1. Collaborative filtering applied to real- time bidding

2. Summary Context : real-time reserve price prediction Reserve price prediction problem Simple benchmark predictors High-dimensional sparse linear regression Setup of the model and online estimation Results on a test set Advanced methods (work in progress) Online matrix factorization using Alternating Least Squares approach Collaborative Kalman filter

3. Context : real-time reserve price prediction 3

4. 2 nd price auction mechanism Buyers send bids Publisher sets a reserve price (the auction won’t be sold below) Buyer with the highest bid wins the auction and displays its ad, paying the maximum between the second highest bid and the reserve price AlephD provides its clients real-time reserve price prediction engine Before each auction, we know the user and the ad placement (tag) The prediction is performed using a random forest (the estimation of the random forest is not detailed here)

5. Context : real-time reserve price prediction Predictors of the winning bid are used as features in the reserve price prediction model At that time, we use some simple user-based, tag-based and user-tag-based predictors Last bid, last-last bid Exponentially-weighted moving average of the bid

6. Context : real-time reserve price prediction We define a simple predictor which will be used as benchmark to assess the performance of advanced approaches Bid prediction is performed by a waterfall of simple predictors at different granularity levels (if it exists) Otherwise : Otherwise : 0

7. Context : real-time reserve price prediction These simple predictors have drawbacks Need to store features for each user, each tag and each user-tag User-tag features are highly predictive, but often non-defined (first observation for this user-tag) User-features are less predictive (aggregate bids on different tags with different worths) Collaborative filtering methods may be used to build user-specific and tag-specific features Bid prediction is obtained by combining user features and tag features

8. High-dimensional sparse linear regression 8

9. Sparse linear regression Notations Set of users : Set of tags : Model The log-bid is the sum of a user bias and a tag bias The model can be expressed as a sparse linear regression Loss function Dataset : Observation (time, user, tag, log-bid) :

10. Sparse linear regression We introduce exponential weights Old observations are forgotten : Online estimation using Alternating Least Squares User biases are estimated when fixing tag biases, and reciprocally The biases can be updated online : after each observation, corresponding user and tag biases numerators and denominators are updated and kept in memory

11. Sparse linear regression This model is tested on a real dataset 7 days of data 120 million auctions 1750 tags, 14 million users, 47 million user-tags

12. Advanced methods 12

13. Matrix factorization using Alternating Least Squares Rank of the factorization : Regul. parameters : Notations User feature vector : Tag feature vector : Users and tags features matrix : Model The log-bid is the sum of user bias, tag bias and cross terms Loss function Non-convex optimization problem

14. Matrix factorization using Alternating Least Squares Online estimation We introduce exponential weights : Iterative estimation of users and tags features : Users and tags features vectors can be updated online by keeping in memory one k X k matrix and one k X 1 vector

15. Matrix factorization using Alternative Least Squares The regularization parameters are updated using SGD Means are directly updated Covariance matrix is decomposed and its squared root is updated :

16. Collaborative Kalman filter Description of a Kalman filter A Kalman filter is described by the following dynamics Update formulas on mean and covariance matrix of the hidden state

17. Collaborative Kalman filter Collaborative kalman filtering is performed using two coupled Kalman filters One Kalman filter uses user features as hidden state, and the other uses tag features as hidden state

18. REAL TIME PREDICTION HAS A NAME contact@alephd.com