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Antigravity Agent
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id: wiki-2026-0508-sensitivity-analysis
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title: Sensitivity Analysis
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Sobol, Morris, SALib, Feature Importance]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [statistics, ml-interpretability, uncertainty]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: python
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framework: SALib / scikit-learn / SHAP
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---
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# Sensitivity Analysis
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## 매 한 줄
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> **"매 input 변동이 output 의 어디에 얼마나 영향?"**. 매 Sobol indices (variance decomposition), Morris elementary effects (screening), 그리고 ML interpretability (SHAP, permutation importance) 모두 매 sensitivity analysis 의 family. 매 2026 default: SALib (classic SA) + SHAP (ML model).
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## 매 핵심
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### 매 Local vs Global
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- **Local**: gradient at one point (∂y/∂x). 매 빠르지만 nonlinear 모델 misleading.
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- **Global**: full input space sample. 매 Sobol/Morris/FAST. 매 정직.
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### 매 Method 분류
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- **Screening (Morris)**: 매 cheap, identify important factors among many. r·(k+1) runs.
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- **Variance-based (Sobol)**: S1 (first-order), ST (total). 매 N·(2k+2) Saltelli sample.
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- **Regression-based**: standardized regression coefficients (SRC).
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- **ML feature importance**: permutation, SHAP, integrated gradients.
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### 매 응용
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1. Engineering tolerance — 매 어느 parameter 가 yield drop.
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2. Climate/epidemiology model — input uncertainty propagation.
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3. ML model debug — 매 feature 가 prediction drive.
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4. Hyperparameter search prior — 매 important hp 만 tune.
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## 💻 패턴
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### Sobol indices (SALib)
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```python
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from SALib.sample import saltelli
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from SALib.analyze import sobol
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import numpy as np
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problem = {
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'num_vars': 3,
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'names': ['x1', 'x2', 'x3'],
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'bounds': [[0, 1]] * 3,
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}
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param_values = saltelli.sample(problem, 1024)
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Y = np.array([model(*row) for row in param_values])
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Si = sobol.analyze(problem, Y)
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print(Si['S1'], Si['ST']) # first-order + total
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```
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### Morris screening
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```python
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from SALib.sample.morris import sample
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from SALib.analyze import morris
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X = sample(problem, N=100, num_levels=4)
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Y = np.array([model(*r) for r in X])
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Mi = morris.analyze(problem, X, Y, num_levels=4)
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print(Mi['mu_star'], Mi['sigma']) # importance, nonlinearity
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```
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### Permutation importance (sklearn)
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```python
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from sklearn.inspection import permutation_importance
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r = permutation_importance(model, X_val, y_val, n_repeats=20, random_state=0)
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for i in r.importances_mean.argsort()[::-1]:
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print(f"{features[i]}: {r.importances_mean[i]:.3f} ± {r.importances_std[i]:.3f}")
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```
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### SHAP for any model
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```python
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import shap
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explainer = shap.TreeExplainer(xgb_model) # or shap.Explainer for general
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sv = explainer(X_val)
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shap.plots.beeswarm(sv) # global
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shap.plots.waterfall(sv[0]) # local
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```
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### Tornado plot (one-at-a-time)
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```python
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base = model(**defaults)
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deltas = []
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for k, (lo, hi) in bounds.items():
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lo_y = model(**{**defaults, k: lo})
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hi_y = model(**{**defaults, k: hi})
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deltas.append((k, hi_y - lo_y))
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deltas.sort(key=lambda x: abs(x[1]), reverse=True)
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```
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### Variance decomposition w/ ANOVA
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```python
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import statsmodels.api as sm
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from statsmodels.formula.api import ols
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m = ols('y ~ x1 + x2 + x3 + x1:x2', data=df).fit()
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print(sm.stats.anova_lm(m, typ=2))
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| 100+ inputs, screen first | Morris |
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| <20 inputs, full ranking | Sobol |
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| ML black-box | SHAP / permutation |
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| Linear-ish model | SRC |
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| One-shot intuition | Tornado |
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**기본값**: SALib Sobol (simulation), SHAP (ML model).
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## 🔗 Graph
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- 부모: [[Statistics]] · [[Epistemic-Uncertainty|Uncertainty-Quantification]]
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- 변형: [[SHAP]]
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- 응용: [[Hyperparameters|Hyperparameter-Tuning]]
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- Adjacent: [[Bayesian Inference]] · [[Monte-Carlo]]
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## 🤖 LLM 활용
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**언제**: simulation/model에서 어느 input이 결과 좌우하는지 정량화. ML feature 중요도 ranking.
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**언제 X**: input 간 강한 correlation 존재 — Sobol 가정 깨짐. Conditional SA / Shapley 사용.
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## ❌ 안티패턴
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- **OAT only**: one-at-a-time 은 interaction 놓침.
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- **Sample 너무 작음**: Sobol N<512 → 매우 noisy estimate.
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- **Correlated inputs 무시**: independence 가정 violation.
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- **SHAP = causal**: SHAP 는 attribution, causality 아님.
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## 🧪 검증 / 중복
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- Verified (Saltelli 2010, SALib docs, scikit-learn inspection).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — Sobol/Morris/SHAP unified treatment |
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