2nd/10_Wiki/Topics/AI_and_ML/Causal-Inference.md

---
id: wiki-2026-0508-causal-inference
title: Causal Inference
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [인과 추론, causal inference, do-calculus, Pearl, DAG, counterfactual, SCM, RCT, propensity score]
duplicate_of: none
source_trust_level: A
confidence_score: 0.93
verification_status: applied
tags: [statistics, causal-inference, dag, do-calculus, pearl, ab-testing, dowhy, econml, observational-study]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python / R
  framework: DoWhy / EconML / CausalML / pgmpy
---

# Causal Inference

## 📌 한 줄 통찰
> **"매 correlation 의 X — 매 cause"**. 매 Judea Pearl 의 ladder. 매 observational 의 limit + 매 RCT / DAG / counterfactual 의 fix. 매 modern AI 의 base capability — 매 LLM 의 weakest area. 매 policy / medical / business 의 critical.

## 📖 핵심

### Pearl's Ladder of Causation
1. **Association** (P(y|x)): 매 correlation. 매 standard ML.
2. **Intervention** (P(y|do(x))): 매 "what if I change x?".
3. **Counterfactual** (P(y_x|x', y')): 매 "what would have happened if?".

→ 매 LLM 의 mostly stuck on step 1.

### 매 핵심 concept

#### Confounder
- 매 X → Y 매 spurious 의 매 Z (common cause).
- 예: 매 ice cream sales ↔ drowning (Z = 매 summer).

#### Mediator
- 매 X → M → Y.

#### Collider
- 매 X → Z ← Y.
- 매 Z 의 condition 의 spurious correlation 의 induce!

#### Backdoor path
- 매 X ← Z → Y.
- 매 Z 의 control 의 close.

#### Frontdoor
- 매 X → M → Y (매 confounder 가 매 X-Y 간 의 unobserved).

### 매 method

#### RCT (gold standard)
- 매 randomization 의 confounder 의 break.
- 매 ethics / cost.

#### Observational + adjustment
- **Propensity Score Matching (PSM)**.
- **Inverse Probability Weighting (IPW)**.
- **Regression discontinuity (RDD)**.
- **Difference-in-differences (DiD)**.
- **Instrumental variables (IV)**.
- **Synthetic control**.

#### Causal graph (DAG)
- 매 explicit assumption.
- 매 do-calculus 의 identify.

#### ML-based
- **Causal forest** (Wager-Athey).
- **Double ML** (Chernozhukov).
- **CausalGAN / counterfactual VAE**.

### 매 Simpson's paradox
- 매 aggregate vs subgroup 의 reverse.
- 매 Berkeley admission, 매 kidney stone treatment.
- → 매 confounder 의 stratify.

### 매 응용
1. **A/B test** + 매 follow-up causal.
2. **Pricing**: 매 price → 매 demand.
3. **Marketing attribution**: 매 channel → 매 conversion.
4. **Medicine**: 매 treatment effect.
5. **Policy**: 매 minimum wage.
6. **Education**: 매 program effect.
7. **Recommender**: 매 click ≠ 매 caused conversion.

### 매 modern tool
- **DoWhy** (Microsoft): 매 4-step framework.
- **EconML** (Microsoft).
- **CausalML** (Uber).
- **pgmpy**: 매 graphical model.
- **GeNIe / Hugin**: 매 visual.
- **DAGitty**: 매 web DAG.

### 매 LLM 의 한계
- 매 association 의 strong.
- 매 spurious 의 confidently 의 emit.
- 매 causal reasoning 의 weak.
- 매 hybrid (LLM + symbolic causal) 의 trend.

## 💻 패턴

### DoWhy (4-step framework)
```python
from dowhy import CausalModel

model = CausalModel(
    data=df,
    treatment='ad_exposure',
    outcome='conversion',
    common_causes=['age', 'income', 'past_purchases'],
)

# 1. Identify
estimand = model.identify_effect(proceed_when_unidentifiable=False)
print(estimand)

# 2. Estimate
estimate = model.estimate_effect(estimand, method_name='backdoor.propensity_score_matching')
print(estimate.value)

# 3. Refute
refutation = model.refute_estimate(estimand, estimate, method_name='placebo_treatment_refuter')
print(refutation)
```

### Propensity Score Matching
```python
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import NearestNeighbors

# 매 propensity score = P(treatment=1 | covariates)
ps_model = LogisticRegression()
ps_model.fit(X_covariates, treatment)
ps = ps_model.predict_proba(X_covariates)[:, 1]

# 매 match treated to control
treated = df[df.treatment == 1]
control = df[df.treatment == 0]

knn = NearestNeighbors(n_neighbors=1).fit(ps[control.index].reshape(-1, 1))
matches = knn.kneighbors(ps[treated.index].reshape(-1, 1), return_distance=False)

# 매 ATE estimate
ate = treated.outcome.mean() - control.iloc[matches.flatten()].outcome.mean()
```

### IPW (Inverse Probability Weighting)
```python
def ipw_ate(df, treatment, outcome, ps):
    weight = np.where(df[treatment] == 1, 1 / ps, 1 / (1 - ps))
    treated_avg = (df[outcome] * df[treatment] * weight).sum() / weight[df[treatment] == 1].sum()
    control_avg = (df[outcome] * (1 - df[treatment]) * weight).sum() / weight[df[treatment] == 0].sum()
    return treated_avg - control_avg
```

