRSh28=">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</latexit>
ij =
1
1 + e oij
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ij<latexit sha1_base64="4beQqzidsGlNBOPduniRdvAWFYs=">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</latexit><latexit sha1_base64="4beQqzidsGlNBOPduniRdvAWFYs=">AAACb3ichVG7SgNBFD1ZXzE+ErVQECQYFC0Md0VQxEKwsfQVFYyE3XWMo/tidxPQkB/wA7Sw8AEi4mfY+AMWfoJYiYKNhTebBVFR7zAzZ87cc+fMjO6a0g+IHmJKQ2NTc0u8NdHW3tGZTHV1r/pOyTNEznBMx1vXNV+Y0ha5QAamWHc9oVm6Kdb0vbna/lpZeL507JVg3xWblla05bY0tICp/Fjel0VLK1TkbrWQylCWwkj/BGoEMohiwUldIY8tODBQggUBGwFjExp8bhtQQXCZ20SFOY+RDPcFqkiwtsRZgjM0Zvd4LPJqI2JtXtdq+qHa4FNM7h4r0xiie7qmF7qjG3qk919rVcIaNS/7POt1rXALycO+5bd/VRbPAXY+VX96DrCNqdCrZO9uyNRuYdT15YPjl+XppaHKMF3QE/s/pwe65RvY5VfjclEsnSDBH6B+f+6fYHU8q1JWXZzIzM5EXxFHPwYxwu89iVnMYwE5PtfFEU5xFntWepUBJV1PVWKRpgdfQhn9AED4jqw=</latexit><latexit sha1_base64="4beQqzidsGlNBOPduniRdvAWFYs=">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</latexit><latexit sha1_base64="4beQqzidsGlNBOPduniRdvAWFYs=">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</latexit>
@C
@oi
=
1
1 + e oij
=
@C
@oj<latexit sha1_base64="O6DpxFueQCYYFkV7ZTa15SFMxM0=">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</latexit><latexit sha1_base64="O6DpxFueQCYYFkV7ZTa15SFMxM0=">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</latexit><latexit sha1_base64="O6DpxFueQCYYFkV7ZTa15SFMxM0=">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</latexit><latexit sha1_base64="O6DpxFueQCYYFkV7ZTa15SFMxM0=">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</latexit>
22
RankNet NDCG
MQ2008 Fold1
23
FRankNet (Factored Rank Net)
• ペアワイズ(だが、リスト
の情報も必要)
• ネットワークの構造は
RankNet と同じ
• 重みの更新手法が異なる点
入力層
隠れ層
出力層
24
FRankNet 重みの更新
• クエリ k に対して
1. 全部の文書ペアで
forwardProp、λi を計算
2. 各文書において
forwardProp、backProp
3. 重みを更新*
• λの計算にはリストが必要
• Mini-batch
i =
X
{i,j}2I
ij
SSX
j:{i,j}2I
ij
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!k =
X
i
i
<latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit>
ij =
1
1 + e oij
<latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit>
25
FRankNet NDCG
MQ2008 Fold1
26
LambdaRank
• FRankNet のλを改良したア
ルゴリズム
• 勾配ベクトル(λ)を直接定
義
• 損失関数を最大化する x1
x2
@C
@o1
>
@C
@o2<latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit><latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit><latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit><latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit>
ij =
| NDCG|
1 + eoij
