1. Online Learning for Collaborative Filtering
Guang Ling, Haiqin Yang, Irwin King, Michael Lyu
Presented by Guang LING

2. Outline Introduction PMF and RMF Online PMF and Online RMF
Experiments and Results
Conclusion and Future Work

3. Introduction We face unprecedentedly large amount of choice!
Search Vs. Recommend

4. Introduction Recommender system emerged Content based filtering
Analyze item content
Collaborative filtering
Rating based

5. Introduction Collaborative filtering Allow user to rate items
Infer user’s taste and item’s feature based on ratings
Match user’s preferences with item’s features

6. Introduction Various methods have been developed
Memory based
User based
Item based
Model based
PMF, RMF
PLSA, PLPA
So, what is the problem? I1 I2 I3 I4 U1 1 5 4 ? U2 2 U3

7. Introduction Unrealistic assumptions Reality All ratings are available
There will be no new rating
Data set are small enough to be handled in main memory
Reality
Ratings are collected over time
New ratings are received constantly
Huge data set cannot be easily handled

8. Introduction We propose online CF algorithm that
Obviate the need to hold all data
Make incremental changes based solely on new rating
Scale linearly with the number of ratings
Extra features
Command explicit regularization effect

9. PMF and RMF Matrix factorization models Factor R into U and V Minimize
Square loss: PMF
Cross entropy: RMF
No. users
No. items

10. PMF Conditional distribution over observed ratings:
Spherical Gaussian priors on user and movie feature vectors:
Maximize posterior:

11. PMF Maximize Equivalent to minimize the following loss:
Using gradient descent to minimize loss:
Squared loss
Regularization

12. RMF Top one probability Minimize cross entropy
The probability that an item i being ranked on top
Minimize cross entropy
Cross entropy measures the divergence between two distributions
Un-normalized KL-divergence

13. RMF Model loss is defined as: Using gradient descent to minimize:
Cross entropy
Regularization

14. Online PMF We propose two online algorithms for PMF
Stochastic gradient descent
Adjust model stochastically for each observation
Regularized dual averaging
Maintain an approximated average gradient
Solve an easy optimization problem at each iteration

15. Stochastic Gradient Descent PMF
Recall the loss function for PMF
Squared loss can be dissected and associated with each observation triplet
Update model using gradient of this loss:

16. Regularized Dual Averaging PMF
Maintain the approximated average gradient
Previous gradient
Gradient due to new observation
Number of items rated by u

17. Regularized Dual Averaging PMF
Solve the following optimization problem to obtain
New user feature vector
New item feature vector

18. Online RMF
Similar to online PMF, we propose two online algorithms for RMF
Stochastic Gradient Descent
Regularized Dual Averaging
However, the challenge is
Loss function cannot be easily dissected

19. Online RMF Recall the loss function for RMF
When a new observation is revealed
Loss due to new item
Decay of previous items

20. Online RMF We approximate the gradient by Decay previous gradient
Gradient with respect to new item
Decay previous gradient
Gradient with respect to new item

21. Online RMF
Stochastic Gradient Descent RMF
Dual Averaging RMF

22. Experiments and Results
Online Vs. Batch algorithms
Performance under different settings
Sensitivity analysis of parameters
Scalability to large dataset

23. Evaluation Metric Root Mean Square Error(RMSE)
The lower the better
Normalized Discounted Cumulative Gain(NDCG)
The higher the better

24. Online Vs. Batch algorithms
We conduct experiments on real life data set
MovieLens: movie rating data set
6,040 users
3,900 movies
1,000,209 ratings
4.25% of user-item rating matrix is known
Simulate three settings
T1: 10% training, 90% testing
T5: 50% training, 50% testing
T9: 90% training, 10% testing

25. Online Vs. Batch algorithms
Shown below is the PMF result T1 T5 T9

26. Online Vs. Batch algorithms
Shown below is the RMF result T1 T5 T9

27. Impact of in PMF denote the regularization parameter Observation
Fewer training data needs more regularization
Results are quite sensitive to regularization
SGD-PMF
DA-PMF

28. Impact of in RMF denote the regularization parameter Observation
Fewer training data needs more regularization
SGD-RMF
RDA-RMF

29. Impact of learning rate
We use to denote the learning rate
It is used in stochastic gradient descent algorithms only
SGD-RMF
SGD-PMF

30. Scalability to large dataset
Yahoo! Music dataset
Largest CF dataset publicly available
252,800,275 ratings
1,000,990 users
624,961 items
Rating value range [0, 100]

31. Scalability to large dataset
Experiment environment
Linux workstation (Xeon Dual Core 2.4 GHz, 32 GB RAM)
Batch PMF: 8 hours for 120 iteration
Online PMF: 10 minutes T1 T5

32. Conclusion and Future Work
We proposed online CF algorithms
Perform comparable or even better than corresponding batch algorithms
Scales linearly with number of ratings
Adjust model incrementally given new observation
Future Work
Theoretical bound for convergence rate
Find better approximation for average gradient of RMF

33. Thanks!
Questions?