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CSE190a Fall 06
Parameter Estimation
Biometrics
CSE 190-a
Lecture 6
CSE190a Fall 06
Announcements
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Readings on E-reserves
•
Project proposal due today
Pattern
Classification
All materials in these slides were taken
from
Pattern Classification (2nd ed)
by R. O.
Duda, P. E. Hart and D. G. Stork, John Wiley
& Sons, 2000
with the permission of the authors and
the publisher
Chapter 3:
Maximum-Likelihood & Bayesian
Parameter Estimation (part 1)
z
Introduction
z
Maximum-Likelihood Estimation
z
Example of a Specific Case
z
The Gaussian Case: unknown
μ
and
σ
z
Bias
z
Pattern Classification
, Chapter 3
4
z
Introduction
z
Data availability in a Bayesian framework
z
We could design an optimal classifier if we knew:
z
P(
ω
i
) (priors)
z
P(x |
ω
i
) (class-conditional densities)
Unfortunately, we rarely have this complete
information!
z
Design a classifier from a training sample
z
No problem with prior estimation
z
Samples are often too small for class-conditional
estimation (large dimension of feature space!)
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Pattern Classification
, Chapter 3
5
z
A priori information about the problem
z
Normality of P(x |
ω
i
)
P(x |
ω
i
) ~ N(
μ
i
,
Σ
i
)
z
Characterized by 2 parameters
z
Estimation techniques
z
Maximum-Likelihood (ML) and the Bayesian
estimations
z
Results are nearly identical, but the approaches
are different
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