<latexit sha1_base64="Zd0wMYDGOG47oidv3HuX7kPA1Ew=">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</latexit><latexit sha1_base64="Zd0wMYDGOG47oidv3HuX7kPA1Ew=">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</latexit><latexit sha1_base64="Zd0wMYDGOG47oidv3HuX7kPA1Ew=">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</latexit><latexit sha1_base64="Zd0wMYDGOG47oidv3HuX7kPA1Ew=">AAACmXicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuYxOQAFackxldnZtUq2CroxqQVJSZX18S4pOaUJCr4uTi719RWGypoK6TGVeeDVdXWxgsoG+gZgIECJsMQylBmgIKAfIHlDDEMKQz5DMkMpQy5DKkMeQwlQHYOQyJDMRBGMxgyGDAUAMViGaqBYkVAViZYPpWhloELqLcUqCoVqCIRKJoNJNOBvGioaB6QDzKzGKw7GWhLDhAXAXUqMKgaXDVYafDZ4ITBaoOXBn9wmlUNNgPklkognQTRm1oQz98lEfydoK5cIF3CkIHQhdfNJQxpDBZgt2YC3V4AFgH5Ihmiv6xq+udgqyDVajWDRQavge5faHDT4DDQB3llX5KXBqYGzWbgAkaAIXpwYzLCjPQMDfQMA02UHZygUcHBIM2gxKABDG9zBgcGD4YAhlCgvbMYDjCcZDjFJM3kyOTB5AVRysQI1SPMgAKYggGMC52T</latexit>
wk = wk + ⌘
@C
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x1
x2
x1
x2
RankNet
LambdaRank
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損失が下がる
27
LambdaRank NDCG
MQ2008 Fold1
28
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
learningtorank-meetup-vol-1-pt2
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learningtorank-meetup-vol-1-pt2

  • 2. 自己紹介 • ロンウイットに12月に入社 • 米国ハワイ州出身 • Williams College(ウィリアムズ大学) • 東北復興支援・ボランティア活動 • ツイッター:@kamu_lau 2
  • 4. 損失関数 • 結果を期待(ラベル)と比較 • 二重誤差(Square Error) • 交差エントロピー誤差 C = X i P0 i log Pi <latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">AAACfnichVHLLgRBFD3ae7wGG2LTMfHYGLdFQiQSYWM5HoPESKe7lVHRr3T3TMJE7P2AhRWJiEj4CBs/YOETxJLExsKdnk4Ewa1U1alT99w6VWX6tgwjosc6pb6hsam5pTXV1t7R2ZXu7lkLvVJgibzl2V6wYRqhsKUr8pGMbLHhB8JwTFusm3sL1f31sghC6bmr0b4vthyj6ModaRkRU3q6f0GdVccKYcnRpZob4aFge0U1p0s9naEsxaH+BFoCMkgi56UvUcA2PFgowYGAi4ixDQMht01oIPjMbaHCXMBIxvsCh0ixtsRZgjMMZvd4LPJqM2FdXldrhrHa4lNs7gErVQzRA13RC93TNT3R+6+1KnGNqpd9ns2aVvh613Hfytu/KofnCLufqj89R9jBdOxVsnc/Zqq3sGr68sHJy8rM8lBlmM7pmf2f0SPd8Q3c8qt1sSSWT5HiD9C+P/dPsDaR1SirLU1m5uaTr2jBAAYxyu89hTksIoc8n3uEC9zgVoEyrIwp47VUpS7R9OJLKNMfuKaRXQ==</latexit><latexit sha1_base64="BtY2KgOiGEY3Xe4gHynu3EDJobY=">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</latexit> 4 C = X i (yi xi)2 <latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">AAACfXicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtIOCvYKsQUl+bGZypoVAIJXYWK+EzNOKN4AWUDPQMwUMBkGEIZygxQEJAvsJwhhiGFIZ8hmaGUIZchlSGPoQTIzmFIZCgGwmgGQwYDhgKgWCxDNVCsCMjKBMunMtQycAH1lgJVpQJVJAJFs4FkOpAXDRXNA/JBZhaDdScDbckB4iKgTgUGVYOrBisNPhucMFht8NLgD06zqsFmgNxSCaSTIHpTC+L5uySCvxPUlQukSxgyELrwurmEIY3BAuzWTKDbC8AiIF8kQ/SXVU3/HGwVpFqtZrDI4DXQ/QsNbhocBvogr+xL8tLA1KDZDFzACDBED25MRpiRnqGBnmGgibKDEzQqOBikGZQYNIDhbc7gwODBEMAQCrS3jmEJw1qGdYz/mVSZdJj0IEqZGKF6hBlQAJM5AI6skb8=</latexit><latexit sha1_base64="6AUnMNHHv6V37hcTV93XTA5a/Wc=">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</latexit>
