Recommendation Systems

Recommendation systems predict what a user will want to see or buy next. They drive 35% of Amazon’s revenue, 80% of Netflix viewing, and 60% of YouTube watch time. The difference between a good and great recommendation system is the difference between suggesting “more shoes” and suggesting the exact shoe the user will love.

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Recommendation Approaches

Collaborative Filtering:
  "Users who liked X also liked Y"
  Based on user behavior patterns
  No need to understand content
  
Content-Based Filtering:
  "You liked action movies, here's another action movie"
  Based on item attributes and user preferences
  Works for new items (no cold start for items)
  
Hybrid:
  Combine collaborative + content-based
  Best of both approaches
  Most production systems are hybrid
  
Knowledge-Based:
  Rules and constraints
  "Budget < $100, size M, color blue"
  Best for high-consideration purchases

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Collaborative Filtering

# User-Item Matrix
#          Movie1  Movie2  Movie3  Movie4
# Alice:     5       3       ?       1
# Bob:       4       ?       4       1  
# Carol:     1       1       5       5
# Dave:      ?       3       4       4

# Alice hasn't rated Movie3
# Similar users (Bob) rated Movie3: 4
# Prediction for Alice on Movie3: ~3.5-4.0

import numpy as np
from scipy.sparse.linalg import svds

class MatrixFactorization:
    def __init__(self, n_factors=50):
        self.n_factors = n_factors
    
    def fit(self, ratings_matrix):
        """Factor rating matrix into user and item latent factors."""
        # Center ratings
        self.user_means = ratings_matrix.mean(axis=1)
        centered = ratings_matrix - self.user_means.reshape(-1, 1)
        
        # SVD decomposition
        U, sigma, Vt = svds(centered, k=self.n_factors)
        self.user_factors = U  # (n_users, n_factors)
        self.item_factors = (np.diag(sigma) @ Vt).T  # (n_items, n_factors)
    
    def predict(self, user_id, item_id):
        """Predict rating for user-item pair."""
        prediction = (
            self.user_means[user_id] +
            self.user_factors[user_id] @ self.item_factors[item_id]
        )
        return np.clip(prediction, 1, 5)
    
    def recommend(self, user_id, n=10):
        """Get top-N recommendations for a user."""
        scores = (
            self.user_means[user_id] +
            self.user_factors[user_id] @ self.item_factors.T
        )
        # Exclude already-rated items
        already_rated = self.get_rated_items(user_id)
        scores[already_rated] = -np.inf
        
        top_indices = np.argsort(scores)[::-1][:n]
        return top_indices, scores[top_indices]

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Evaluation Metrics

# Offline evaluation
def evaluate_recommendations(model, test_data):
    metrics = {
        # Ranking quality
        "precision@10": precision_at_k(model, test_data, k=10),
        "recall@10": recall_at_k(model, test_data, k=10),
        "ndcg@10": ndcg_at_k(model, test_data, k=10),
        "map@10": mean_average_precision(model, test_data, k=10),
        
        # Coverage
        "catalog_coverage": len(recommended_items) / len(all_items),
        "user_coverage": len(users_with_recs) / len(all_users),
        
        # Diversity
        "intra_list_diversity": average_pairwise_distance(recommendations),
        
        # Novelty
        "novelty": average_self_information(recommendations),
    }
    return metrics

# Online evaluation (A/B test)
online_metrics = {
    "ctr": "Click-through rate on recommendations",
    "conversion_rate": "Purchase rate from recommendations",
    "revenue_per_user": "Revenue attributed to recommendations",
    "engagement_time": "Time spent with recommended content",
    "diversity_of_consumption": "Breadth of categories consumed",
}

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Cold Start Problem

New user cold start:
  Problem: No history, can't find similar users
  Solutions:
    1. Ask preferences during onboarding
    2. Recommend popular/trending items
    3. Use demographic-based recommendations
    4. Content-based using first few interactions

New item cold start:
  Problem: No user interactions with new item
  Solutions:
    1. Content-based features (genre, description)
    2. Explore/exploit: show to random users
    3. Editorial curation for launch period
    4. Similar item features from existing catalog

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Anti-Patterns

Anti-Pattern	Consequence	Fix
Popularity bias only	Filter bubble, no personalization	Balance popularity with diversity
No exploration	Users never see new/niche items	Explore/exploit (epsilon-greedy, Thompson sampling)
Offline metrics only	Model optimizes for proxy, not real engagement	A/B test recommendations
Training on implicit feedback only	Biased toward easy-to-measure actions	Combine implicit + explicit signals
No freshness	Stale recommendations	Time-decay, recency weighting

Recommendations are not just about accuracy. Diversity, novelty, and serendipity are what keep users engaged long-term.