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Frontiers in Applications of Machine Learning. Chris Bishop Microsoft 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). - PowerPoint PPT Presentation
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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.