  • 5. 精度評価指標 • 損失ではランク全体の精度が見えな い • アルゴリズムの性能を評価するもの • 例:NDCG、MAP、MRR など DCG@k = kX j=1 G(yj)⌘(j) G(yj) = 2yj 1 ⌘(j) = 1 log(j + 1)<latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit><latexit sha1_base64="y7maz3GxJVki3qvh90hNgaHRl2s=">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</latexit> NDCG@k = 1 Zk DCG@k <latexit sha1_base64="RM1su2ggM3jSrptwET0LfvClXms=">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</latexit><latexit 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  • 6. パーセプトロンとPRank パーセプトロン(Perceptron) • パーセプトロンは、生き物の神経メカニズムを単純に モデルしたもの • 複数の信号を受け取り、ひとつの信号を出力 出力 入力 PRank • 入力層のノード数は文書の特徴量 • 出力ノード1個 • ランキング順位数と同じ数のしきい値を用意 • 出力を初めて超えるしきい値の番号が予測値(クラス) • 符号に基づいて重みを更新 6
  • 7. PRank xd w Abstract ument is used to produce the equations used in the Learning- sentation. ons ~xd = x1 . . . xn ~! = !1 !2 . . . !n (1) ~! · ~x = 0 B B B B B B @ !1 !2 . . . !n 1 C C C C C C A x1 x2 . . . xn (2) 𝝉 = クラスの符号の数 = i番目のしきい値(符号のみ)bi ~! = ~! + (⌧ ⇥ ~x) bi = bi 1 ~b = b1 . . . bm ~! = !1 . . . !n ~xd = x1 . . . xn ~! = 0 . . . 0 ~b = 0 . . . 1 重みとしきい値の初期値 7
  • 8. PRank 重みの更新 b1 b2 b3 b4 b5 w x w x 8
  • 10. PRank の利点と欠点 • 単純パーセプトロンはシン プルで学習ができる • 不安定な評価と損失 • 線形非分離な問題を解けな い モデル 10
  • 11. OAP-BPM • 複数のPRank • bernoulli number という確率で 文書の特徴を各PRankに入力 • PRank に文書の特徴を入力し た場合、OAP を以下の式で重 みを更新 PRank1 PRank2 PRank3 OAP 文書 b b b ~W = ~W + ~wi N ~W<latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit><latexit sha1_base64="eCP6JyRHmvy5ZPoGKXu1EmqkSxY=">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</latexit> 11
  • 13. ニューラルネットワークと 多層パーセプトロン • 複数のノードの層で構造 • 各ノードは相前後する層の全てのノードにリ ンク • リンクは重み付き • 隠れ層と出力層の入力信号はwx+b • 一つか複数の入力 • 一つの出力 • 活性化関数 • g(x) = 出力 入力層 隠れ層 1 隠れ層 2 出力層 13
  • 15. 最急降下法と 確率的勾配降下法 • 最急降下法(Gradient Descent; Batch Gradient Descent) • 関数の勾配ベクトルと逆の傾きへ向かうと、極小値に近づく • エポック(全データ)ごとに重みを更新→ 時間がかかる • 確率的勾配降下法(Stochastic Gradient Descent, SGD) • 勾配ベクトルをデータの一部(mini-batch)で近似 ~! = ~! ⌘~r · C(~!)<latexit sha1_base64="C+ojduwYEID5BhfpgaV7/WhHJBI=">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</latexit><latexit sha1_base64="C+ojduwYEID5BhfpgaV7/WhHJBI=">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</latexit><latexit sha1_base64="C+ojduwYEID5BhfpgaV7/WhHJBI=">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</latexit><latexit sha1_base64="C+ojduwYEID5BhfpgaV7/WhHJBI=">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</latexit> -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -1 1 2 3 4 15
  • 16. バックプロパゲーション 隠れ層 2 出力層 (oi = A(Ii))<latexit sha1_base64="e/bqynqxifSovS9ZB3kQYM9PG/Q=">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</latexit><latexit 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  • 17. NNRank • ポイントワイズ • 出力層のノード数はクラス(分 類)の数 • 出力活性化関数:Sigmoid • ネットワークは直接文書を分類 • しきい値が初めて出力を超える ノードの番号が予測の星の数 入力層 隠れ層 1 出力層 しきい値: 0.5 0.9 0.7 0.4 2 0.9 0.4 0.7 1 0.4 0.6 0.7 0星の数 17
