RBM Tutorial: Restricted Boltzmann Machine

RBM Tutorial: Restricted Boltzmann Machine#

Sandbox Model — Experimental

This model is part of the CoreRec Sandbox — an experimental collection of algorithms for research and exploration. Sandbox models are not production-tested and may have incomplete implementations. For production-ready models, see the Production Models.

Introduction#

RBM uses a probabilistic graphical model with visible (ratings) and hidden (latent features) units to learn user preferences.

Paper: Salakhutdinov et al. 2007 - Restricted Boltzmann Machines for Collaborative Filtering

How RBM Works#

Architecture#

Energy-Based Probabilistic Model:

  1. Visible Units: User ratings for items

  2. Hidden Units: Latent user preferences

  3. Bipartite Structure: No visible-visible or hidden-hidden connections

  4. Training: Contrastive Divergence (CD-k)

Key Innovation: Generative model that can sample new ratings

Architecture:

Visible (Ratings) ↔ Weights W ↔ Hidden (Features)
      ↓                              ↓
  Biases a                      Biases b

No connections within visible or hidden layers!

Mathematical Foundation#

Energy Function:

E(v,h) = -Σ_i a_i·v_i - Σ_j b_j·h_j - Σ_i Σ_j v_i·h_j·w_ij

Probability:

P(v,h) = exp(-E(v,h)) / Z
where Z = Σ_{v',h'} exp(-E(v',h'))  # partition function

Conditional Probabilities:

P(h_j=1|v) = σ(b_j + Σ_i v_i·w_ij)
P(v_i=1|h) = σ(a_i + Σ_j h_j·w_ij)

Contrastive Divergence Update:

ΔW = ε(<v_0 h_0^T> - <v_k h_k^T>)

where v_0 is data, v_k is reconstruction after k Gibbs steps

Reference Implementation#

Implementation Note

The code examples below are reference implementations for learning purposes. This is a sandbox model and has not been production-tested. Verify behavior thoroughly before using in production.

Step 1: Import and Load Data#

from corerec.sandbox.collaborative_full.rbm import RBM
from cr_learn import ml_1m
from sklearn.model_selection import train_test_split
import numpy as np

# Load dataset with CORRECT API
data = ml_1m.load()  # Returns dict with 'ratings', 'users', 'movies'
ratings_df = data['ratings']  # DataFrame with user_id, movie_id, rating, timestamp

print(f"Loaded {len(ratings_df)} ratings")

# Split data
train_df, test_df = train_test_split(ratings_df, test_size=0.2, random_state=42)

# Extract arrays for model
train_users = train_df['user_id'].values
train_items = train_df['movie_id'].values
train_ratings = train_df['rating'].values

test_users = test_df['user_id'].values
test_items = test_df['movie_id'].values
test_ratings = test_df['rating'].values

Step 2: Initialize Model#

model = RBM(
    name="RBM_Model",
    n_hidden=200,
    learning_rate=0.01,
    momentum=0.5,
    n_epochs=100,
    cd_steps=1,
    epochs=20,
    batch_size=256,
    verbose=True
)

print(f"Initialized {model.name}")

Step 3: Train#

model.fit(
    user_ids=train_users,
    item_ids=train_items,
    ratings=train_ratings
)

print("Training complete!")

Step 4: Predict#

# Single prediction
score = model.predict(user_id=1, item_id=100)
print(f"Predicted score: {score:.3f}")

# Batch predictions
test_predictions = model.batch_predict(list(zip(test_users[:100], test_items[:100])))

Step 5: Recommend#

# Get top-10 recommendations for user
user_id = 1
recommendations = model.recommend(
    user_id=user_id,
    top_k=10
)

print(f"Top-10 recommendations for User {user_id}:")
for rank, item_id in enumerate(recommendations, 1):
    print(f"  {rank}. Item {item_id}")

Step 6: Evaluate#

from sklearn.metrics import mean_squared_error
import numpy as np

# Predict all test ratings
test_pred = [model.predict(u, i) for u, i in zip(test_users, test_items)]
rmse = np.sqrt(mean_squared_error(test_ratings, test_pred))
print(f"Test RMSE: {rmse:.4f}")

Step 7: Save & Load#

# Save model
model.save('artifacts/rbm_model')

# Load model
loaded = RBM.load('artifacts/rbm_model')
test_score = loaded.predict(1, 100)
print(f"Loaded model prediction: {test_score:.3f}")

Key Takeaways#

When to Use RBM#

✅ Ideal For:

  • Explicit ratings (discrete values)

  • Need generative capability (sample ratings)

  • Feature learning from ratings

  • Cold-start scenarios (can infer from partial data)

  • Research and experimentation

❌ Not For:

  • Large-scale production (slow training)

  • Implicit feedback

  • need online updates (batch model)

  • Interpretability required

Best Practices#

  1. Hidden Units: 100-500 typical

  2. CD Steps (k): k=1 works well (CD-1)

  3. Learning Rate: 0.01-0.1, use learning rate decay

  4. Momentum: 0.5 → 0.9 over training

  5. Weight Decay: 0.0001-0.001

  6. Mini-batch: 100-1000 users per batch

  7. Epochs: 50-200 epochs

  8. Initialization: Small random weights ~N(0, 0.01)

Scaling & Production Considerations#

If you plan to move this sandbox model toward production use, consider:

  • Data Volume: Test with realistic dataset sizes; sandbox implementations may not be optimized for large-scale data.

  • Distributed Training: For datasets exceeding single-machine memory, consider wrapping the model in distributed training frameworks (e.g., PyTorch DDP, Horovod).

  • Hyperparameter Tuning: Use systematic search (Optuna, Ray Tune) rather than manual tuning. The defaults in sandbox models are not tuned for any specific domain.

  • Serving Latency: Profile inference time. Some architectures (e.g., attention-based) may need quantization or ONNX export for low-latency serving.

  • Monitoring: Implement A/B testing and online metrics (CTR, engagement, diversity) before replacing an existing system.

  • Validation: Write comprehensive unit tests and integration tests before deploying. Sandbox models do not have CI coverage.

Further Reading#

  • Paper: Salakhutdinov et al. 2007 - Restricted Boltzmann Machines for Collaborative Filtering

  • GitHub Repository

Contents