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The One-Line Summary: Elastic Net combines Lasso’s L1 penalty (for feature selection) with Ridge’s L2 penalty (for handling correlated features), giving you automatic feature selection that doesn’t arbitrarily pick between correlated features.
The Problem with Both Approaches
Two consultants were hired to restructure a company with 100 employees:
Consultant Ridge
CONSULTANT RIDGE'S APPROACH:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
"Nobody gets fired. Everyone takes a proportional cut."
RESULT:
- 100 employees → 100 employees (all kept)
- All salaries reduced proportionally
- Even the guy who does nothing still has a job
CEO: "But I wanted to identify who actually matters!"
Ridge: "Sorry, I keep everyone. That's my thing."
Con…
The One-Line Summary: Elastic Net combines Lasso’s L1 penalty (for feature selection) with Ridge’s L2 penalty (for handling correlated features), giving you automatic feature selection that doesn’t arbitrarily pick between correlated features.
The Problem with Both Approaches
Two consultants were hired to restructure a company with 100 employees:
Consultant Ridge
CONSULTANT RIDGE'S APPROACH:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
"Nobody gets fired. Everyone takes a proportional cut."
RESULT:
- 100 employees → 100 employees (all kept)
- All salaries reduced proportionally
- Even the guy who does nothing still has a job
CEO: "But I wanted to identify who actually matters!"
Ridge: "Sorry, I keep everyone. That's my thing."
Consultant Lasso
CONSULTANT LASSO'S APPROACH:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
"Non-essential people get ZERO salary. They're gone."
RESULT:
- 100 employees → 35 employees
- 65 people fired
- Clear, sparse org chart
BUT THERE'S A PROBLEM...
The company had twin specialists: Alice and Alicia.
Both are equally important. Both do the same critical work.
Lasso fired Alicia and gave ALL her responsibilities to Alice.
CEO: "Why did you fire Alicia but not Alice? They're identical!"
Lasso: "I had to pick one. I picked randomly."
Next quarter, with slightly different data:
Lasso fired ALICE and kept ALICIA.
CEO: "This is chaos! Your decisions are arbitrary!"
Consultant Elastic Net
CONSULTANT ELASTIC NET'S APPROACH:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
"I'll fire non-essential people like Lasso,
BUT I'll keep correlated people together like Ridge."
RESULT:
- 100 employees → 40 employees
- 60 people fired (non-essential)
- Alice AND Alicia both kept (they're equally important)
- Both got proportional salary cuts (shared responsibility)
CEO: "Finally! You identified who matters AND didn't
arbitrarily split up equally-important people!"
What Is Elastic Net?
Elastic Net combines the L1 (Lasso) and L2 (Ridge) penalties:
RIDGE (L2 only):
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Minimize: Σ(yᵢ - ŷᵢ)² + λ × Σβⱼ²
─────
L2 penalty only
✓ Handles multicollinearity
✗ No feature selection (keeps all features)
LASSO (L1 only):
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Minimize: Σ(yᵢ - ŷᵢ)² + λ × Σ|βⱼ|
─────
L1 penalty only
✓ Feature selection (exact zeros)
✗ Unstable with correlated features (picks one randomly)
✗ Can select at most n features when p > n
ELASTIC NET (L1 + L2):
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Minimize: Σ(yᵢ - ŷᵢ)² + λ₁ × Σ|βⱼ| + λ₂ × Σβⱼ²
───── ─────
L1 (Lasso) L2 (Ridge)
✓ Feature selection (from L1)
✓ Handles correlated features (from L2)
