Recommendation systems

Netflix's catalogue and your viewing history are both enormous, and the intersection is tiny. Most users have rated or watched a vanishing fraction of the items, so the data is a matrix that is almost entirely blank. A recommender's job is to fill in the blanks well enough to order them — and to do so while a user's tastes and an item's popularity are both moving.

The matrix below is small enough to read. Click a blank to accept the model's prediction, clear a rating to remove evidence, and switch between user-based and item-based reasoning. Every cell is recomputed from the ratings in front of you.

Similarity and the neighbourhood model #

For users $u$ and $v$ with mean ratings $\bar r_u, \bar r_v$, the mean-centred cosine similarity over co-rated items $I_{uv}$ is

$$\mathrm{sim}(u,v) = \frac{\sum_{i \in I_{uv}} (r_{ui} - \bar r_u)(r_{vi} - \bar r_v)} {\sqrt{\sum_{i \in I_{uv}} (r_{ui} - \bar r_u)^2}\;\sqrt{\sum_{i \in I_{uv}} (r_{vi} - \bar r_v)^2}}.$$

Subtracting each user's mean removes the "easy grader" effect. A prediction for a blank cell is then a similarity-weighted average of neighbours' deviations:

$$\hat r_{ui} = \bar r_u + \frac{\sum_{v \neq u} \mathrm{sim}(u,v)\,(r_{vi} - \bar r_v)} {\sum_{v \neq u} \lvert \mathrm{sim}(u,v)\rvert}.$$

Only positive similarities contribute, so dissimilar users do not drag the prediction the wrong way.

Matrix factorisation #

Neighbourhood models need overlap to measure similarity, which is exactly what sparse data lacks. Latent-factor models instead learn a low-rank structure: a vector $p_u \in \mathbb{R}^k$ for each user and $q_i \in \mathbb{R}^k$ for each item, with predictions $\hat r_{ui} = p_u \cdot q_i$. The vectors are fit by minimising regularised squared error over the observed entries only:

$$\min_{P,Q} \sum_{(u,i)\,\text{observed}} \left(r_{ui} - p_u \cdot q_i\right)^2 + \lambda\left(\lVert p_u \rVert^2 + \lVert q_i \rVert^2\right).$$

The regularisation is essential — with so few observed entries, an unregularised factorisation simply memorises them. The learned dimensions are not interpretable labels like "likes science fiction"; they are whatever directions best explain co-occurrence.

Ranking, not rating, and the cold start #

A recommender is usually judged not on rating accuracy but on ranking: is the item the user actually engaged with near the top of the list? RMSE and ranking metrics (precision@k, NDCG, recall@k) can disagree sharply, and the metric that matters is the one tied to the product decision. Two problems no amount of modelling removes:

• Cold start. A brand-new user or item has no interactions, so neither similarity nor latent factors exist for it. The usual fixes are content features, popularity priors, and deliberate exploration.
• Feedback loops. Recommending an item generates the interactions that justify recommending it again, which narrows the catalogue and can amplify bias. Deployed systems deliberately inject exploration to counter this.

Check yourself

Eduspheria wiki · Data, MLOps & Deployment, Features & recommenders

0 / 5 answered

1. 1Why is mean-centring applied before computing user-user cosine similarity?

   A.To make all ratings positiveB.To speed up the dot productC.To remove each user's rating biasD.To fill missing cells

   Check Show answerMultiple choice
2. 2A user has rated 3 of 6 items. How many blanks does a recommender need to score for that user?

   Check Show answerNumeric answer
3. 3What is the problem called when a new user or item has no interactions to base recommendations on?

   Check Show answerShort answer
4. 4In matrix factorisation the loss is computed over every cell of the ratings matrix, including the blank ones.

   TrueFalse

   Check Show answerTrue / false
5. 5Which metric is most aligned with a product goal of putting relevant items near the top of a recommendation list?

   A.Mean absolute errorB.Precision@kC.R-squaredD.RMSE of ratings

   Check Show answerMultiple choice

From the exam paper

Modeled on NITJ AI-505, End-Sem December 2024

0 / 5 answered

1. 1StreamFlix holds user demographics, movie genres and release years, a ratings matrix, viewing logs and user tags. Which design makes the best use of all of these signals?

   A.A global popularity ranking with no personalisationB.Pure content-based filtering on genres onlyC.Pure collaborative filtering on ratings onlyD.A hybrid that combines collaborative signal with content features and tags

   Check Show answerMultiple choice
2. 2What is the name of the situation in which a brand-new StreamFlix user has no ratings or viewing history to base recommendations on?

   Check Show answerShort answer
3. 3StreamFlix wants to know whether the movies a user actually watched landed near the top of the recommended list. Which metric best matches that goal?

   A.Precision at k or NDCGB.Mean absolute errorC.R-squared of ratingsD.RMSE of predicted ratings

   Check Show answerMultiple choice
4. 4Collaborative filtering is at its strongest precisely when the ratings matrix is extremely sparse.

   TrueFalse

   Check Show answerTrue / false
5. 5What name is given to the collaborative-filtering obstacle created by having far more users and items than observed ratings, which matrix factorisation addresses by learning hidden features?

   Check Show answerShort answer

Where next: data pipelines — how the clean tables that feed all of this get built and kept correct.