docs(10_Wiki): Topic_Business/General/Graphic/Programming을 Topics/ 하위로 이동
최상위 10_Wiki/Topic_*였던 4개 카테고리 폴더를 10_Wiki/Topics/Topic_* 로 재배치. 콘텐츠 변경 없음(순수 폴더 이동) — Topics/ 하위 나머지 폴더는 이미 지난 커밋에서 전부 정리된 상태(잔존 항목은 에이전트 운영 상태 및 사용자가 보존을 요청한 업데이트0615/무제 3.canvas 뿐).
This commit is contained in:
Antigravity Agent
@@ -0,0 +1,218 @@
|
||||
---
|
||||
id: wiki-2026-0508-l1-and-l2-regularization
|
||||
title: L1 and L2 Regularization
|
||||
category: 10_Wiki/Topics
|
||||
status: verified
|
||||
canonical_id: self
|
||||
aliases: [L1, L2, Lasso, Ridge, ElasticNet, weight decay, regularization]
|
||||
duplicate_of: none
|
||||
source_trust_level: A
|
||||
confidence_score: 0.97
|
||||
verification_status: applied
|
||||
tags: [machine-learning, regularization, l1, l2, lasso, ridge, weight-decay]
|
||||
raw_sources: []
|
||||
last_reinforced: 2026-05-10
|
||||
github_commit: pending
|
||||
tech_stack:
|
||||
language: Python
|
||||
framework: scikit-learn / PyTorch
|
||||
---
|
||||
|
||||
# L1 and L2 Regularization
|
||||
|
||||
## 매 한 줄
|
||||
> **"매 weight 의 magnitude 의 의 의 의 penalize"**. L1 (Lasso) → 매 sparsity. L2 (Ridge) → 매 small. ElasticNet (combine). 매 modern: 매 weight decay (DL), 매 AdamW의 decoupled. 매 dropout 도 regularizer.
|
||||
|
||||
## 매 핵심
|
||||
|
||||
### 매 L1 (Lasso)
|
||||
- 매 penalty: λ Σ |wᵢ|.
|
||||
- 매 effect: 매 sparse solutions (zeros).
|
||||
- 매 응용: 매 feature selection.
|
||||
|
||||
### 매 L2 (Ridge)
|
||||
- 매 penalty: λ Σ wᵢ².
|
||||
- 매 effect: 매 small but non-zero.
|
||||
- 매 응용: 매 multicollinearity.
|
||||
|
||||
### 매 ElasticNet
|
||||
- 매 α L1 + (1-α) L2.
|
||||
|
||||
### 매 modern DL
|
||||
- **Weight decay** (= L2).
|
||||
- **AdamW**: 매 decoupled weight decay (Loshchilov 2019).
|
||||
- **Dropout**: 매 implicit reg.
|
||||
- **Batch norm**: 매 implicit reg.
|
||||
- **Early stopping**: 매 implicit reg.
|
||||
|
||||
### 매 응용
|
||||
1. **Linear regression**: Ridge, Lasso.
|
||||
2. **Logistic regression**: 매 class_weight + L2.
|
||||
3. **DL training**: weight decay.
|
||||
4. **Feature selection**: Lasso.
|
||||
|
||||
## 💻 패턴
|
||||
|
||||
### Ridge (sklearn)
|
||||
```python
|
||||
from sklearn.linear_model import Ridge
|
||||
model = Ridge(alpha=1.0).fit(X, y)
|
||||
```
|
||||
|
||||
### Lasso (sklearn)
|
||||
```python
|
||||
from sklearn.linear_model import Lasso
|
||||
model = Lasso(alpha=0.1).fit(X, y)
|
||||
print((model.coef_ == 0).sum(), 'zero coefficients')
|
||||
```
|
||||
|
||||
### ElasticNet
|
||||
```python
|
||||
from sklearn.linear_model import ElasticNet
|
||||
model = ElasticNet(alpha=0.1, l1_ratio=0.5).fit(X, y)
|
||||
```
|
||||
|
||||
### Logistic + L2
|
||||
```python
|
||||
from sklearn.linear_model import LogisticRegression
|
||||
model = LogisticRegression(penalty='l2', C=1.0).fit(X, y)
|
||||
# 매 C = 1/alpha (inverse strength)
|
||||
```
|
||||
|
||||
### PyTorch weight decay
|
||||
```python
|
||||
import torch
|
||||
optim = torch.optim.SGD(model.parameters(), lr=0.01, weight_decay=1e-4)
|
||||
# 매 = L2 in SGD
|
||||
```
|
||||
|
||||
### AdamW (decoupled, recommended)
|
||||
```python
|
||||
optim = torch.optim.AdamW(model.parameters(), lr=1e-3, weight_decay=0.01)
|
||||
# 매 better than Adam + weight_decay
|
||||
```
|
||||
|
||||
### Manual L1 in PyTorch
|
||||
```python
|
||||
def l1_penalty(model, lam=1e-5):
|
||||
return lam * sum(p.abs().sum() for p in model.parameters())
|
||||
|
||||
loss = task_loss + l1_penalty(model)
|
||||
```
|
||||
|
||||
### CV-tune α (sklearn)
|
||||
```python
|
||||
from sklearn.linear_model import RidgeCV
|
||||
model = RidgeCV(alphas=[0.01, 0.1, 1, 10, 100]).fit(X, y)
|
||||
print(model.alpha_)
|
||||
```
|
||||
|
||||
### LassoCV
|
||||
```python
|
||||