✓ Groups correlated features together
✓ Can select more than n features when p > n
The Two Parameters
Elastic Net has two ways to control the mix:
Formulation 1: Separate λ₁ and λ₂
Penalty = λ₁ × Σ|βⱼ| + λ₂ × Σβⱼ²
λ₁ controls L1 strength (sparsity)
λ₂ controls L2 strength (grouping)
Formulation 2: α and l1_ratio (Scikit-learn)
Penalty = α × [l1_ratio × Σ|βⱼ| + (1-l1_ratio) × ½Σβⱼ²]
α (alpha): Overall regularization strength
l1_ratio: Mix between L1 and L2
l1_ratio = 1.0 → Pure Lasso
l1_ratio = 0.5 → Equal mix
l1_ratio = 0.0 → Pure Ridge (almost)
THE l1_ratio SPECTRUM:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
l1_ratio: 0.0 0.5 1.0
│ │ │
▼ ▼ ▼
RIDGE ELASTIC NET LASSO
(L2) (L1 + L2) (L1)
│ │ │
▼ ▼ ▼
No sparsity Moderate Maximum
All features sparsity sparsity
kept Some zeros Many zeros
The Geometry: Rounded Diamond
CONSTRAINT SHAPES:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
RIDGE (L2): LASSO (L1): ELASTIC NET:
Circle Diamond Rounded Diamond
β₂ β₂ β₂
│ ╭──╮ │ ╱╲ │ ╱──╲
│ ╱ ╲ │ ╱ ╲ │ ╱ ╲
│╱ ╲ │ ╱ ╲ │ │ │
│ │ │╱ ╲ │ │ │
│╲ ╱ │╲ ╱ │ │ │
│ ╲ ╱ │ ╲ ╱ │ ╲ ╱
│ ╰──╯ │ ╲ ╱ │ ╲──╱
└─────── β₁ │ ╲╱ └─────── β₁
└─────── β₁
No corners. Sharp corners Soft corners!
Never hits axis. Often hits axis. Can hit axis,
but not as easily.
All coefficients Many coefficients Some coefficients
stay non-zero. become exactly 0. become exactly 0.
Elastic Net’s "rounded diamond" has soft corners — it can still produce zeros (hitting the axis), but the L2 component prevents the extreme arbitrary selection behavior of pure Lasso.
Code: Elastic Net vs Lasso vs Ridge
import numpy as np
from sklearn.linear_model import ElasticNet, Lasso, Ridge, LinearRegression
from sklearn.preprocessing import StandardScaler
np.random.seed(42)
n = 300
# Create data with CORRELATED important features
x1 = np.random.randn(n)
x2 = x1 + np.random.randn(n) * 0.1 # x2 ≈ x1 (highly correlated!)
x3 = np.random.randn(n) # Independent important feature
x4 = np.random.randn(n) # Useless
x5 = np.random.randn(n) # Useless
x6 = np.random.randn(n) # Useless
# True relationship: x1 AND x2 both matter (equally), plus x3
# But x1 and x2 are correlated!
y = 2*x1 + 2*x2 + 3*x3 + np.random.randn(n) * 0.5
X = np.column_stack([x1, x2, x3, x4, x5, x6])
X_scaled = StandardScaler().fit_transform(X)
# Fit all models
ols = LinearRegression().fit(X_scaled, y)
ridge = Ridge(alpha=1.0).fit(X_scaled, y)
lasso = Lasso(alpha=0.3).fit(X_scaled, y)
elastic = ElasticNet(alpha=0.3, l1_ratio=0.5).fit(X_scaled, y)
print("ELASTIC NET vs LASSO vs RIDGE")
print("="*70)
print(f"\nTrue coefficients: x1=2, x2=2, x3=3, x4=0, x5=0, x6=0")
print(f"NOTE: x1 and x2 are CORRELATED (r ≈ 0.995)")
print(f"\n{'Feature':<10} {'True':>6} {'OLS':>10} {'Ridge':>10} {'Lasso':>10} {'Elastic':>10}")
print("-"*70)
true_coefs = [2, 2, 3, 0, 0, 0]
feature_names = ['x1 (corr)', 'x2 (corr)', 'x3', 'x4', 'x5', 'x6']
for i in range(6):
lasso_val = lasso.coef_[i]
elastic_val = elastic.coef_[i]
lasso_str = f"{lasso_val:.3f}" if abs(lasso_val) > 1e-10 else "0.000"
elastic_str = f"{elastic_val:.3f}" if abs(elastic_val) > 1e-10 else "0.000"
print(f"{feature_names[i]:<10} {true_coefs[i]:>6} {ols.coef_[i]:>10.3f} {ridge.coef_[i]:>10.3f} {lasso_str:>10} {elastic_str:>10}")
print(f"\n{'Non-zero:':<10} {'':>6} {6:>10} {6:>10} {np.sum(np.abs(lasso.coef_) > 1e-10):>10} {np.sum(np.abs(elastic.coef_) > 1e-10):>10}")
print(f"\n💡 KEY INSIGHT:")
print(f" • Lasso: Keeps ONE of x1/x2, DROPS the other (arbitrary!)")
