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Introduction to Ensemble Learning Featuring Successes in the Netflix Prize Competition Todd Holloway Two Lecture Series for B551 November 20 & 27, 2007 Indiana University
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
1-Slide Intro to Supervised Learning We want to approximate a function, Find a function  h  among a fixed subclass of functions for which the error  E ( h ) is minimal, Given examples, Independent of  h The distance from of  f Variance of the predictions
[object Object],[object Object],[object Object],[object Object],[object Object],Bias and Variance
Bias and Variance from  Elder, John.  From Trees to Forests and Rule Sets - A Unified Overview of Ensemble Methods.  2007. ,[object Object],[object Object],[object Object]
Definition ,[object Object],[object Object]
Teaser:  How good are ensemble methods? Let’s look at the Netflix Prize Competition…
[object Object],[object Object],[object Object],[object Object],[object Object],Began October 2006
[object Object],[object Object]
from  http://www.research.att.com/~volinsky/netflix/ However, improvement slowed…
Today, the top team has posted a 8.5% improvement. Ensemble methods are the best performers…
“ Thanks to Paul Harrison's collaboration, a simple mix of our solutions improved our result from 6.31 to 6.75” Rookies
“ My approach is to  combine the results of many methods  (also two-way interactions between them) using linear regression on the test set. The best method in my ensemble is regularized SVD with biases, post processed with kernel ridge regression” Arek Paterek http://rainbow.mimuw.edu.pl/~ap/ap_kdd.pdf
“ When the predictions of  multiple  RBM models and  multiple  SVD models are linearly combined, we achieve an error rate that is well over 6% better than the score of Netflix’s own system.” U of Toronto http://www.cs.toronto.edu/~rsalakhu/papers/rbmcf.pdf
Gravity home.mit.bme.hu/~gtakacs/download/ gravity .pdf
“ Our common team blends the result of team Gravity and team Dinosaur Planet.” Might have guessed from the name… When Gravity and  Dinosaurs Unite
And, yes, the top team which is from AT&T… “ Our final solution (RMSE=0.8712) consists of blending 107 individual results. “ BellKor / KorBell
Some Intuitions on Why Ensemble Methods Work…
Intuitions ,[object Object],[object Object],[object Object],[object Object],See  Domingos, P. Occam’s two razors: the sharp and the blunt.  KDD.  1998.
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Intuitions
Strategies ,[object Object],[object Object],[object Object],[object Object]
Boosting ,[object Object],[object Object],[object Object],[object Object]
AdaBoost Algorithm 1. Initialize Weights 2. Construct a classifier.  Compute the error. 3. Update the weights, and repeat step 2. … 4. Finally, sum hypotheses…
Classifications (colors) and  Weights (size) after  1 iteration Of AdaBoost 3 iterations 20 iterations from  Elder, John.  From Trees to Forests and Rule Sets - A Unified Overview of Ensemble Methods.  2007.
AdaBoost ,[object Object],[object Object],[object Object],[object Object],[object Object]
BrownBoost ,[object Object],[object Object]
Bagging (Constructing for Diversity) ,[object Object],[object Object],[object Object],Leo Breiman
Random forests ,[object Object],[object Object]
Random forests ,[object Object],[object Object],[object Object],[object Object],Calculate the best split based on these.
Breiman, Leo (2001). "Random Forests". Machine Learning 45 (1), 5-32
Questions / Comments?
Sources ,[object Object],[object Object],[object Object],[object Object],[object Object]

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ensemble learning

  • 1. Introduction to Ensemble Learning Featuring Successes in the Netflix Prize Competition Todd Holloway Two Lecture Series for B551 November 20 & 27, 2007 Indiana University
  • 2.
  • 3. 1-Slide Intro to Supervised Learning We want to approximate a function, Find a function h among a fixed subclass of functions for which the error E ( h ) is minimal, Given examples, Independent of h The distance from of f Variance of the predictions
  • 4.
  • 5.
  • 6.
  • 7. Teaser: How good are ensemble methods? Let’s look at the Netflix Prize Competition…
  • 8.
  • 9.
  • 10. from http://www.research.att.com/~volinsky/netflix/ However, improvement slowed…
  • 11. Today, the top team has posted a 8.5% improvement. Ensemble methods are the best performers…
  • 12. “ Thanks to Paul Harrison's collaboration, a simple mix of our solutions improved our result from 6.31 to 6.75” Rookies
  • 13. “ My approach is to combine the results of many methods (also two-way interactions between them) using linear regression on the test set. The best method in my ensemble is regularized SVD with biases, post processed with kernel ridge regression” Arek Paterek http://rainbow.mimuw.edu.pl/~ap/ap_kdd.pdf
  • 14. “ When the predictions of multiple RBM models and multiple SVD models are linearly combined, we achieve an error rate that is well over 6% better than the score of Netflix’s own system.” U of Toronto http://www.cs.toronto.edu/~rsalakhu/papers/rbmcf.pdf
  • 16. “ Our common team blends the result of team Gravity and team Dinosaur Planet.” Might have guessed from the name… When Gravity and Dinosaurs Unite
  • 17. And, yes, the top team which is from AT&T… “ Our final solution (RMSE=0.8712) consists of blending 107 individual results. “ BellKor / KorBell
  • 18. Some Intuitions on Why Ensemble Methods Work…
  • 19.
  • 20.
  • 21.
  • 22.
  • 23. AdaBoost Algorithm 1. Initialize Weights 2. Construct a classifier. Compute the error. 3. Update the weights, and repeat step 2. … 4. Finally, sum hypotheses…
  • 24. Classifications (colors) and Weights (size) after 1 iteration Of AdaBoost 3 iterations 20 iterations from Elder, John. From Trees to Forests and Rule Sets - A Unified Overview of Ensemble Methods. 2007.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30. Breiman, Leo (2001). "Random Forests". Machine Learning 45 (1), 5-32
  • 32.

Editor's Notes

  1. Matrix Factorization-SVD (MF), K-Nearest neighbor (NB), Clustering (CL).
  2. KDD 1998 Best paper award went to an argument against Ockham’s razor. Complexity is not related to overfiting. Mention use of Ockham’s razor in Naïve Bayes.
  3. Note: if weights can’t be used directly, they can be used to generate a weighted sample of the example. Point is that the construction of a classifier
  4. Note after 1 iteration the step classes of a single decision tree.
  5. Originally rejected (journal of statistics). Can also create multiple NN using different random initial weights for diversity. Owns trademark on Random forests.
  6. Grow trees deep to avoid bias.