from sklearn.linear_model import LassoCV
|
||||
model = LassoCV(alphas=np.logspace(-4, 0, 50), cv=5).fit(X, y)
|
||||
```
|
||||
|
||||
### Path plot (regularization strength sweep)
|
||||
```python
|
||||
import matplotlib.pyplot as plt
|
||||
alphas = np.logspace(-4, 1, 50)
|
||||
coefs = []
|
||||
for a in alphas:
|
||||
coefs.append(Lasso(alpha=a).fit(X, y).coef_)
|
||||
plt.plot(alphas, coefs)
|
||||
plt.xscale('log')
|
||||
plt.xlabel('alpha'); plt.ylabel('coefficient')
|
||||
```
|
||||
|
||||
### Group L1 (group lasso)
|
||||
```python
|
||||
def group_lasso_penalty(weights, groups, lam):
|
||||
total = 0
|
||||
for group in groups:
|
||||
total += lam * np.sqrt(sum(weights[i]**2 for i in group))
|
||||
return total
|
||||
```
|
||||
|
||||
### Different decay per layer (DL)
|
||||
```python
|
||||
optim = torch.optim.AdamW([
|
||||
{'params': model.encoder.parameters(), 'weight_decay': 0.01},
|
||||
{'params': model.head.parameters(), 'weight_decay': 0.001},
|
||||
])
|
||||
```
|
||||
|
||||
### Bias / norm exclude (best practice)
|
||||
```python
|
||||
def get_param_groups(model, weight_decay):
|
||||
decay, no_decay = [], []
|
||||
for name, p in model.named_parameters():
|
||||
if p.requires_grad:
|
||||
if 'bias' in name or 'norm' in name: no_decay.append(p)
|
||||
else: decay.append(p)
|
||||
return [
|
||||
{'params': decay, 'weight_decay': weight_decay},
|
||||
{'params': no_decay, 'weight_decay': 0},
|
||||
]
|
||||
|
||||
optim = torch.optim.AdamW(get_param_groups(model, 0.01), lr=1e-3)
|
||||
```
|
||||
|
||||
### Effect on bias-variance
|
||||
```python
|
||||
def reg_effect(alphas, X_train, y_train, X_val, y_val):
|
||||
train_err, val_err = [], []
|
||||
for a in alphas:
|
||||
m = Ridge(alpha=a).fit(X_train, y_train)
|
||||
train_err.append(((m.predict(X_train) - y_train) ** 2).mean())
|
||||
val_err.append(((m.predict(X_val) - y_val) ** 2).mean())
|
||||
return train_err, val_err
|
||||
# 매 high alpha → train ↑, val ↓ (until point) → val ↑ (over-reg)
|
||||
```
|
||||
|
||||
### Sparsity-induced (modern DL)
|
||||
```python
|
||||
def magnitude_pruning(model, sparsity=0.5):
|
||||
"""매 매 layer 의 의 의 의 magnitude bottom-x% 의 zero out."""
|
||||
for name, p in model.named_parameters():
|
||||
if 'weight' in name:
|
||||
threshold = p.abs().flatten().kthvalue(int(p.numel() * sparsity)).values
|
||||
p.data[p.abs() < threshold] = 0
|
||||
```
|
||||
|
||||
## 매 결정 기준
|
||||
| 상황 | Method |
|
||||
|---|---|
|
||||
| Linear | Ridge / Lasso / ElasticNet |
|
||||
| Feature selection | Lasso |
|
||||
| Multicollinearity | Ridge |
|
||||
| DL | AdamW weight decay |
|
||||
| Sparsity goal | Lasso / pruning |
|
||||
| Best DL practice | AdamW + exclude bias/norm |
|
||||
|
||||
**기본값**: 매 DL = AdamW + 0.01-0.1 weight decay + bias/norm exclude. 매 linear = ElasticNet CV. 매 sparsity = Lasso.
|
||||
|
||||
## 🔗 Graph
|
||||
- 부모: [[L1-and-L2-Regularization|Regularization]] · [[Optimization]]
|
||||
- 변형: [[Lasso]] · [[Ridge]] · [[ElasticNet]] · [[Weight-Decay]]
|
||||
- Adjacent: [[Generalization-in-AI]]
|
||||
|
||||
## 🤖 LLM 활용
|
||||
**언제**: 매 모든 ML training.
|
||||
**언제 X**: 매 underfit (no need).
|
||||
|
||||
## ❌ 안티패턴
|
||||
- **Adam + weight_decay**: 매 use AdamW.
|
||||
- **Same decay for bias / norm**: 매 hurt training.
|
||||
- **No CV α**: 매 wrong strength.
|
||||
- **L1 for DL** (without sparsity goal): 매 unstable.
|
||||
|
||||
## 🧪 검증 / 중복
|
||||
- Verified (Hastie-Tibshirani-Friedman, Loshchilov AdamW 2019).
|
||||
- 신뢰도 A.
|
||||
|
||||
## 🕓 Changelog
|
||||
| 날짜 | 변경 |
|
||||
|---|---|
|
||||
| 2026-05-08 | Phase 1 |
|
||||
| 2026-05-10 | Manual cleanup — L1/L2 + 매 sklearn / AdamW / param groups / pruning code |
|
||||
Reference in New Issue
Block a user