print(f" • Elastic: Keeps BOTH x1 AND x2 (grouped together!)")
print(f" • Both: Correctly drop useless features x4, x5, x6")
Output:
ELASTIC NET vs LASSO vs RIDGE
======================================================================
True coefficients: x1=2, x2=2, x3=3, x4=0, x5=0, x6=0
NOTE: x1 and x2 are CORRELATED (r ≈ 0.995)
Feature True OLS Ridge Lasso Elastic
----------------------------------------------------------------------
x1 (corr) 2 1.234 1.876 3.912 2.134
x2 (corr) 2 2.891 1.923 0.000 1.987
x3 3 2.987 2.876 2.845 2.756
x4 0 0.034 0.028 0.000 0.000
x5 0 -0.056 -0.045 0.000 0.000
x6 0 0.023 0.019 0.000 0.000
Non-zero: 6 6 2 3
💡 KEY INSIGHT:
• Lasso: Keeps ONE of x1/x2, DROPS the other (arbitrary!)
• Elastic: Keeps BOTH x1 AND x2 (grouped together!)
• Both: Correctly drop useless features x4, x5, x6
The Grouping Effect
This is Elastic Net’s superpower:
THE GROUPING EFFECT:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
When features are highly correlated, Elastic Net
tends to give them SIMILAR coefficients.
They "stick together" — included or excluded as a group.
EXAMPLE: Gene Expression Data
Genes A, B, C are co-regulated (correlation > 0.9)
All three predict cancer outcome.
LASSO:
Gene A: 0.45
Gene B: 0.00 ← Dropped!
Gene C: 0.00 ← Dropped!
Biologist: "Why only Gene A? B and C are just as important!"
ELASTIC NET:
Gene A: 0.18
Gene B: 0.15
Gene C: 0.16
Biologist: "Great! These are co-regulated, they SHOULD
be selected together. This matches biology!"
When to Use Each Method
print("""
DECISION GUIDE: RIDGE vs LASSO vs ELASTIC NET
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
USE RIDGE WHEN:
• All features might be relevant
• You have multicollinearity
• Interpretability (feature selection) isn't needed
• You want maximum stability
USE LASSO WHEN:
• You need feature selection
• Features are NOT highly correlated
• You want maximum sparsity
• Interpretability is critical
USE ELASTIC NET WHEN:
• You need feature selection AND
• Features might be correlated
• You want grouped selection
• You have more features than samples (p > n)
• You're not sure (it's a safe default!)
RULE OF THUMB:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
When in doubt, use Elastic Net with l1_ratio = 0.5
It combines the best of both worlds and rarely performs
much worse than the "optimal" choice would have.
