FY2022/2022年度

Causal Inference Team
Shohei Shimizu
因果推論チーム 清⽔ 昌平
AIのための因果推論でも要 (かなめ)

統計的因果探索とは• 公平性 (Kusner et al., 2017)• 説明性• データを用いて因果グラフを推測するための方法論
仮定
••
•
•

データ関数形
分布
未観測共通原因の有無
非巡回 or 巡回 など

因果グラフ

推測

Maeda and Shimizu (2020)

統計的因果推論では因果グラフが要(かなめ)• データから介入効果を推定

Messerli, (2012), New England Journal of Medicine• 介入効果を「正しく」推定するには因果グラフが必要 (e.g., バックドア基準)

#$賞
受賞
者
(数

チョコレート消費量

LiNGAM Python package!

T. Ikeuchi, M. Ide, Y. Zeng, T. N. Maeda, and S. Shimizu.
Python package for causal discovery based on LiNGAM.
Journal of Machine Learning Research, 24(14): 1-8, 2023.

• 因果探索の研究開発

!

"!!

!"

A3. For each discrete variable xi , its value equals 1 if the linear function of its parent variables
xpa(i) plus a Logistic error term ei isS larger
than0, otherwise, its value equals 0. That is,HORT
TITLE
S.
Shimizu.
StatisticalCausal
Discovery:
LiNGAMapproach.
(Pin Statistics,1, SpringerBriefs
ei + ci + j2pa(i)bij xj > 0Springer Japan, 2022.
xi =, ei ⇠ Logistic(0, 1),(2)0, otherwise

A1. Observed variables xi (i = 1, . . . , p) form a3 Directed Acyclic Graph (DAG).
A2. The value assigned to each continuous variable xi is a linear function of its parent variables
denoted by xpa(i) plus a non-Gaussian error term ei , that is,
Xxi = ei + c i +bij xj , ei ⇠ N on Gaussian(·),(1)• 有向道や有向辺のブートストラップ確率• 例えば、閾値0.05を越えるものを解釈

j2pa(i)where the error terms ei are continuous random variables with non-Gaussian densities, andthe error variables ei are independent of each other. The coefficients bij and intercepts ci areconstants.

総合効果:
20.9

99%

96%

10%

x3x3x3x3

…

x0x2

…

x1x1

https://lingam.readthedocs.io/en/latest/tutorial/bootstrap.html

モデル仮定の評価– 多重共線性– 領域知識

研究内容

連続変数と離散変数が混在する場合

をtars
ぜひ

• 連続変数？

We consider linear mixed causal models. Speaking concretely, suppose we are given p observed
random variables, including discrete and continuous ones, i.e., X = {x1 , ..., xp }. Since a categorical variable with T categories can be regarded as (T 1) binary variables, we assume that eachdiscrete variable is binary (Wei et al., 2018). Further, we use the following assumptions from Li andShimizu (2018):(i) Forthethemixed
that containbothand discrete
data, weprove thewhereerrorcausal
terms models
ei are identicalto thosein continuous
Eq.(1), but follow
the Logistic
distribution.
identifiability conditions in bivariate as well as multivariate cases. with which we enrich theidentifiability
spacefor causal
causal discovery
withIfmixed
data.model for mixed data satisfies asDefinition
1 (LinearMixedmodel, LiM)
a causal
sumptions A1-A3, then this SCM is called a Linear Mixed causal model, abbreviated as LiM.
(ii) We propose a score-based optimization method to infer the causal
structure between mixed(因果グラフが識別可能
data. Experiments on synthetic and real-world data demonstrateourbxproposed
method’s
effi1,+e+c>
0con , f dis |f con (x, e) = bx + e + c, f dis (x, e) =LetF={f} be a set
cacy, compared with other methods.
0, otherwiseof two functions which work on continuous and discrete variables, respectively, where x, e, b and c
2.arePreliminaryand Model
Definitiona random variableof X, error
term, coefficient and intercept, respectively. P = {P con , P dis }denotes the set of probabilistic distributions for continuous and discrete variables. Using these
We consider linear mixed causal models. Speaking concretely, suppose we are given p observed
notations, our model can be rewritten as:
random variables, including discrete and continuous ones, i.e., X = {x1 , ..., xp }. Since a categorical variable with T categories xcanregarded1)(ebinaryvariables, we assume that eachfi (xei ⇠ P(3)i =bepai , ei ),as (Ti ),discrete variable is binary (Wei et al., 2018). Further, we use the following assumptions from Li andwhere fi(2018):
2 F, and P (ei ) 2 P.
Shimizu• https://github.com/cdt15/lingam– Gaussianity test
– ヒストグラム• (ii)転移学習(Zhang et al., 2013; Zhang et al., 2020; Bareinboim et al., 2016)
We propose a score-based optimization method to infer the causal structure between mixed
data. Experiments on synthetic (Teshimaand real-world
data demonstrate our proposed method’s effi• 科学的知識の取り込みet al., 2021)
cacy, compared with other methods.
• さまざまな因果に関するクエリー(介入効果等) に答えられるかを判定するために因果グラフが必要
2. Preliminary
and Model Definition• データからわかる限界の理論的解明
where the error terms ei are continuous random variables with non-Gaussian
densities,
and!#!#the error variables ei are independent of each other. The coefficients bij and intercepts ci are• 領域知識とデータから、その時点で可能な!$"!
!$constants.
最大限の因果グラフを分析者に提供!(賞 | do(チョコ))=!!"# [!(賞 | チョコ, GDP)]• 分析前– 原因の確率 (Galhotra et al., 2021)(Pearl, 2001)(i)–Forthemixedcausalmodels
thatcontainbothcontinuousanddiscretedata,
we prove the予測メカニズム解析 (Blobaum et al., 2017; Sani et al., 2020)
identifiability conditions in bivariate as well as multivariate cases. with which we enrich the–identifiability
個体レベルの最適介入(Kiritoshi et al., 2021)
space for causal discovery
with mixed data.

