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Uplift Modelling with Generalization
Guarantee?
AI Lab経済学実装チーム 森脇大輔?
概要?
● フランスのDSP会社Criteo AI Labの論文?
● アップリフトモデリング(後述)を訓練するときの目的関数をファンシー注1
な道具を
使って再定義し、実データである程度注2
の有効性を示した?
?
?
?
注1 グラフ理論やラデマッハ複雑度?
注2 既存手法に打ち勝ったわけではない
準備:アップリフトモデリングとは?
● ある特徴量Xi
をもつユーザーが介入Ti
を受けたときに結果Yi
がどのように変化する
か予測する?
○ ユーザーレベルの処置効果ともいわれる?
○ 潜在結果変数の考え方を用いると Y ∈ {0,1}について?
f(Xi
) = P(Yi
=1|Xi
, Ti
= 1) - P(Yi
=1|Xi
, Ti
= 0)?
で示すことができる?
準備:アップリフトモデリングの評価?
● アップリフトスコアf(Xi
)と実現した介入効果Yi
T
-YC
i
を使ってアップリフトカーブを描き
その下の面積(Area Under Uplift Curve, AUUC)で評価?
● ランキング性能のみを評価していることに注意?
青線の下の部分?
研究のモチベーション?
● モデル学習時はlog lossなど通常の機械学習の損失関数を用いるため、モデル選
択のためにAUUCで評価し直している?
○ log lossやMSEは予測精度を評価、AUUCはランキング精度を評価?
○ 予測精度が低いモデルが選ばれることも?
○ 汎化能力が限定的?
● AUUCの下限を定義して、直接最大化するAUUC-maxを提案?
提案手法:AUUC-max?
実際には損失の最小化問題として定義 ?
あるデータの組i,jの優劣の予測に対する損失
?
正則化項的ななにか
?
ハイパラ?
重みのベクトル?
介入群のデータ? 統制群のデータ?
介入群の中で正例? 介入群の中で负例?
AUUCからランキング損失への変換?
i, jのデータの組に対する損失
?
予測スコア順に並んだユーザーの結果変数の累積平均をF関数とすると
?
AUUCは介入群と統制群のF関数の原点からの積分の差
?
AUUC?
それぞれ統制群と介入群それぞれでランキング損失を考える
?
y, y’のデータの組について二項積変換を行う
?
?
介入群はできるだけ最初に正例を集めたい(c.f. 統制群はできるだけ最初
に負例を集めたい)
?
z = (x, x’)のスコアの差を予測するh関数のクラスH
このとき、各群の損失
Surry and Radcliff (2011)?
otherwise?
局所分数ラデマッハ複雑度?
得られた損失の上限を得るためにラデマッハ複雑度を使いたい
?
(左図)各インスタンスはラベルの違う2つのデータの組となっている
?
したがって、iidではないのでラデマッハ複雑度を適用できない(右図)
?
データの組の集合を
カバーとしたときに、ちょうど全体をカバーするよ
うにデータをわける(全部色をつけるイメージ)
?
右図のように色分けると、それぞれのカバー(色)の中ではiidとなって
いる(右図)?
色分けられたカバーをC、ラデマッハ変数をσとすると、局所分ラデ
マッハ複雑度は以下のように定義される
?
重みは各カバーのエッジの数にもとづく
?
分散の最大値がrとなる関数クラ
スF?
AUUCの下限?
ラデマッハ複雑度を用いるとAUUCの期待値の下限は
?
となる?
データによる定数なので無視
?
モデルによって変わる
?
ここで、?
はすでに定義したランキング損失
?
は依存性のあるデータに関する集中不等式(Ralaivola+ 2015)からきたなにか
?
s関数は損失を微分可能にするためのsigmoid変換や多項式変換を行う
?
なにか?
花文字Eの正体は?
花文字Rの上限は以下のように得られる
?
ここでRとΛは特徴量表現と重みのノルムの上限
?
既存手法CVTとAUUC-maxの挙動を確かめてみた?
● CVTは学習に使用した損失に関して
は訓練とテストで高い相関があった
が、AUUCと訓練データにおける損失
は相関が小さかった?
● AUUC-maxはいずれも相関が高かっ
た?
計算されたバウンドと実際のAUUC?
?
● 採用した手法がさまざまな提案手法の中
でもっともタイトなバウンド?
様々なアップリフトの手法と性能をAUUCで比較?
? ● データ?
○ Hillstrom: メールマーケティングのデータ ?
○ Criteo-Uplift: DSPのデータ ?
● モデル?
○ TM two-model?
○ CVT class variable transformation ?
○ SVM-DP SVMで直接アップリフトを予測する手法 ?
○ DDR, SDR 著者たちの提案手法。データの依存関係を考慮した手法 ?
○ TARNET ニューラルネットワークベースの因果推論手法 ?
○ GANITW GANベースの個別因果効果予測 ?
結果?
Hillstromでは、AUUC-maxがもっともよかった?
結果2?
大きいデータにおいては、SVM-DPが一番良かった?
まとめ?
● AUUCの下限を直接最大化するアップリフトモデリングの訓練手法を提案した?
● 最適化可能なリスク関数を導出するためにさまざまな手法を組み合わせており参
考になった?
○ とはいえ、既存手法よりめちゃくちゃよかったわけではないし、なんならTMとか
とそこまで差分があるわけでもない?
○ 組み合わせ技でここまでやるのがすごい?
● なお、AUCなどの評価指標を直接最適化する手法はあまりうまく行かないことが多
いらしい?

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Uplift modelling with generalization guarantee