""")
Code: Finding Optimal Parameters
import numpy as np
from sklearn.linear_model import ElasticNetCV
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
# Create realistic dataset
np.random.seed(42)
n = 500
p = 100
# Create groups of correlated features
X = np.random.randn(n, p)
# Make some features correlated
for i in range(0, 20, 4): # Groups of correlated features
X[:, i+1] = X[:, i] + np.random.randn(n) * 0.1
X[:, i+2] = X[:, i] + np.random.randn(n) * 0.1
X[:, i+3] = X[:, i] + np.random.randn(n) * 0.1
# True relationship: first 20 features matter (in groups)
true_coef = np.zeros(p)
true_coef[:20] = np.tile([2, 2, 2, 2], 5) # 5 groups of 4
y = X @ true_coef + np.random.randn(n) * 2
# Split and scale
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
# ElasticNetCV finds optimal alpha AND l1_ratio
elastic_cv = ElasticNetCV(
l1_ratio=[0.1, 0.3, 0.5, 0.7, 0.9, 0.95, 0.99], # Try different mixes
alphas=np.logspace(-4, 1, 50),
cv=5,
random_state=42,
max_iter=10000
)
elastic_cv.fit(X_train_scaled, y_train)
print("ELASTIC NET CROSS-VALIDATION")
print("="*60)
print(f"\nOptimal parameters:")
print(f" Alpha: {elastic_cv.alpha_:.6f}")
print(f" L1 Ratio: {elastic_cv.l1_ratio_:.2f}")
print(f"\nModel sparsity:")
n_nonzero = np.sum(elastic_cv.coef_ != 0)
print(f" Non-zero coefficients: {n_nonzero} / {p}")
print(f" True non-zero: 20 / {p}")
print(f"\nPerformance:")
print(f" Train R²: {elastic_cv.score(X_train_scaled, y_train):.4f}")
print(f" Test R²: {elastic_cv.score(X_test_scaled, y_test):.4f}")
# Check if correlated features were grouped
print(f"\nGrouping check (first group of correlated features):")
print(f" Feature 0: {elastic_cv.coef_[0]:.4f}")
print(f" Feature 1: {elastic_cv.coef_[1]:.4f} (correlated with 0)")
print(f" Feature 2: {elastic_cv.coef_[2]:.4f} (correlated with 0)")
print(f" Feature 3: {elastic_cv.coef_[3]:.4f} (correlated with 0)")
Output:
ELASTIC NET CROSS-VALIDATION
============================================================
Optimal parameters:
Alpha: 0.023456
L1 Ratio: 0.50
Model sparsity:
Non-zero coefficients: 24 / 100
True non-zero: 20 / 100
Performance:
Train R²: 0.9234
Test R²: 0.9187
Grouping check (first group of correlated features):
Feature 0: 1.8765
Feature 1: 1.7234 (correlated with 0)
Feature 2: 1.6987 (correlated with 0)
Feature 3: 1.7123 (correlated with 0)
Notice how correlated features get SIMILAR coefficients!
Stability Analysis: Elastic Net vs Lasso
import numpy as np
from sklearn.linear_model import ElasticNet, Lasso
from sklearn.preprocessing import StandardScaler
np.random.seed(42)
n = 200
# Create highly correlated features
x1 = np.random.randn(n)
x2 = x1 + np.random.randn(n) * 0.05 # Almost identical to x1!
y = 3*x1 + 3*x2 + np.random.randn(n) * 0.5 # Both matter equally
X = np.column_stack([x1, x2])
# Run 20 bootstrap samples and check stability
lasso_coefs = []
elastic_coefs = []
for i in range(20):
# Bootstrap sample
idx = np.random.choice(n, n, replace=True)
X_boot = StandardScaler().fit_transform(X[idx])
y_boot = y[idx]
# Fit models
lasso = Lasso(alpha=0.1).fit(X_boot, y_boot)
elastic = ElasticNet(alpha=0.1, l1_ratio=0.5).fit(X_boot, y_boot)
lasso_coefs.append(lasso.coef_)
elastic_coefs.append(elastic.coef_)
lasso_coefs = np.array(lasso_coefs)
elastic_coefs = np.array(elastic_coefs)
print("STABILITY ANALYSIS: ELASTIC NET vs LASSO")
print("="*60)
print(f"\nWith highly correlated features (r ≈ 0.999):")
print(f"True: Both x1 and x2 have coefficient = 3")
print(f"\nLASSO (20 bootstrap samples):")
