Frontiers in Applications of Machine Learning Chris Bishop Microsoft Research

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Presentation transcript:

Frontiers in Applications of Machine Learning Chris Bishop Microsoft Research

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

Directed Graphs General factorization:

Undirected Graphs Clique Maximal Clique

Factor Graphs

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)

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)

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)

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

Illustration: Bayesian Ranking Ralf Herbrich Tom Minka Thore Graepel

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

“Ordering with Draws” Likelihood Player 1 wins Players 1 and 2 draw Player2 wins s 1 - s 2 Probability density Performance of player 1 Performance of player 2 Player 1 wins Player 2 wins Players 1 and 2 draw d 1 =

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

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

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

Convergence Level Number of Games char (Elo) SQLWildman (Elo) char (TrueSkill ™ ) SQLWildman (TrueSkill ™ )

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’ ’

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

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.