Thanks to Jure Leskovec, Anand Rajaraman, Jeff Ullman

Transcription

1 Thanks to Jure Leskovec, Anand Rajaraman, Jeff Ullman

2 Overview of Recommender Systems Content-based Systems Collaborative Filtering J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,

3 Customer X Buys Metallica CD Buys Megadeth CD Customer Y Does search on Metallica Recommender system suggests Megadeth from data collected about customer X J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,

4 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Examples: Search Recommendations Items Products, web sites, blogs, news items,

5 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 6 Shelf space is a scarce commodity for traditional retailers Also: TV networks, movie theaters, Web enables near-zero-cost dissemination of information about products From scarcity to abundance More choice necessitates better filters Recommendation engines How Into Thin Air made Touching the Void a bestseller:

6 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 7 Source: Chris Anderson (00)

7 Read to learn more! J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 8

8 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 9 Editorial and hand curated List of favorites Lists of essential items Simple aggregates Top 0, Most Popular, Recent Uploads Tailored to individual users Amazon, Netflix,

9 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 0 X = set of Customers S = set of Items Utility function u: X S R R = set of ratings R is a totally ordered set e.g., 0- stars, real number in [0,]

10 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Avatar LOTR Matrix Pirates Alice 0. Bob Carol 0. David 0.

11 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, () Gathering known ratings for matrix How to collect the data in the utility matrix () Extrapolate unknown ratings from the known ones Mainly interested in high unknown ratings We are not interested in knowing what you don t like but what you like () Evaluating extrapolation methods How to measure success/performance of recommendation methods

12 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Explicit Ask people to rate items Doesn t work well in practice people can t be bothered Implicit Learn ratings from user actions E.g., purchase implies high rating What about low ratings?

13 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Key problem: Utility matrix U is sparse Most people have not rated most items Cold start: New items have no ratings New users have no history Three approaches to recommender systems: ) Content-based ) Collaborative ) Latent factor based Today!

14

15 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 6 Main idea: Recommend items to customer x similar to previous items rated highly by x Example: Movie recommendations Recommend movies with same actor(s), director, genre, Websites, blogs, news Recommend other sites with similar content

16 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 7 Item profiles likes recommend build match Red Circles Triangles User profile

17 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 8 For each item, create an item profile Profile is a set (vector) of features Movies: author, title, actor, director, Text: Set of important words in document How to pick important features? Usual heuristic from text mining is TF-IDF (Term frequency * Inverse Doc Frequency) Term Feature Document Item

18 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 9 f ij = frequency of term (feature) i in doc (item) j n i = number of docs that mention term i N = total number of docs Note: we normalize TF to discount for longer documents TF-IDF score: w ij = TF ij IDF i Doc profile = set of words with highest TF-IDF scores, together with their scores

19 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 0 User profile possibilities: Weighted average of rated item profiles Variation: weight by difference from average rating for item Prediction heuristic: Given user profile x and item profile i, estimate u(x, i) = cos(x, i) = x i x i

20 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, +: No need for data on other users No cold-start or sparsity problems +: Able to recommend to users with unique tastes +: Able to recommend new & unpopular items No first-rater problem +: Able to provide explanations Can provide explanations of recommended items by listing content-features that caused an item to be recommended

21 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, : Finding the appropriate features is hard E.g., images, movies, music : Recommendations for new users How to build a user profile? : Overspecialization Never recommends items outside user s content profile People might have multiple interests Unable to exploit quality judgments of other users

22 Harnessing quality judgments of other users

23 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Consider user x Find set N of other users whose ratings are similar to x s ratings Estimate x s ratings based on ratings of users in N x N

24 Let r x be the vector of user x s ratings Jaccard similarity measure Problem: Ignores the value of the rating Cosine similarity measure sim(x, y) = cos(r x, r y ) = r x r y r x r y Problem: Treats missing ratings as negative Pearson correlation coefficient S xy = items rated by both users x and y sim x, y = s S xy r xs r x r ys r y s S xy r xs r x s Sxy r ys r y r x = [*, _, _, *, ***] r y = [*, _, **, **, _] r x, r y as sets: r x = {,, } r y = {,, } r x, r y as points: r x = {, 0, 0,, } r y = {, 0,,, 0} r x, r y avg. rating of x, y J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,