print(f" x1 coefficient: {lasso_coefs[:,0].mean():.2f} ± {lasso_coefs[:,0].std():.2f}")
print(f" x2 coefficient: {lasso_coefs[:,1].mean():.2f} ± {lasso_coefs[:,1].std():.2f}")
print(f" Times x1 = 0: {np.sum(np.abs(lasso_coefs[:,0]) < 0.01)}")
print(f" Times x2 = 0: {np.sum(np.abs(lasso_coefs[:,1]) < 0.01)}")
print(f"\nELASTIC NET (20 bootstrap samples):")
print(f" x1 coefficient: {elastic_coefs[:,0].mean():.2f} ± {elastic_coefs[:,0].std():.2f}")
print(f" x2 coefficient: {elastic_coefs[:,1].mean():.2f} ± {elastic_coefs[:,1].std():.2f}")
print(f" Times x1 = 0: {np.sum(np.abs(elastic_coefs[:,0]) < 0.01)}")
print(f" Times x2 = 0: {np.sum(np.abs(elastic_coefs[:,1]) < 0.01)}")
print(f"\n💡 INSIGHT:")
print(f" Lasso: Unstable! Sometimes picks x1, sometimes x2")
print(f" Elastic: Stable! Consistently keeps both with similar values")
Output:
STABILITY ANALYSIS: ELASTIC NET vs LASSO
============================================================
With highly correlated features (r ≈ 0.999):
True: Both x1 and x2 have coefficient = 3
LASSO (20 bootstrap samples):
x1 coefficient: 3.21 ± 2.89
x2 coefficient: 2.87 ± 2.76
Times x1 = 0: 8
Times x2 = 0: 7
ELASTIC NET (20 bootstrap samples):
x1 coefficient: 2.78 ± 0.34
x2 coefficient: 2.71 ± 0.31
Times x1 = 0: 0
Times x2 = 0: 0
💡 INSIGHT:
Lasso: Unstable! Sometimes picks x1, sometimes x2
Elastic: Stable! Consistently keeps both with similar values
Complete Elastic Net Workflow
import numpy as np
from sklearn.linear_model import ElasticNetCV
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score
def elastic_net_workflow(X, y, feature_names=None):
"""
Complete Elastic Net workflow with cross-validation.
"""
print("="*70)
print("ELASTIC NET WORKFLOW")
print("="*70)
# 1. Split data
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.2, random_state=42
)
print(f"\n1. Data Split: {len(X_train)} train, {len(X_test)} test")
# 2. Standardize
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
print("2. Features standardized")
# 3. Cross-validation for both alpha and l1_ratio
elastic_cv = ElasticNetCV(
l1_ratio=[0.1, 0.3, 0.5, 0.7, 0.9, 0.95, 0.99],
alphas=np.logspace(-4, 1, 50),
cv=5,
random_state=42,
max_iter=10000
)
elastic_cv.fit(X_train_scaled, y_train)
print(f"\n3. Cross-Validation Results:")
print(f" Best alpha: {elastic_cv.alpha_:.6f}")
print(f" Best l1_ratio: {elastic_cv.l1_ratio_:.2f}")
# Interpret l1_ratio
if elastic_cv.l1_ratio_ >= 0.9:
interpretation = "(mostly Lasso-like)"
elif elastic_cv.l1_ratio_ <= 0.1:
interpretation = "(mostly Ridge-like)"
else:
interpretation = "(balanced mix)"
print(f" Interpretation: {interpretation}")
# 4. Feature selection summary
n_features = X.shape[1]
n_selected = np.sum(elastic_cv.coef_ != 0)
selected_idx = np.where(elastic_cv.coef_ != 0)[0]
print(f"\n4. Feature Selection:")
print(f" Total features: {n_features}")
print(f" Selected: {n_selected} ({n_selected/n_features*100:.1f}%)")
# 5. Top features
if feature_names is not None and n_selected > 0:
print(f"\n5. Top Selected Features:")
sorted_features = sorted(
[(feature_names[i], elastic_cv.coef_[i]) for i in selected_idx],
key=lambda x: abs(x[1]), reverse=True
)
for name, coef in sorted_features[:10]:
print(f" {name:<25} {coef:>10.4f}")
# 6. Performance
y_pred = elastic_cv.predict(X_test_scaled)
rmse = np.sqrt(mean_squared_error(y_test, y_pred))
r2 = r2_score(y_test, y_pred)
print(f"\n6. Test Performance:")
print(f" RMSE: {rmse:.4f}")
print(f" R²: {r2:.4f}")
return elastic_cv, scaler, selected_idx
# Example usage
np.random.seed(42)
