Recommender Systems

Recommender systems make up domain ten of the syllabus. In Round 2, they can appear as a practical task that does not fit the usual classification template.

Collaborative versus content-based

• Collaborative filtering uses the ratings of other users. It needs no item features and can surface genuinely surprising recommendations, but it fails on new users and new items.
• Content-based filtering uses item features and the user's own history. It handles new items well but tends to recommend more of the same.
• Hybrid systems combine them, which is why nearly every real system is one.

Identifying which family a described scenario needs is a standard multiple-choice question.

Similarity

Cosine similarity between rating vectors:

Pearson correlation is cosine similarity on mean-centred vectors, which corrects for users who rate systematically high or low. Computing either by hand on a small user-item matrix is a natural fill-in-the-blank question - practise it.

User-Based and item-based

User-based CF finds similar users and averages their ratings for the target item. Item-based CF finds items similar to those the user already liked.

Item-based is generally preferred in practice: item-item similarities change more slowly than user tastes, so they can be precomputed, and there are usually fewer items than users.

Matrix factorisation

Approximate the rating matrix as $R \approx PQ^\top$, learning $k$ latent factors per user and per item, fitting only on observed entries:

Two examinable points. You cannot simply take the SVD of $R$, because SVD requires a complete matrix and filling gaps with zeros asserts that unrated means rated-zero. And adding user and item bias terms - $\hat r_{ui} = \mu + b_u + b_i + p_u^\top q_i$ - usually helps more than adding latent factors, because much of the variance is just that some users rate generously and some items are popular.

Cold start

• New user - no history. Use popularity, ask for a few initial preferences, or use demographics.
• New item - no ratings. Content-based similarity is the answer.
• New system - neither is available.

This is the most frequently asked recommender question, because the answer is a design argument rather than a formula.

Evaluating

Rating prediction uses RMSE or MAE; ranking uses precision@k, recall@k, or NDCG. Beyond accuracy, coverage and diversity matter - a system that always recommends the same ten popular items scores acceptably and serves nobody.

Match the scenario to collaborative, content-based, or hybrid. Pearson is cosine on centred vectors; practise computing both by hand.

Item-based CF is more stable than user-based. Bias terms often beat extra factors; never SVD a matrix with missing entries.