The document discusses Spotify's use of collaborative filtering for music recommendations, focusing on techniques like matrix completion and latent factor models. It highlights the challenges of parallelization and explores various methods for measuring item similarity, such as cosine similarity and Pearson correlation. Additionally, the text touches on the need for scalable solutions in different domains, presents the importance of A/B testing, and concludes with a hiring note.

1. Music recommendations at Spotify
Erik Bernhardsson
erikbern@spotify.com

2. Recommendation stuff at Spotify

3. Collaborative filtering

4. Collaborative filtering
Idea:
- If two movies x, y get similar ratings then they are probably similar
- If a lot of users all listen to tracks x, y, z, then those tracks are
probably similar

5. Get data

6. … lots of data

7. Aggregate data
Throw away temporal information and just look at the number of times

8. OK, so now we have a big matrix

9. … very big matrix

10. Supervised collaborative filtering is pretty much matrix completion

11. Supervised learning: Matrix completion

12. Supervised: evaluating rec quality

13. Unsupervised learning
- Trying to estimate the density
- i.e. predict probability of future events

14. Try to predict the future given the past

15. How can we find similar items

16. We can calculate correlation coefficient as an item similarity
- Use something like Pearson, Jaccard, …

17. Amazon did this for “customers who bought this also bought”
- US patent 7113917

18. Parallelization is hard though

19. Parallelization is hard though

20. Can speed this up using various LSH tricks
- Twitter: Dimension Independent Similarity Computation (DISCO)

21. Are there other approaches?

22. Natural Language Processing has a lot of similar problems
…matrix factorization is one idea

23. Matrix factorization

24. Matrix factorization
- Want to get user vectors and item vectors
- Assume f latent factors (dimensions) for each user/item

25. Probabilistic Latent Semantic Analysis (PLSA)
- Hofmann, 1999
- Also called PLSI

26. PLSA, cont.
+ a bunch of constraints:

27. PLSA, cont.
Optimization problem: maximize log-likelihood

28. PLSA, cont.

33. “Collaborative Filtering for Implicit Feedback Datasets”
- Hu, Koren, Volinsky (2008)

34. “Collaborative Filtering for Implicit Feedback Datasets”, cont.

35. “Collaborative Filtering for Implicit Feedback Datasets”, cont.

36. “Collaborative Filtering for Implicit Feedback Datasets”, cont.

37. “Collaborative Filtering for Implicit Feedback Datasets”, cont.

38. Here is another method we use

39. What happens each iteration
- Assign all latent vectors small random values
- Perform gradient ascent to optimize log-likelihood

40. What happens each iteration
- Assign all latent vectors small random values
- Perform gradient ascent to optimize log-likelihood

41. What happens each iteration
- Assign all latent vectors small random values
- Perform gradient ascent to optimize log-likelihood

42. Calculate derivative and do gradient ascent
- Assign all latent vectors small random values
- Perform gradient ascent to optimize log-likelihood

43. 2D iteration example

44. Vectors are pretty nice because things are now super fast
- User-item score is a dot product:
- Item-item similarity score is a cosine similarity:
- Both cases have trivial complexity in the number of factors f:

45. Example: item similarity as a cosine of vectors

46. Two dimensional example for tracks

47. We can rank all tracks by the user’s vector

48. So how do we implement this?

49. One iteration of a matrix factorization algorithm
“Google News personalization: scalable online collaborative filtering”

51. So now we solved the problem of recommendations right?

52. Actually what we really want is to apply it to other domains

53. Radio
- Artist radio: find related tracks
- Optimize ensemble model based on skip/thumbs data

54. Learning from feedback is actually pretty hard

55. A/B testing

56. A/B testing

57. A/B testing

58. A/B testing

59. More applications!!!

62. Last but not least: we’re hiring!

63. Thank you