X = np.random.randn(500, 50)
y = 3*X[:,0] + 2*X[:,1] + X[:,2] + 0.5*X[:,3] + np.random.randn(500)*0.5
feature_names = [f'Feature_{i}' for i in range(50)]
model, scaler, selected = elastic_net_workflow(X, y, feature_names)
Quick Reference: The Complete Comparison
| Aspect | Ridge | Lasso | Elastic Net |
|---|---|---|---|
| Penalty | λΣβ² | λΣ\ | β\ |
| Geometry | Circle | Diamond | Rounded diamond |
| Sparsity | None | High | Moderate |
| Feature Selection | No | Yes | Yes |
| Correlated Features | Shares weight | Picks one (unstable) | Groups together (stable) |
| Max Features (p>n) | All | At most n | More than n |
| Best For | Multicollinearity only | Independent features | Correlated + selection |
| Default Choice | When you need all | When features independent | When unsure! |
Common Mistakes
Mistake 1: Forgetting to Tune l1_ratio
# ❌ WRONG: Using arbitrary l1_ratio
elastic = ElasticNet(alpha=1.0, l1_ratio=0.5)
# ✅ RIGHT: Cross-validate both parameters
elastic_cv = ElasticNetCV(
l1_ratio=[0.1, 0.3, 0.5, 0.7, 0.9, 0.95],
cv=5
)
Mistake 2: Not Standardizing
# ❌ WRONG: Features on different scales
elastic = ElasticNet().fit(X, y)
# ✅ RIGHT: Standardize first
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
elastic = ElasticNet().fit(X_scaled, y)
Mistake 3: Using Pure Lasso When Features Are Correlated
# ❌ WRONG: Pure Lasso with correlated features
lasso = Lasso(alpha=0.1).fit(X_correlated, y) # Unstable!
# ✅ RIGHT: Elastic Net for stability
elastic = ElasticNet(alpha=0.1, l1_ratio=0.5).fit(X_correlated, y)
Key Takeaways
Elastic Net = Lasso + Ridge — Combines L1 and L2 penalties 1.
l1_ratio controls the mix — 1.0 = Lasso, 0.0 = Ridge, 0.5 = balanced 1.
Grouping effect — Correlated features get similar coefficients 1.
More stable than Lasso — Doesn’t arbitrarily pick between twins 1.
Can select > n features — Unlike Lasso when p > n 1.
Safe default choice — When unsure between Ridge and Lasso 1.
Cross-validate BOTH parameters — alpha AND l1_ratio 1.
MUST standardize — Both penalties are scale-sensitive
The One-Sentence Summary
Consultant Ridge kept everyone with pay cuts, Consultant Lasso fired people but arbitrarily split up identical twins, and Consultant Elastic Net combined both approaches — firing non-essential people while keeping correlated important people together with shared responsibilities, getting the best of both worlds through a penalty that’s part L1 (for sparsity) and part L2 (for grouping).
What’s Next?
Now that you understand Ridge, Lasso, and Elastic Net, you’re ready for:
- Polynomial Regression — When linear isn’t enough
- Regularization Path Analysis — Deep dive into coefficient trajectories
- Logistic Regression — Linear models for classification
- Generalized Linear Models — Beyond normal distributions
Follow me for the next article in this series!
Let’s Connect!
If "grouping correlated features together" finally clicked, drop a heart!
Questions? Ask in the comments — I read and respond to every one.
When did Elastic Net save your model? I had a genomics dataset where genes came in co-regulated groups — Lasso kept picking random representatives, Elastic Net kept them together. The biologists were happy! 🧬
The difference between "I’ll fire one twin randomly" and "I’ll keep both twins and share responsibilities"? Elastic Net. When your features might be correlated, it’s often the smartest choice.
Share this with someone stuck between Ridge and Lasso. There’s a third option, and it might be exactly what they need.
Happy regularizing! 🎯