10/16/2009
1
Statistical Learning Theory
Example: Smart Investing
Task: Pick stock analyst based on past performance.
Experiment:
–
Have analyst predict “next day up/down” for 10 days.
–
Pick analyst that makes the fewest errors.
Situation 1:
–
1 stock analyst {A1}, A1 makes 5 errors
Situation 2
Situation 2:
–
3 stock analysts {A1,B1,B2}, B2 best with 1 error
Situation 3:
–
1003 stock analysts {A1,B1,B2,C1,…,C1000},
C543 best with 0 errors
Which analysts are you most confident in:
A1, B2, or C543?
Outline
Questions in Statistical Learning Theory:
–
How good is the learned rule after
n
examples?
–
How many examples do I need before the learned rule is accurate?
–
What can be learned and what cannot?
–
Is there a universally best learning algorithm?
In particular, we will address:
What is the true error of
h
if we only know the training error of
h
?
–
Finite hypothesis spaces and zero training error
–
(Finite hypothesis spaces and non
‐
zero training error)
Game: Randomized 20
‐
Questions
Game: 20
‐
Questions
–
I think of object
f
–
For
i
= 1 to 20
•
You get to ask 20 yes/no questions about
f
and I have to answer
truthfully
–
You make a guess
h
–
You win, if
f=h
Game: Randomized 20
‐
Questions
–
I pick function
f
H
, where f
: X
{
‐
1,+1}
–
For
i
= 1 to 20
•
World delivers instances
x
X
with probability
P(x)
and I have to tell
you
f(x)
–
You form hypothesis
h
H
trying to guess my
f
H
–
You win if
f(x)=h(x)
with probability at least
1
‐ε
for
x
drawn
according to
P(x).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 JOACHIMS
 Artificial Intelligence, Machine Learning, Dtrain, hypothesis space, training error, statistical learning theory

Click to edit the document details