  • 18. 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  • 20. RankNet • Microsoft が開発 • Bing で使われている • 様々なアルゴリズムのベース • ペアワイズ • 入力次元:文書1個の特徴量 • 出力ノード1個 • 出力活性化関数:Sigmoid 入力層 隠れ層 出力層 20
  • 21. RankNet • 交差エントロピー誤差 • バックプロパゲーションに は2つの文書が必要 oij ⌘ f(~xi) f( ~xj)<latexit sha1_base64="BHpjhXe1W9x38YpjP/MTY7w+IuQ=">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</latexit><latexit 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sha1_base64="BHpjhXe1W9x38YpjP/MTY7w+IuQ=">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</latexit> P 0 ij = 8 >< >: 0 yi < yj 1 2 yi = yj 1 yi > yj<latexit 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  • 22. RankNet 重みの更新 1. 文書i で forwardProp 2. 文書j で forwardProp 3. o を計算 4. で backProp 5. 文書i で forwardProp 6. で backProp 7. updateWeights** (sj)<latexit sha1_base64="maLPbcvr7hn91Ka5EbwWb6KaxwU=">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</latexit><latexit 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  • 24. FRankNet (Factored Rank Net) • ペアワイズ(だが、リスト の情報も必要) • ネットワークの構造は RankNet と同じ • 重みの更新手法が異なる点 入力層 隠れ層 出力層 24
  • 25. FRankNet 重みの更新 • クエリ k に対して 1. 全部の文書ペアで forwardProp、λi を計算 2. 各文書において forwardProp、backProp 3. 重みを更新* • λの計算にはリストが必要 • Mini-batch i = X {i,j}2I ij SSX j:{i,j}2I ij <latexit sha1_base64="xl5Y9BC+MC/PWcSG3J3f0anU6ng=">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</latexit><latexit 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sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit><latexit sha1_base64="qiXFRxSFv//JCRbcA7wSEo0WIAI=">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</latexit> ij = 1 1 + e oij <latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit><latexit sha1_base64="9gvufywzNFEvs4GFHjCeosgKBHU=">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</latexit> 25
  • 27. LambdaRank • FRankNet のλを改良したア ルゴリズム • 勾配ベクトル(λ)を直接定 義 • 損失関数を最大化する x1 x2 @C @o1 > @C @o2<latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">AAACpnichVFNLyxBFD0ajze8Z7CR2HRMiNXktkiIhfjYWImvMRIj86r71VDR093prpmEyfwBf8DCikTkxc+wsbFE/ASxJLGxcKenE0F4t1JVp07dc+tUlR24KtJEdy1Ga1v7j47On6mu7l+/e9K9feuRXwkdmXN81w83bBFJV3kyp5V25UYQSlG2XZm3d+cb+/mqDCPle2t6L5BbZbHtqZJyhGaqmJ4tlELh1AqBCLUSrjlff8N+0aqb0+a3GWP1YjpDWYrD/AysBGSQxJKfPkMBf+HDQQVlSHjQjF0IRNw2YYEQMLeFGnMhIxXvS9SRYm2FsyRnCGZ3edzm1WbCerxu1IxitcOnuNxDVpoYpmv6R490Sed0Ty9f1qrFNRpe9ni2m1oZFHsOBlaf/6sq86yx86b61rNGCZOxV8Xeg5hp3MJp6qv7h4+rUyvDtRE6oQf2f0x3dME38KpPzumyXDlCij/A+vjcn8H6WNairLU8npmZS76iE4MYwii/9wRmsIAl5PjcM1zhBrfGqLFo5Ix8M9VoSTT9eBfGn1fcg6Op</latexit><latexit 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sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit><latexit sha1_base64="iHxeis5ptrrn4QqMgMO5h4Gy9k4=">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</latexit> ij = | NDCG| 1 + eoij <latexit 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