---
id: wiki-2026-0508-epistemic-uncertainty
title: Epistemic Uncertainty
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [epistemic uncertainty, model uncertainty, reducible uncertainty, Bayesian DL, deep ensemble]
duplicate_of: none
source_trust_level: A
confidence_score: 0.96
verification_status: applied
tags: [ai, probability, statistics, epistemic-uncertainty, bayesian, deep-learning, uncertainty]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / Pyro / NumPyro
---

# Epistemic Uncertainty

## 매 한 줄
> **"매 reducible — 매 data ↑ 매 reduce"**. 매 vs aleatoric (irreducible noise). 매 ML / DL 의 핵심 개념. 매 Bayesian neural net, 매 deep ensemble, 매 MC dropout, 매 SWAG. 매 OOD / safety / AL critical.

## 매 핵심

### 매 epistemic vs aleatoric
- **Epistemic**: 매 model 의 부족 — 매 reducible.
- **Aleatoric**: 매 data 의 noise — 매 irreducible.
- **Total**: 매 sum.

### 매 method
- **Bayesian DL**: 매 weight posterior.
- **Deep ensemble** (Lakshminarayanan): 매 N 모델.
- **MC Dropout** (Gal & Ghahramani): 매 dropout at inference.
- **SWAG** (Maddox): 매 SGD trajectory.
- **Laplace approximation**.
- **Variational inference**.
- **Conformal prediction**: 매 distribution-free.

### 매 응용
1. **Active learning**: 매 uncertain → label.
2. **OOD detection**: 매 epistemic ↑.
3. **Safety-critical**: 매 abstain.
4. **Bayesian opt**: 매 acquisition.
5. **Reinforcement learning**: 매 exploration.
6. **Medical / autonomous**: 매 reject low-conf.

### 매 modern context
- **LLM**: 매 token entropy + sampled response.
- **Foundation model**: 매 calibration.
- **Conformal**: 매 marginal coverage guarantee.

## 💻 패턴

### Deep ensemble
```python
import torch

def train_ensemble(create_model, X, y, n=5):
    return [create_model().fit(X, y, seed=s) for s in range(n)]

def ensemble_predict(models, x):
    preds = torch.stack([m(x) for m in models])
    mean = preds.mean(0)
    epistemic = preds.var(0)  # 매 model disagreement
    return mean, epistemic
```

### MC Dropout
```python
class MCDropoutNet(torch.nn.Module):
    def __init__(self, in_dim, hid, out_dim, p=0.2):
        super().__init__()
        self.fc1 = torch.nn.Linear(in_dim, hid)
        self.dropout = torch.nn.Dropout(p)
        self.fc2 = torch.nn.Linear(hid, out_dim)
    
    def forward(self, x):
        return self.fc2(self.dropout(torch.relu(self.fc1(x))))

def mc_predict(model, x, T=50):
    model.train()  # 매 dropout active
    preds = torch.stack([model(x) for _ in range(T)])
    return preds.mean(0), preds.var(0)
```

### Bayesian linear regression (Pyro)
```python
import pyro
import pyro.distributions as dist

def bayesian_lin(X, y):
    w = pyro.sample('w', dist.Normal(torch.zeros(X.shape[1]), torch.ones(X.shape[1])).to_event(1))
    sigma = pyro.sample('sigma', dist.HalfNormal(1.0))
    with pyro.plate('data', len(X)):
        pyro.sample('obs', dist.Normal(X @ w, sigma), obs=y)
```

### SWAG (Maddox 2019)
```python
class SWAG:
    """매 SGD iterates 의 Gaussian fit."""
    def __init__(self, model):
        self.mean = self._flatten(model)
        self.sq_mean = self._flatten(model) ** 2
        self.D = []
        self.K = 20  # 매 low-rank
        self.n = 0
    
    def collect(self, model):
        flat = self._flatten(model)
        self.n += 1
        self.mean = (self.n - 1) / self.n * self.mean + flat / self.n
        self.sq_mean = (self.n - 1) / self.n * self.sq_mean + flat ** 2 / self.n
        if self.n > self.K:
            self.D.pop(0)
        self.D.append(flat - self.mean)
    
    def sample(self):
        var = torch.relu(self.sq_mean - self.mean ** 2)
        z1 = torch.randn_like(self.mean) * torch.sqrt(var) / 2 ** 0.5
        D_mat = torch.stack(self.D)
        z2 = D_mat.T @ torch.randn(len(self.D)) / (2 * (self.K - 1)) ** 0.5
        return self.mean + z1 + z2
```

