ALS Tutorial: Alternating Least Squares

ALS Tutorial: Alternating Least Squares#

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#

ALS alternates between fixing user factors and solving for item factors (and vice versa) to efficiently factorize large sparse matrices.

Paper: Hu et al. 2008 - Collaborative Filtering for Implicit Feedback

How ALS Works#

Architecture#

Alternating Optimization for Scalability:

  1. Initialization: Random user and item factors

  2. Fix Items, Solve Users: Solve for all user factors in parallel

  3. Fix Users, Solve Items: Solve for all item factors in parallel

  4. Repeat: Alternate until convergence

Key Innovation: Closed-form solution per iteration, highly parallelizable

Objective:

min Σ_(u,i) c_ui(p_ui - x_u^T y_i)² + λ(Σ||x_u||² + Σ||y_i||²)

Mathematical Foundation#

User Update (parallel over all users):

x_u = (Y^T C^u Y + λI)^(-1) Y^T C^u p^u

where:

  • Y: item factor matrix

  • C^u: confidence diagonal matrix for user u

  • p^u: preference vector for user u

Item Update (parallel over all items):

y_i = (X^T C^i X + λI)^(-1) X^T C^i p^i

Confidence:

c_ui = 1 + α · r_ui

for implicit feedback r_ui

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.mf_base.als_base import ALS_base as ALS
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 = ALS(
    name="ALS_Model",
    n_factors=100,
    regularization=0.01,
    alpha=40,
    iterations=15,
    epochs=20,
    batch_size=256,
    learning_rate=0.001,
    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/als_model')

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

Key Takeaways#

When to Use ALS#

✅ Perfect For:

  • Very large scale (billions of interactions)

  • Implicit feedback (views, clicks)

  • Distributed/parallel computation

  • Production systems at scale

  • Spark, Hadoop environments

❌ Not For:

  • Small datasets (<10K) - SGD simpler

  • Explicit ratings - SGD more flexible

  • Need online updates - ALS is batch

  • Dense features - use neural models

Best Practices#

  1. Factors: 50-200 typically

  2. Confidence α: 40 is common (tune 10-100)

  3. Regularization λ: 0.01-0.1

  4. Iterations: 10-20 sufficient

  5. Parallelization: Partition by user/item blocks

  6. Implicit: Always use confidence weighting

  7. Caching: Cache Y^T Y and X^T X

  8. Convergence: Monitor RMSE on validation

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: Hu et al. 2008 - Collaborative Filtering for Implicit Feedback

  • GitHub Repository

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