Setup

• Items: movies, songs, products, etc. (often many thousands)
• Users: watchers, listeners, purchasers, etc. (often many millions)
• Feedback: 5-star ratings, not -clicking ‘next’, purchases, etc.

Key Assumptions

• Can represent ratings numerically as a user/item matrix
• Users only rate a small number of items (the matrix is sparse)

Two Types of Recommender Systems: 1. Content Filtering 2. Collaborative Filtering

Content Filtering

• Example: Pandora.com music recommendations (Music Genome Project)
• Con: Assumes access to side information about items (e.g. properties of a song)
• Pro: Got a new item to add? No problem, just be sure to include the side information

Collaborative Filtering

• Example: Netflix movie recommendations
• Pro: Does not assume access to side information about items (e.g. does not need to know about movie genres)
• Con: Does not work on new items that have no ratings
• Common insight: personal tastes are correlated
  • If Alice and Bob both like X and Alice likes Y then Bob is more likely to like Y, especially (perhaps) if Bob knows Alice

Two Types of Collaborative Filtering 1. Neighborhood Methods 2. Latent Factor Methods

Neighborhood Methods

![[Screen Shot 2024-04-28 at 18.51.04.png]]

Latent Factor Methods

![[Screen Shot 2024-04-28 at 18.51.38.png]]

Matrix Factorization

• Many different ways of factorizing a matrix
  1. Unconstrained Matrix Factorization
  2. Singular Value Decomposition
  3. Non-negative Matrix Factorization
• MF is just another example of a common recipe: 1. define a model 2. define an objective function 3. optimize with SGD

Low-rank Matrix Factorization

![[Screen Shot 2024-04-28 at 18.53.13.png]]

Regression vs. Collaborative Filtering

![[Screen Shot 2024-04-28 at 18.58.16.png]]

Unconstrained Matrix Factorization

![[Screen Shot 2024-04-28 at 18.58.49.png]] ![[Screen Shot 2024-04-28 at 19.00.08.png]]

![[Screen Shot 2024-04-28 at 19.00.36.png]] ![[Screen Shot 2024-04-28 at 19.00.49.png]]