Frontiers in Applications of Machine Learning

1. Frontiers in Applicationsof Machine Learning Chris Bishop Microsoft Research http://research.microsoft.com/~cmbishop

2. A New Framework for ML • Bayesian formulation • Probabilistic graphical models • Deterministic approximate inference algorithms (based on local message-passing)

3. Directed Graphs General factorization:

4. Undirected Graphs Clique Maximal Clique

5. Factor Graphs

6. The Sum-Product Algorithm y f3(x,y) v w x f1(v,w) f2(w,x) z f4(x,z)

7. Messages: From Factors To Variables y f3(x,y) w x f2(w,x) z f4(x,z)

8. Messages: From Variables To Factors y f3(x,y) x f2(w,x) z f4(x,z)

9. VB / Loopy BP / EP Monte Carlo Approximate Inference Algorithms True distribution Local messagepassing on the graph

10. Illustration: Bayesian Ranking Ralf Herbrich Tom Minka Thore Graepel

11. Two Player Match Outcome Model s1 s2 p1 p2 y12

12. “Ordering with Draws” Likelihood 7 0.2 Player 2 wins 0.18 6 0.16 Players 1 and 2 draw 5 0.14 0.12 4 Probability density Performance of player 2 0.1 3 0.08 0.06 2 Players 1 and 2 draw Player2 wins 0.04 Player 1 wins Player 1 wins 1 0.02 0 0 0 1 2 3 4 5 6 7 -8 -6 -4 -2 0 2 4 Performance of player 1 d = s - s 1 2 1

13. Two Team Match Outcome Model s1 s2 s3 s4 t1 t2 y12 Skill of a team is the sum of the skills of its members

14. Multiple Team Match Outcome Model s1 s2 s3 s4 t1 t2 t3 y12 y23

15. Efficient Approximate Inference Gaussian Prior Factors s1 s2 s3 s4 Ranking Likelihood Factors t1 t2 t3 y12 y23

16. Convergence 40 35 30 25 Level 20 15 char (TrueSkill™) 10 SQLWildman (TrueSkill™) char (Elo) 5 SQLWildman (Elo) 0 0 100 200 300 400 Number of Games

17. Skill Beliefs and Skill Dynamics s1 s2 s1’ s2’ p1 p2 p1’ p2’ y12 y12 ’ Dynamics via a Markov chain on skills

18. Bayesian Ranking: TrueSkillTM • Xbox 360 Live: launched September 2005 • every 360 game uses TrueSkillTM to match players • 7.1 million active users, 2.5 million matches per day • First “planet-scale” application of Bayesian methods

19. http://research.microsoft.com/~cmbishop Further Reading A New Framework for Machine Learning, C. M. Bishop (2008) Invited paper at the 2008 World Congress on Computational Intelligence. Lecture Notes in Computer Science LNCS 5050, 1–24. Springer.