### Conformal prediction
```python
def conformal_interval(model, X_cal, y_cal, X_test, alpha=0.1):
    """매 marginal coverage 1-alpha."""
    cal_preds = model.predict(X_cal)
    cal_residuals = np.abs(y_cal - cal_preds)
    q = np.quantile(cal_residuals, 1 - alpha, method='higher')
    
    test_preds = model.predict(X_test)
    return test_preds - q, test_preds + q  # 매 [lower, upper]
```

### LLM token uncertainty
```python
def token_entropy(model, prompt, n_tokens=10):
    inputs = tokenizer(prompt, return_tensors='pt')
    with torch.no_grad():
        out = model(**inputs)
    logits = out.logits[0, -n_tokens:]
    probs = logits.softmax(-1)
    return -(probs * probs.clamp(min=1e-10).log()).sum(-1)
```

### Active learning (uncertainty sampling)
```python
def active_learn(unlabeled, model, n_query=10):
    _, epistemic = ensemble_predict(model, unlabeled)
    most_uncertain = epistemic.argsort()[-n_query:]
    return unlabeled[most_uncertain]
```

### OOD detection (Mahalanobis)
```python
def mahalanobis_score(test_features, train_features):
    mu = train_features.mean(0)
    cov = np.cov(train_features.T)
    inv = np.linalg.pinv(cov)
    diff = test_features - mu
    return np.sqrt(np.einsum('bi,ij,bj->b', diff, inv, diff))
```

### Bayesian optimization (UCB)
```python
def ucb_acquisition(mean, std, kappa=2.0):
    return mean + kappa * std

def bayes_opt_step(gp, X_pool):
    mean, std = gp.predict(X_pool, return_std=True)
    return X_pool[ucb_acquisition(mean, std).argmax()]
```

### Disagreement-based exploration (RL)
```python
def epistemic_bonus(ensemble_q_values, state, action):
    qs = [m(state)[action] for m in ensemble_q_values]
    return np.std(qs)  # 매 disagreement = explore here
```

### Calibration (temperature scaling)
```python
def temperature_scale(logits, T):
    return (logits / T).softmax(-1)

def fit_temperature(logits, labels):
    T = torch.tensor(1.0, requires_grad=True)
    optim = torch.optim.LBFGS([T])
    def closure():
        optim.zero_grad()
        loss = F.cross_entropy(logits / T, labels)
        loss.backward()
        return loss
    optim.step(closure)
    return T.item()
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Best practical | Deep ensemble (5x) |
| Tight budget | MC Dropout |
| Distribution-free | Conformal |
| Bayesian rigor | Pyro / NumPyro VI |
| LLM | Sampled responses + token entropy |
| Active learning | Uncertainty sampling |
| RL exploration | Ensemble disagreement |
| Safety | Conformal + abstain |

**기본값**: 매 deep ensemble (5x) + 매 conformal calibration + 매 abstention threshold + 매 OOD detection.

## 🔗 Graph
- 부모: [[Probability]] · [[Statistics]]
- 응용: [[Active-Learning]] · [[OOD-Detection]] · [[Bayesian-Optimization]]
- Adjacent: [[Ensemble-Methods]] · [[Epistemology]]

## 🤖 LLM 활용
**언제**: 매 safety-critical. 매 active learning. 매 OOD risk. 매 medical / AV.
**언제 X**: 매 toy problem. 매 abundant data + simple task.

## ❌ 안티패턴
- **Confuse epistemic / aleatoric**: 매 reducibility 의 wrong.
- **Single model 의 uncertainty 의 trust**: 매 ensemble 필요.
- **No calibration**: 매 number 의 meaning X.
- **High-confidence OOD**: 매 detect 의 fail.
- **Conformal without exchangeability**: 매 coverage 의 lose.

## 🧪 검증 / 중복
- Verified (Lakshminarayanan 2017, Gal 2016, Maddox SWAG, Vovk Conformal).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-04-26 | UNCERT auto |
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — epi vs ale + 매 ensemble / MC dropout / SWAG / conformal / AL code |