j2pa(i)

賞x1z (雇用)– 未観測共通原因を許す
A2. The value assigned to each continuous variable xi is a linear function of its parent variables– 離散と連続が混在
denoted by xpa(i) plus a non-Gaussian error term ei , that is, Original
推測
結果– 非線形X""xi = ei + c i +bij xj , ei ⇠ N on Gaussian(·),
(1)
– 巡回!
!

GDP
チョコy (適性)x (性別)

A1. Observed variables xi (i = 1, . . . , p) form a Directed Acyclic Graph (DAG).

– チョコ消費量を変えるとノーベル賞受賞者の数はどのくらい増えるのか(減るのか)– 機械学習のする予測!
"• チョコ消費がこのくらいならノーベル賞数このくらい？
• ノーベル賞数がこのくらいならチョコ消費このくらい？

S HORT T ITLE

• 分析後– 誤差(残差)の独立性評価• 例えば、HSIC (Gretton et al., 2005)– マルコフバウンダリーによる予測の良さで評価(Biza et al., 2020) (実装準備中)– 複数のデータセットでの結果を比較– 領域知識による評価

x1

A3. For each discrete variable xi , its value equals 1 if the linear function of its parent variables
xpa(i) plus a Logistic error term ei is larger than 0, otherwise, its value equals 0. That is,(P1, ei + ci + j2pa(i) bij xj > 0
xi =, ei ⇠ Logistic(0, 1),(2)0, otherwise
where the error terms ei are identical to those in Eq.(1), but follow the Logistic distribution.
Definition 1 (Linear Mixed causal model, LiM) If a causal model for mixed data satisfies assumptions A1-A3, then this SCM is called a Linear MixedY.causal
model,
abbreviatedasF.LiM.
Zeng, S.
Shimizu,H. Matsui,Sun.
(Causal Discoveryfor Linear Mixed Data.
1,bx+ e + c >on0
InProc.
theFirst
Conference
con
dis
con
dis
Let F = {f , f |f (x, e) = bx + e + c, f (x, e) =} be a set
Causal Learning
Reasoning (CLeaR2022),0, andotherwise
pages 994-1009,
Eureka,whereCA, x, e, b and cof two functions which work on continuous and discrete variables,respectively,
are a random variable of X, error term, coefficient and intercept, respectively. P = {P con , P dis }denotes the set of probabilistic distributions for continuous and discrete variables. Using thesenotations, our model can be rewritten as:
xi = fi (xpai , ei ),ei ⇠ P (ei ),今後: 仮定を緩めていく(3)