### Difference-in-Differences (DiD)
```python
import statsmodels.api as sm

# 매 panel data: pre/post × treatment/control
df['post'] = (df['period'] >= treatment_period).astype(int)
df['treated'] = (df['group'] == 'treated').astype(int)
df['interaction'] = df['post'] * df['treated']

model = sm.OLS(df['outcome'], sm.add_constant(df[['post', 'treated', 'interaction']])).fit()
# 매 interaction coefficient = 매 DiD treatment effect
print(model.summary())
```

### Causal Forest (heterogeneous treatment effect)
```python
from econml.dml import CausalForestDML

cf = CausalForestDML(
    n_estimators=200,
    discrete_treatment=True,
    random_state=42,
)
cf.fit(Y=df['outcome'], T=df['treatment'], X=df[features], W=df[confounders])

# 매 individual treatment effect
ites = cf.effect(df_test[features])

# 매 confidence interval
lower, upper = cf.effect_interval(df_test[features], alpha=0.05)
```

### DAG + Pearl's do-calculus (pgmpy)
```python
from pgmpy.models import BayesianNetwork
from pgmpy.factors.discrete import TabularCPD
from pgmpy.inference.CausalInference import CausalInference

# 매 X → Y, X → Z → Y
model = BayesianNetwork([('X', 'Y'), ('X', 'Z'), ('Z', 'Y')])
# ... add CPDs ...

ci = CausalInference(model)

# 매 P(Y | do(X = 1))
result = ci.query(variables=['Y'], do={'X': 1})
print(result)
```

### Synthetic control (state policy effect)
```python
# 매 weighted combination of control units 의 treated 의 mimic
from synthetic_control import SyntheticControl  # 매 hypothetical lib

sc = SyntheticControl(
    treated_unit='California',
    control_pool=other_states,
    pre_period=range(1990, 2000),
    post_period=range(2000, 2010),
)
sc.fit(predictors=['gdp', 'unemployment', 'income'])
effect = sc.treatment_effect()
```

### Refutation (sensitivity analysis)
```python
from dowhy import CausalModel

# 1. Placebo treatment
refute_placebo = model.refute_estimate(
    estimand, estimate, method_name='placebo_treatment_refuter',
)
# 매 effect 의 0 가까이 → 매 robust.

# 2. Random common cause
refute_random = model.refute_estimate(
    estimand, estimate, method_name='random_common_cause',
)

# 3. Data subset
refute_subset = model.refute_estimate(
    estimand, estimate, method_name='data_subset_refuter',
)
```

### Simpson's paradox detector
```python
def detect_simpson(df, x_col, y_col, group_col):
    # 매 aggregate
    overall_corr = df[[x_col, y_col]].corr().iloc[0, 1]
    
    # 매 subgroup
    subgroup_corrs = df.groupby(group_col).apply(
        lambda g: g[[x_col, y_col]].corr().iloc[0, 1]
    )
    
    if overall_corr > 0 and (subgroup_corrs < 0).all():
        return f"Simpson's paradox: overall +, subgroups all -"
    if overall_corr < 0 and (subgroup_corrs > 0).all():
        return f"Simpson's paradox: overall -, subgroups all +"
    return None
```

## 🤔 결정 기준
| 상황 | Method |
|---|---|
| New feature launch | A/B test (RCT) |
| Historical data | DoWhy + matching |
| Heterogeneous effect | Causal Forest |
| Panel data | DiD |
| Cutoff threshold | RDD |
| Hidden confounder + IV | Instrumental Variables |
| Single treated unit | Synthetic Control |
| ML-aware confounder | Double ML |

**기본값**: 매 RCT first. 매 observational 가 DoWhy + sensitivity refute.

## 🔗 Graph
- 부모: [[Statistics]] · [[Decision Theory]]
- 변형: [[DAG]] · [[Do-Calculus]] · [[Counterfactual]]
- Adjacent: [[Bayesian Statistics]] · [[Anthropic-Principle]] · [[Beliefs]] · [[Algorithmic Fairness]]

## 🤖 LLM 활용
**언제**: 매 policy decision. 매 marketing attribution. 매 medical treatment. 매 root cause analysis. 매 fairness counterfactual.
**언제 X**: 매 pure prediction (ML 의 OK). 매 LLM 의 alone (weak on step 2-3).

## ❌ 안티패턴
- **Correlation = causation**: 매 classic mistake.
- **Collider 의 control**: 매 spurious correlation 의 induce.
- **No DAG**: 매 hidden assumption.
- **Single method**: 매 sensitivity 의 X.
- **No refutation**: 매 fragile estimate.
- **Simpson's paradox 의 unaware**: 매 misleading.
- **LLM 의 causal claim 의 trust**: 매 association level 만.

## 🧪 검증 / 중복
- Verified (Pearl "Book of Why", Hernán "Causal Inference: What If", DoWhy paper).
- 신뢰도 A.
- Related: [[Bayesian Statistics]] · [[Algorithmic Fairness]] · [[Bias-Correction-Algorithm]] · [[A/B Testing]] · [[Anthropic-Principle]].

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Pearl ladder + DAG + 매 DoWhy / PSM / DiD / Causal Forest code |