Recommender Systems

1. Recommender Systems Jia-Bin Huang Virginia Tech ECE-5424G / CS-5824 Spring 2019

2. Administrative • HW 4 due April 10

3. Unsupervised Learning • Clustering, K-Mean • Expectation maximization • Dimensionality reduction • Anomaly detection • Recommendation system

4. Motivating example: Monitoring machines in a data center (Memory use) (CPU load) (Memory use) (CPU load)

5. Multivariate Gaussian (normal) distribution • . Don’t model separately • Model all in one go. • Parameters: (covariance matrix)

6. Multivariate Gaussian (normal) examples

7. Multivariate Gaussian (normal) examples

8. Multivariate Gaussian (normal) examples

9. Anomaly detection using the multivariate Gaussian distribution • Fit model by setting 2 Give a new example , compute Flag an anomaly if

10. Original model Automatically captures correlations between features Computationally more expensive Must have or else is non-invertible Original model Manually create features to capture anomalies where take unusual combinations of values Computationally cheaper (alternatively, scales better) OK even if training set size is small

11. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

12. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

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15. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

16. Example: Predicting movie ratings • User rates movies using zero to five stars • no. users • no. movies • if user has rated movie • rating given by user to movie

17. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

18. Content-based recommender systems For each user , learn a parameter . Predict user as rating movie with stars.

19. Content-based recommender systems For each user , learn a parameter . Predict user as rating movie with stars.

20. Problem formulation • if user has rated movie • rating given by user to movie • parameter vector for user • feature vector for user • For each user predicted rating: • no. of movies rated by user j Goal: learn :

21. Optimization objective • Learn (parameter for user ): Learn

22. Optimization algorithm Gradient descent update: (for ) (for )

23. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

24. Problem motivation

25. Problem motivation

26. Optimization algorithm • Given , to learn : • Given , to learn :

27. Collaborative filtering • Given (and movie ratings), Can estimate • Given Can estimate

28. Collaborative filtering optimization objective • Given , estimate • Given , estimate

29. Collaborative filtering optimization objective • Given , estimate • Given , estimate • Minimize and simultaneously

30. Collaborative filtering optimization objective

31. Collaborative filtering algorithm • Initialize to small random values • Minimize using gradient descent (or an advanced optimization algorithm). For every • For a user with parameter and movie with (learned) feature , predict a star rating of

32. Collaborative filtering

33. Collaborative filtering • Predicted ratings: Low-rank matrix factorization

34. Finding related movies/products • For each product , we learn a feature vector : romance, : action, : comedy, … • How to find movie relate to movie ? Small movie j and I are “similar”

35. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization

36. Users who have not rated any movies

37. Users who have not rated any movies

38. Mean normalization For user , on movie predict: User 5 (Eve): Learn

39. Recommender Systems • Motivation • Problem formulation • Content-based recommendations • Collaborative filtering • Mean normalization