25 Cosine sim: sim(x, y) = i r xi r yi i r xi i r yi Intuitively we want: sim(a, B) > sim(a, C) Jaccard similarity: / < / Cosine similarity: 0.86 > 0. Considers missing ratings as negative Solution: subtract the (row) mean sim A,B vs. A,C: 0.09 > -0.9 Notice cosine sim. is correlation when data is centered at 0 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 6

26 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 7 From similarity metric to recommendations: Let r x be the vector of user x s ratings Let N be the set of k users most similar to x who have rated item i Prediction for item s of user x: r xi = k r xi = y N r yi y N s xy r yi Shorthand: s xy = sim x, y y N s xy Other options? Many other tricks possible

27 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 8 So far: User-user collaborative filtering Another view: Item-item For item i, find other similar items Estimate rating for item i based on ratings for similar items Can use same similarity metrics and prediction functions as in user-user model r xi j N ( i; x) s ij j N ( i; x) s r ij xj s ij similarity of items i and j r xj rating of user u on item j N(i;x) set items rated by x similar to i

28 users movies - unknown rating - rating between to 9 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,

29 ? 6 users - estimate rating of movie by user 0 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, movies

30 movies users? sim(,m) Neighbor selection: Identify movies similar to movie, rated by user J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Here we use Pearson correlation as similarity: ) Subtract mean rating m i from each movie i m = (++++)/ =.6 row : [-.6, 0, -0.6, 0, 0,., 0, 0,., 0, 0., 0] ) Compute cosine similarities between rows

31 movies J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, users? sim(,m) Compute similarity weights: s, =0., s,6 =0.9

32 movies J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, users Predict by taking weighted average: r. = (0.* + 0.9*) / (0.+0.9) =.6 r ix = j N(i;x) s ij r jx s ij

33 Define similarity s ij of items i and j Select k nearest neighbors N(i; x) Before: Items most similar to i, that were rated by x Estimate rating r xi as the weighted average: r xi j N ( i; x) s j N ( i; x) ij s r ij xj r xi b xi j N ( i; x) s ij ( r j N ( i; x) xj s ij b xj ) baseline estimate for r xi μ = overall mean movie rating b x = rating deviation of user x b xi = μ + b x + b i = (avg. rating of user x) μ b i = rating deviation of movie i J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets,

34 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Avatar LOTR Matrix Pirates Alice 0.8 Bob Carol David 0. In practice, it has been observed that item-item often works better than user-user Why? Items are simpler, users have multiple tastes

35 + Works for any kind of item No feature selection needed - Cold Start: Need enough users in the system to find a match - Sparsity: The user/ratings matrix is sparse Hard to find users that have rated the same items - First rater: Cannot recommend an item that has not been previously rated New items, Esoteric items - Popularity bias: Cannot recommend items to someone with unique taste Tends to recommend popular items J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 6

36 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 7 Implement two or more different recommenders and combine predictions Perhaps using a linear model Add content-based methods to collaborative filtering Item profiles for new item problem Demographics to deal with new user problem

37 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Evaluation - Error metrics - Complexity / Speed

38 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 9 movies users

39 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, 0 users movies????? Test Data Set

40 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Compare predictions with known ratings Root-mean-square error (RMSE) xi r xi r xi where r xi is predicted, r xi is the true rating of x on i Precision at top 0: % of those in top 0 Rank Correlation: Spearman s correlation between system s and user s complete rankings Another approach: 0/ model Coverage: Number of items/users for which system can make predictions Precision: Accuracy of predictions Receiver operating characteristic (ROC) Tradeoff curve between false positives and false negatives

41 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Narrow focus on accuracy sometimes misses the point Prediction Diversity Prediction Context Order of predictions In practice, we care only to predict high ratings: RMSE might penalize a method that does well for high ratings and badly for others

42 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Expensive step is finding k most similar customers: O( X ) Too expensive to do at runtime Could pre-compute Naïve pre-computation takes time O(k X ) X set of customers Efficient methods for finding k most similar customers Near-neighbor search in high dimensions (LSH) Clustering Dimensionality reduction

43 J. Leskovec, A. Rajaraman, J. Ullman: Mining of Massive Datasets, Leverage all the data Don t try to reduce data size in an effort to make fancy algorithms work Simple methods on large data do best Add more data e.g., add IMDB data on genres More data beats better algorithms