Learning. R&N: ch 19, ch 20. Types of Learning. Supervised Learning - classification, prediction Unsupervised Learning – clustering, segmentation, pattern discovery Reinforcement Learning – learning MDPs, online learning. Supervised Learning.
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Learning
R&N: ch 19, ch 20
Need to provide H
with some “structure”
Explicit representationof hypothesis space H
any-color
dark
pale
black
blue
white
yellow
(r=1) v … v (r=10) v (r=J) v (r=Q) v (r=K) ANY-RANK(r)(r=1) v … v (r=10) NUM(r) (r=J) v (r=Q) v (r=K) FACE(r)(s=) v (s=) v (s=) v (s=) ANY-SUIT(s)(s=) v (s=) BLACK(s)(s=) v (s=) RED(s)
The extension of a hypothesis h is the set of objects that satisfies h
aa
na
ab
4a
nb
a
4b
n
4
a
a
n
b
f
r
1
10
j
k
…
…
aa
aa
na
ab
4a
nb
a
4b
n
…
…
1
4
4
k
G
We replace every hypothesis in S whose extension does not contain 4 by its generalization set
Now suppose that 4 is given as a positive example
S
aa
na
ab
Here, both G and S have size 1.
This is not the case in general!
4a
nb
a
4b
n
4
Generalization
set of 4
The generalization setof an hypothesis h is theset of the hypotheses that are immediately moregeneral than h
aa
na
ab
4a
nb
a
4b
n
Let 7 be the next (positive) example
4
aa
na
ab
4a
nb
a
4b
n
Let 7 be the next (positive) example
4
Specializationset of aa
aa
na
ab
nb
a
n
Let 5 be the next (negative) example
G and S, and all hypotheses in between form exactly the version space
ab
nb
a
n
No
Yes
Maybe
At this stage …
ab
nb
a
n
Do 8, 6, jsatisfy CONCEPT?
ab
nb
a
n
Let 2 be the next (positive) example
ab
nb
Let j be the next (negative) example
+ 4 7 2
–5 j
nb
NUM(r) BLACK(s) IN-CLASS([r,s])
Let us return to the
version space …
… and let 8 be the next (negative) example
ab
nb
a
The only most specific
hypothesis disagrees with
this example, so no
hypothesis in H agrees with all examples
n
Let us return to the
version space …
… and let jbe the next (positive) example
ab
nb
a
The only most general
hypothesis disagrees with
this example, so no
hypothesis in H agrees with all examples
n
Using the generalization sets of the hypotheses
This step was not needed in the card example
aa
na
ab
nb
a
n
k=1
k=6
x
likelihood
prior
we need:
how do we make diagnosis?
what is the structure of the corresponding BN?
my symptoms are: sneeze & cough, what isthe diagnosis?
where nx is shorthand for the counts of events in
training set
what is:
P(Allergy)?
P(Sneeze| Allergy)?
P(Cough| Allergy)?
many other smoothing
schemes…
where n is number of possible values for d
and e is assumed to have 2 possible values
Neural Networks
Perceptron Video
Output units
Hidden units
Input units