The slide set describing our approach to the KDD Cup 2011, presented at the KDD Cup workshop in San Diego, California.

1. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items
Bayesian Personalized Ranking
for Non-Uniformly Sampled Items
Zeno Gantner, Lucas Drumond, Christoph Freudenthaler,
Lars Schmidt-Thieme
University of Hildesheim
21 August 2011
Zeno Gantner et al., University of Hildesheim 1 / 15

2. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Questions (and Answers)
What?
Who? Which?
How?
Where?
Why?
Zeno Gantner et al., University of Hildesheim 2 / 15

3. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Which problem to solve?
Which problem to solve?
Rating Prediction (Track 1)
vs.
Item Prediction (Track 2)
Zeno Gantner et al., University of Hildesheim 3 / 15

4. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items How did we tackle the problem?
How did we tackle the problem?
Bayesian Personalized Ranking:
2
BPR(DS ) = argmax ln σ(ˆu,i (Θ) − ˆu,j (Θ) )−λ Θ
s s
Θ
(u,i,j)∈DS
DS contains all pairs of positive and negative items for each user,
1
σ(x) = 1+e −x is the logistic function,
Θ represents the model parameters,
ˆu,i (Θ) is the predicted score for user u and item i, and
s
λ Θ 2 is a regularization term to prevent overfitting.
interpretation 1: reduce ranking to pairwise classif. [Balcan et al. 2008]
interpretation 2: optimize for smoothed area under the ROC curve (AUC)
Model: matrix factorization
Learning: stochastic gradient ascent
[Rendle et al., UAI 2009]
Zeno Gantner et al., University of Hildesheim 4 / 15

5. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items How did we tackle the problem?
How did we tackle the problem?
2
BPR(DS ) = argmax ln σ(ˆu,i − ˆu,j ) − λ Θ
s s
Θ
(u,i,j)∈DS
problem: all negative items j are given the same weight
Zeno Gantner et al., University of Hildesheim 5 / 15

6. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items How did we tackle the problem?
How did we tackle the problem?
2
BPR(DS ) = argmax ln σ(ˆu,i − ˆu,j ) − λ Θ
s s
Θ
(u,i,j)∈DS
problem: all negative items j are given the same weight
solution: adapt weights in the optimization criterion (and sampling
probabilities in the learning algorithm)
WBPR(DS ) = argmax wu wi wj ln σ(ˆu,i − ˆu,j ) − λ Θ 2 ,
s s
Θ
(u,i,j)∈DS
where
+
wj = δ(j ∈ Iu ). (1)
u∈U
Zeno Gantner et al., University of Hildesheim 5 / 15

7. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Why did we not win?
But also: Why did we perform better than others?
Why did we perform better than others?
straightforward model that matches the prediction task pretty well
scalability (e.g. k = 480 factors per user/item)
integration of rating information (see paper)
ensembles (see paper)
Why did we not win?
. . . two possible answers . . .
Zeno Gantner et al., University of Hildesheim 6 / 15

8. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Taxonomy
Zeno Gantner et al., University of Hildesheim 7 / 15

9. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Learn the right contrast
rating < 80
rating >= 80 liked?
no rating
rating >= 80
rated? no rating
rating < 80
rating >= 80 ? no rating
Zeno Gantner et al., University of Hildesheim 8 / 15

10. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Learn the right contrast
rating < 80
rating >= 80 liked?
no rating
rating >= 80
rated? no rating
rating < 80
rating >= 80 ? no rating
Zeno Gantner et al., University of Hildesheim 9 / 15

11. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Learn the right contrast
rating < 80
rating >= 80 liked?
no rating
rating >= 80
rated? no rating
rating < 80
rating >= 80 ? no rating
Zeno Gantner et al., University of Hildesheim 10 / 15

12. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Why did we not win?
Learn the right contrast
rating < 80
rating >= 80 liked?
no rating
rating >= 80
rated? no rating
rating < 80
rating >= 80 ? no rating
Zeno Gantner et al., University of Hildesheim 11 / 15

13. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Where?
Where next?
classification → ranking → pairwise classification
pairwise classification: try other losses, e.g. soft margin (hinge) loss
Bayesian2 Personalized Ranking
beyond KDD Cup: consider different sampling schemes . . .
Zeno Gantner et al., University of Hildesheim 12 / 15

14. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Summary
Summary
Use matrix factorization optimized for Bayesian
Personalized Ranking (BPR) to solve the item
ranking problem.
BPR reduces ranking (in this case: binary
variables) to pairwise classification.
Extend BPR to use different sampling scheme:
Weighted BPR (WBPR).
Open question: Learn a different contrast?
Details can be found in the paper.
Code: http://ismll.de/mymedialite/
examples/kddcup2011.html
advertisement: Contribute to http://recsyswiki.com!
Zeno Gantner et al., University of Hildesheim 13 / 15

15. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Questions
Zeno Gantner et al., University of Hildesheim 14 / 15

16. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items
Acknowledgements
Thank you
The organizers, for hosting a great competition.
The participants, for sharing their insights.
Funding
German Research Council (Deutsche Forschungsgemeinschaft, DFG) project
Multirelational Factorization Models.
Development of the MyMediaLite software was co-funded by the European
Commission FP7 project MyMedia under the grant agreement no. 215006.
Picture credits
by Michael Sauers, under Creative Commons by-nc-sa 2.0
http://www.flickr.com/photos/travelinlibrarian/223839049/
by Rob Starling, under Creative Commons by-sa 2.0
http://en.wikipedia.org/wiki/File:Air_New_Zealand_B747-400_ZK-SUI_at_LHR.jpg
Zeno Gantner et al., University of Hildesheim 15 / 15

17. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items
Numbers?
k error in %
“liked” contrast
320 5.52
480 5.08
“rated” contrast
320 5.15
480 4.87
Estimated error on validation split (not leaderboard).
Zeno Gantner et al., University of Hildesheim 16 / 15

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Zeno Gantner et al., University of Hildesheim 17 / 15

19. Bayesian Personalized Rankingfor Non-Uniformly Sampled Items Advertisement
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