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Information about Ranking and Diversity in Recommendations - RecSys Stammtisch at...

Slides from my talk at the RecSys Stammtisch at SoundCloud in Berlin. The presentation is split in two part one focusing on ranking and relevance and one on diversity and how to achieve it using genres. We introduce a novel diversity metric called Binomial Diversity.

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Thanks Linas Baltrunas Telefonica Yue Shi TU Delft Saul Vargas Universidad Autonoma de Madrid Pablo Castells Universidad Autonoma de Madrid

Telefonica Research in Barcelona • User Modeling: Recommender Systems • Data Mining, Machine Learning • Multimedia Indexing and Analysis • HCI • Mobile Computing • Systems and Networking • http://www.tid.es

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Collaborative Filtering + + + + + + + + X ↵ik fij = hUi Mj i i hUk Mj i , Mj + |Fi | + k2Fi

Tensor Factorization CP-Decomposition HOSVD Fijkijk S ⇥U Ui ,⇥M j , CkC Ck F = = hU i M Mj ⇥ i Karatzoglou et al. @ Recsys 2010

Publications in Ranking CIKM 2013: GAPfm: Optimal Top-N Recommendations for Graded Relevance Domains RecSys 2013: xCLiMF: Optimizing Expected Reciprocal Rank for Data with Multiple Levels of Relevance RecSys 2012: CLiMF: Learning to Maximize Reciprocal Rank with Collaborative Less-is-More Filtering * Best Paper Award SIGIR 2012: TFMAP: Optimizing MAP for Top-N Context-aware Recommendation Machine Learning Journal, 2008: Improving Maximum Margin Matrix Factorization * Best Machine Learning Paper Award at ECML PKDD 2008 RecSys 2010: List-wise Learning to Rank with Matrix Factorization for Collaborative Filtering NIPS 2007: CoFiRank - Maximum Margin Matrix Factorization for Collaborative Ranking

Recommendations are ranked lists

Popular Ranking Methods • In order to generate the ranked item list, we need some relative utility score for each item • Popularity is the obvious baseline • Score could depend on the user (personalized) • Score could also depend on the other items in the list (list-wise) • One popular way to rank the items in RS is to sort the items according to the rating prediction • Works for the domains with ratings • Wastes the modeling power for the irrelevant items

Graphical Notation Relevant Irrelevant Irrelevant Irrelevant Irrelevant Irrelevant Relevant Relevant

Ranking using latent representation • If user = [-100, -100] • 2d latent factor • We get the corresponding ranking

Matrix Factorization (for ranking) • Randomly initialize item vectors • Randomly initialize user vectors • While not converged • Compute rating prediction error • Update user factors • Update item factors • Lets say user is [-100, -100] • Compute the square error • (5-<[-100, -100], [0.180, 0.19]>)2=1764 • Update the user and item to the direction where the error is reduced (according to the gradient of the loss) 8 items with ratings and random factors

Learning: Stochastic Gradient Descent with Square Error Loss

SquareUser: [3, 1], RMSE=6.7 Loss

Learning to Rank for Top-‐k RecSys • Usually we care about accurate ranking and not ra=ng predic=on • Square Error loss op=mizes to accurately predict 1s and 5s. • RS should get the top items right -‐> Ranking problem • Why not to learn how to rank directly? • Learning to Rank methods provide up to 30% performance improvements in oﬀ-‐line evalua=ons • It is possible, but a more complex task

Example: average precision (AP) • AP: we compute the precision at each relevant position and average them AP = |S| X P (k) k=1 |S| P@1+ P@2 + P@4 1 /1+ 2 / 2 + 3 / 4 = = 0.92 3 3

Why is hard? Non Smoothness Example: AP u:[-20,-20] u:[20,20]

AP vs RMSE

The Non-smoothness of Average Precision AP = |S| X P (k) k=1 |S| APm = PN 1 i=1 ymi N N X ymi X i=1 rmi j=1 ymj I(rmj rmi ) ymi is 1 if item i is relevant for user m and 0 otherwise I(·) indicator function (1 if it is true, 0 otherwise) rmi Rank of item i for user m

How can we get a smooth-AP? • We replace non smooth parts of MAP with smooth approxima=on 1 rmi ⇡ g(fmi ) = g(hUm , Vi i) g(x) = 1/(1 + e x )

How can we get a smooth-MAP? • We replace non smooth parts of MAP with smooth approxima=on I(rmj rmi ) ⇡ g(fmj fmi ) = g(hUm , Vj Vi i) g(x) = 1/(1 + e x )

Smooth version of MAP u:[-20,-20] u:[20,20]

Sometimes approximation is not very good…

Ranking Inconsistencies • Achieving a perfect ranking for all users is not possible • Two Sources of Inconsistencies: • 1) Factor Models (all models) have limited expressive power and cannot learn the perfect ranking for all users • 2) Ranking functions approximations are inconsistent e.g. A >B & B>C but C > A

Summary on Ranking 101

Area Under the ROC Curve (AUC) 1 AU C := + |S ||S | S+ X XS i j I(Ri < Rj )

Reciprocal Rank (RR) 1 RR := Ri

Average Precision (AP) AP = |S| X P (k) k=1 |S|

AP vs RR

Normalized Discounted Cumulative Gain (nDCG) DCG = X 2score(i) i 1 log2 (i + 2)

Relevance solved! Is that all? • Ranking “solves” the relevance problem • Can we be happy with the results?

Relevance solved! Is that all? • Coverage • Diversity • Novelty • Serendipity

Diversity in Recommendations • Diversity using Genres • Movies, Music, Books • Diversity should fulfill: • Coverage • Redundancy • Size Awareness

Diversity methods for RecSys • Topic List Diversification or • Maximal Margin Relevance fM M R (i; S) = (1 ) rel(i) + min dist(i, j) j2S

Diversity methods for RecSys • Intent-Aware IR metrics ERR IA = X s p(s)ERR

Example Action Comedy Sci-Fi Western Action Thriller Sci-Fi Western Adventure Western

Genres Action (517) 154 Comedy (1267) 125 8 11 6 60 37 4 146 2 639 187 21 9 0 30 8 3 9 4 4 232 171 11 1 75 Drama (1711) 86 10 202 870 Romance (583) 46 Thriller (600)

Genres and Popularity

Binomial Diversity • We base a new Diversity Metric on the Binomial Distribution ✓ ◆ N k P (X = k) = p (1 k p) N k

User Genre Relevance • Fraction of Items of genre “g” user interacted with Iu p00 g kg = |Iu | • Global fraction of items of genre “g” • Mix P Iu u kg 0 pg = P u |Iu | pg = (1 ↵) 0 pg +↵ 00 pg

Coverage • Product of the probabilities of the genres not represented in the list not being picked by random Coverage(R) = Y g 2G(R) / P (Xg = 0) 1/|G|

Non-Redundancy P (Xg k | Xg > 0) = 1 N onRed(R) = Y g2G(R) k 1 X l=1 P (Xg P (Xg = l | Xg > 0) R kg | Xg > 0)1/|G(R)|

Non-Redundancy

Binomial Diversity BinomDiv(R) = Coverage(R) · N onRed(R)

Re-Ranking • Re-Rank based on Relevance and Binomial Diversity fBinomDiv (i; S) = (1 ) normrel (rel(i)) + normdiv (div(i; S)) normX (x) = x µX X

Example

Thanks! • Questions?

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