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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:

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

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

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

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

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

Online RMF Stochastic Gradient Descent RMF Dual Averaging RMF

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

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

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

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

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

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

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

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

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]

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

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

Thanks! Questions?