Data Mining Techniques

Transcription

1 Data Mining Techniques CS 60 - Section - Fall 06 Lecture Jan-Willem van de Meent (credit: Andrew Ng, Alex Smola, Yehuda Koren, Stanford CS6)

2 Recommender Systems

3 The Long Tail (from:

4 The Long Tail (from:

5 The Long Tail (from:

6 Problem Setting

7 Problem Setting

8 Problem Setting

9 Problem Setting Task: Predict user preferences for unseen items

10 Content-based Filtering serious The Color Purple Amadeus Braveheart Geared towards females Sense and Sensibility Ocean s Lethal Weapon Geared towards males Dave The Princess Diaries The Lion King Independence Day Gus Dumb and Dumber escapist

11 Content-based Filtering serious The Color Purple Amadeus Braveheart Geared towards females Sense and Sensibility Ocean s Lethal Weapon Geared towards males Dave The Princess Diaries The Lion King Independence Day Gus Dumb and Dumber escapist Idea: Predict rating using item features on a per-user basis

12 Content-based Filtering serious The Color Purple Amadeus Braveheart Geared towards females Sense and Sensibility Ocean s Lethal Weapon Geared towards males Dave The Princess Diaries The Lion King Independence Day Gus Dumb and Dumber escapist Idea: Predict rating using user features on a per-item basis

13 Collaborative Filtering # # # Joe # Idea: Predict rating based on similarity to other users

14 Problem Setting Task: Predict user preferences for unseen items Content-based filtering: Model user/item features Collaborative filtering: Implicit similarity of users items

15 Recommender Systems Movie recommendation (Netflix) Related product recommendation (Amazon) Web page ranking (Google) Social recommendation (Facebook) News content recommendation (Yahoo) Priority inbox & spam filtering (Google) Online dating (OK Cupid) Computational Advertising (Everyone)

16 Challenges Scalability Millions of objects 00s of millions of users Cold start Changing user base Changing inventory Imbalanced dataset User activity / item reviews power law distributed Ratings are not missing at random

17 Running Example: Netflix Data Training data Test data user movie date score user movie date score /7/0 6 /6/0? 8//0 96 9//0? /6/0 7 8/8/0? //0 //0? 768 7//0 7 6//0? 76 //0 8//0? 8//00 9//00? 68 9/0/0 8 8/7/0? //0 9 //0? /8/00 7 7/6/0? // //0? 6 6 6// //0? Released as part of $M competition by Netflix in 006 Prize awarded to BellKor in 009

18 Running Yardstick: RMSE rmse(s) = s S X (ˆr ui r ui ) (i,u)s

19 Running Yardstick: RMSE rmse(s) = s S X (i,u)s (ˆr ui r ui ) (doesn t tell you how to actually do recommendation)

20 Ratings aren t everything Netflix then Netflix now

21 Content-based Filtering

22 Item-based Features

23 Item-based Features

24 Item-based Features

25 Per-user Regression Learn a set of regression coefficients for each user w u = argmin w r u Xw

26 Bias

27 Bias

28 Bias Moonrise Kingdom 0. 0.

29 Bias Moonrise Kingdom Problem: Some movies are universally loved / hated

30 Bias Moonrise Kingdom Problem: Some movies are universally loved / hated some users are more picky than others

31 Bias Moonrise Kingdom Problem: Some movies are universally loved / hated some users are more picky than others Solution: Introduce a per-movie and per-user bias

32 Temporal Effects

33 Changes in user behavior Netflix changed rating labels 00

34 Movies get better with time?

35 Temporal Effects Solution: Model temporal effects in bias not weights

36 Neighborhood Methods

37 Neighborhood Based Methods # # # Joe # Users and items form a bipartite graph (edges are ratings)

38 Neighborhood Based Methods (user, user) similarity predict rating based on average from k-nearest users good if item base is smaller than user base good if item base changes rapidly (item,item) similarity predict rating based on average from k-nearest items good if the user base is small good if user base changes rapidly

39 Parzen-Window Style CF ˆr ui = b ui + P js k (i,u) s ij(r uj b uj ) P js k (i,u) s ij b ui = µ + b u + b i Define a similarity sij between items Find set sk(i,u) of k-nearest neighbors to i that were rated by user u Predict rating using weighted average over set How should we define sij?

40 Pearson Correlation Coefficient User ratings for item i:??????????? User ratings for item j:??????????? s ij = Cov[r ui,r uj ] Std[r ui ]Std[r uj ]

41 (item,item) similarity Empirical estimate of Pearson correlation coefficient P uu(i,j) (r ui b ui )(r uj b uj ) ˆ ij = q P uu(i,j) (r ui b ui ) P uu(i,j) (r uj b uj ) Regularize towards 0 for small support s ij = U(i, j) U(i, j) + ˆ ij Regularize towards baseline for small neighborhood P js ˆr ui = b ui + k (i,u) s ij(r uj b uj ) + P js k (i,u) s ij

42 Similarity for binary labels Pearson correlation not meaningful for binary labels (e.g. Views, Purchases, Clicks) Jaccard similarity Observed / Expected ratio s ij = m ij + m i + m j m ij s ij = observed expected m ij + m i m j /m m i users acting on i m ij users acting on both i and j m total number of users

43 Matrix Factorization Methods

44 Matrix Factorization Moonrise Kingdom 0. 0.

45 Matrix Factorization Moonrise Kingdom Idea: pose as (biased) matrix factorization problem

46 Matrix Factorization items ~ ~ items users users A rank- SVD approximation

47 Prediction items ~ ~ items users A rank- SVD approximation users?

48 Prediction items ~ ~ items users. A rank- SVD approximation users

49 SVD with missing values ~ Pose as regression problem Regularize using Frobenius norm

50 Alternating Least Squares ~ (regress wu given X)

51 Alternating Least Squares ~ (regress wu given X) L: closed form solution w =(X T X + I) X T y Remember ridge regression?

52 Alternating Least Squares ~ (regress xi given W) (regress wu given X)

53 Stochastic Gradient Descent ~ No need for locking Multicore updates asynchronously (Recht, Re, Wright, 0 - Hogwild)

54 Netflix Prize

55 Netflix Prize Training data 00 million ratings, 80,000 users, 7,770 movies 6 years of data: Test data Last few ratings of each user (.8 million) Evaluation criterion: Root Mean Square Error (RMSE) Competition,700+ teams Netflix s system RMSE: 0.9 $ million prize for 0% improvement on Netflix

56 Improvements RMSE Factor models: Error vs. #parameters Add biases NMF BiasSVD SVD++ SVD v. SVD v. SVD v Millions of Parameters Do SGD, but also learn biases μ, bu and bi

57 Improvements RMSE Factor models: Error vs. #parameters who rated what NMF BiasSVD SVD++ SVD v. SVD v. SVD v Millions of Parameters Account for fact that ratings are not missing at random.

58 Improvements Factor models: Error vs. #parameters NMF BiasSVD SVD++ RMSE temporal effects SVD v. SVD v. SVD v Millions of Parameters Account for drift in user and item biases

59 Improvements Factor models: Error vs. #parameters NMF BiasSVD SVD++ RMSE temporal effects SVD v. SVD v. SVD v Millions of Parameters Still pretty far from 0.86 grand prize

60 Winning Solution from BellKor

61 Last 0 days June 6 th submission triggers 0-day last call

62 Last 0 days June 6 th submission triggers 0-day last call

63 BellKor fends off competitors by a hair

64 BellKor fends off competitors by a hair