Frontiers in Applications of Machine Learning

Frontiers in Applicationsof Machine Learning

Chris BishopMicrosoft Research

http://research.microsoft.com/~cmbishop

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

v w x

f1(v,w) f2(w,x)

y

f3(x,y)

z

f4(x,z)

Messages: From Factors To Variables

w x

f2(w,x)

y

f3(x,y)

z

f4(x,z)

Messages: From Variables To Factors

x

f2(w,x)

y

f3(x,y)

z

f4(x,z)

Approximate Inference Algorithms

True distribution Monte Carlo VB / Loopy BP / EP

Local messagepassing on the graph

Illustration: Bayesian Ranking

Ralf HerbrichTom MinkaThore Graepel

Two Player Match Outcome Model

y12y12

p1

p1

p2

p2

s1s1 s2s2

“Ordering with Draws” Likelihood

-8 -6 -4 -2 0 2 40

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Player 1 wins

Pla

yers

1 a

nd 2

dra

w

Player2 wins

s1 - s2

Pro

ba

bili

ty d

en

sity

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

Performance of player 1

Pe

rfo

rma

nce

of

pla

yer

2

Player 1 wins

Player 2 wins

Player

s 1 a

nd 2

dra

w

d1 =

Two Team Match Outcome Model

• Skill of a team is the sum of the skills of its members

y1

2

y1

2

t1t1 t2t2

s2s2 s3s3s1s1 s4s4

Multiple Team Match Outcome Model

s1s1 s2s2 s3s3 s4s4

t1t1

y12y12

t2t2 t3t3

y23y23

Efficient Approximate Inference

s1s1 s2s2 s3s3 s4s4

t1t1

y1

2

y1

2

t2t2 t3t3

y2

3

y2

3

Gaussian Prior Factors

Ranking Likelihood Factors

Convergence

0

5

10

15

20

25

30

35

40L

eve

l

0 100 200 300 400

Number of Games

char (Elo)

SQLWildman (Elo)

char (TrueSkill™)

SQLWildman (TrueSkill™)

Skill Beliefs and Skill Dynamics

Dynamics via a Markov chain on skills

y1

2

y1

2

p1p1 p2p2

y1

2

y1

2

p1

’p1

’p2

’p2

’

s1s1 s2s2 s1’s1’ s2’s2’

’

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

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.