1. Frontiers in Applications of 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 vwx f1(v,w)f1(v,w)f2(w,x)f2(w,x) y f3(x,y)f3(x,y) z f4(x,z)f4(x,z)

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

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

9. Approximate Inference Algorithms True distributionMonte Carlo VB / Loopy BP / EP Local message passing on the graph

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

11. Two Player Match Outcome Model y 12 p1p1 p1p1 p2p2 p2p2 s1s1 s1s1 s2s2 s2s2

12. “Ordering with Draws” Likelihood -8-6-4-2024 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Player 1 wins Players 1 and 2 draw Player2 wins s 1 - s 2 Probability density 01234567 0 1 2 3 4 5 6 7 Performance of player 1 Performance of player 2 Player 1 wins Player 2 wins Players 1 and 2 draw d 1 =

13. Two Team Match Outcome Model Skill of a team is the sum of the skills of its members y 12 t1t1 t1t1 t2t2 t2t2 s2s2 s2s2 s3s3 s3s3 s1s1 s1s1 s4s4 s4s4

14. Multiple Team Match Outcome Model s1s1 s1s1 s2s2 s2s2 s3s3 s3s3 s4s4 s4s4 t1t1 t1t1 y 12 t2t2 t2t2 t3t3 t3t3 y 23

15. Efficient Approximate Inference s1s1 s1s1 s2s2 s2s2 s3s3 s3s3 s4s4 s4s4 t1t1 t1t1 y 12 t2t2 t2t2 t3t3 t3t3 y 23 Gaussian Prior Factors Ranking Likelihood Factors

16. Convergence 0 5 10 15 20 25 30 35 40 Level 0100200300400 Number of Games char (Elo) SQLWildman (Elo) char (TrueSkill ™ ) SQLWildman (TrueSkill ™ )

17. Skill Beliefs and Skill Dynamics Dynamics via a Markov chain on skills y 12 p1p1 p1p1 p2p2 p2p2 p1’p1’ p1’p1’ p2’p2’ p2’p2’ s1s1 s1s1 s2s2 s2s2 s1’s1’ s1’s1’ s2’s2’ s2’s2’ ’

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

19. Further Reading http://research.microsoft.com/~cmbishop 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.