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Руководство по эксплуатации;pdf

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Review of Leture 17
•
Sampling bias
Hi
•
Oam's Razor
The simplest model that
ts the data is also the
most plausible.
P(x)
testing
training
x
•
Hi
Data snooping
Cumulative Prot %
30
snooping
20
10
omplexity of h ←→ omplexity of H
unlikely event ←→ signiant if it happens
0
-10
0
no snooping
100
200
300
Day
400
500
Learning From Data
Yaser S. Abu-Mostafa
California Institute of Tehnology
Leture 18:
Epilogue
Sponsored by Calteh's Provost Oe, E&AS Division, and IST
•
Thursday, May 31, 2012
Outline
•
The map of mahine learning
•
Bayesian learning
•
Aggregation methods
•
Aknowledgments
AM
L
Creator: Yaser Abu-Mostafa - LFD Leture 18
2/23
It's a jungle out there
semi−supervised learning
stochastic gradient descent
overfitting
Gaussian processes
distribution−free
collaborative filtering
deterministic noise
linear regression
VC dimension
nonlinear transformation
decision trees
data snooping
sampling bias
Q learning
SVM
learning curves
mixture of expe
neural networks
no free
training versus testing
RBF
noisy targets
Bayesian prior
active learning
linear models
bias−variance tradeoff
weak learners
ordinal regression
logistic regression
data contamination
cross validation
ensemble learning
types of learning
xploration versus exploitation
error measures
is learning feasible?
clustering
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Creator: Yaser Abu-Mostafa - LFD Leture 18
regularization
kernel methods
hidden Markov mod
perceptrons
graphical models
soft−order constraint
weight decay
Occam’s razor
Boltzmann mach
3/23
The map
THEORY
TECHNIQUES
models
VC
bias−variance
complexity
linear
methods
supervised
regularization
neural networks
SVM
nearest neighbors
bayesian
PARADIGMS
RBF
gaussian processes
unsupervised
validation
reinforcement
aggregation
active
input processing
online
SVD
graphical models
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
4/23
Outline
•
The map of mahine learning
•
Bayesian learning
•
Aggregation methods
•
Aknowledgments
AM
L
Creator: Yaser Abu-Mostafa - LFD Leture 18
5/23
Probabilisti approah
Hi
Extend probabilisti role to all omponents
P (D | h = f )
How about
deides whih
P (h = f | D)
?
h
UNKNOWN TARGET DISTRIBUTION
P(y |
x)
target function f: X
Y
UNKNOWN
INPUT
DISTRIBUTION
plus noise
P( x )
(likelihood)
x1 , ... , xN
DATA SET
D = ( x1 , y1 ), ... , ( xN , yN )
x
g ( x )~
~ f (x )
LEARNING
ALGORITHM
FINAL
HYPOTHESIS
g: X Y
A
HYPOTHESIS SET
H
Hi
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
6/23
The prior
P (h = f | D)
requires an additional probability distribution:
P (D | h = f ) P (h = f )
P (h = f | D) =
∝ P (D | h = f ) P (h = f )
P (D)
P (h = f )
is the
P (h = f | D)
prior
is the
posterior
Given the prior, we have the full distribution
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
7/23
Example of a prior
Consider a pereptron:
A possible prior on
w:
h is
Eah
determined by
wi
w = w0, w1, · · · , wd
is independent, uniform over
[−1, 1]
This determines the prior over
Given
D,
we an ompute
h
-
P (h = f )
P (D | h = f )
Putting them together, we get
P (h = f | D)
∝ P (h = f )P (D | h = f )
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Creator: Yaser Abu-Mostafa - LFD Leture 18
8/23
A prior is an assumption
Even the most neutral prior:
Hi
x
is unknown
x
is random
P(x)
−1
−1
1
1
x
Hi
The true equivalent would be:
Hi
x
is unknown
x
is random
δ(x−a)
−1
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
1
−1
a
1
x
Hi
9/23
If we knew the prior
...
we ould ompute
P (h = f | D)
for every
=⇒
h∈H
we an nd the most probable
we an derive
E(h(x))
we an derive the
h given the data
for every
x
error bar for every x
we an derive everything in a prinipled way
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
10/23
When is Bayesian learning justied?
1. The prior is
valid
trumps all other methods
2. The prior is
irrelevant
just a omputational atalyst
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
11/23
Outline
•
The map of mahine learning
•
Bayesian learning
•
Aggregation methods
•
Aknowledgments
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
12/23
What is aggregation?
Combining dierent solutions
Hi
h 1 , h2 , · · · , hT
that were trained on
D:
Hi
Regression: take an average
Classiation: take a vote
a.k.a.
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
ensemble learning
and
boosting
13/23
Dierent from 2-layer learning
Hi
In a 2-layer model, all units learn
In aggregation, they learn
training data
jointly:
Learning
Algorithm
independently then get ombined:
Hi
Hi
training data
Learning
Algorithm
Hi
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
14/23
Two types of aggregation
1. After the fat: ombines existing solutions
Example. Netix teams merging
blending
2. Before the fat: reates solutions to be ombined
Example. Bagging - resampling D
Hi
training data
Learning
Algorithm
Hi
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
15/23
Deorrelation - boosting
Create
h 1 , · · · , ht , · · ·
sequentially: Make
ht
deorrelated with previous
h's:
Hi
training data
Learning
Algorithm
Hi
Emphasize points in
Choose weight of
AM
L
Creator: Yaser Abu-Mostafa - LFD Leture 18
ht
D
that were mislassied
based on
E (ht)
in
16/23
Blending - after the fat
For regression,
h 1 , h2 , · · · , hT
−→
g(x) =
T
X
αt ht(x)
t=1
Prinipled hoie of
αt's:
minimize the error on an aggregation data set
Some
αt's
pseudo-inverse
an ome out negative
Most valuable
ht
in the blend?
Unorrelated ht's help the blend
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
17/23
Outline
•
The map of mahine learning
•
Bayesian learning
•
Aggregation methods
•
Aknowledgments
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
18/23
Course ontent
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Professor
Malik Magdon-Ismail, RPI
Professor
Hsuan-Tien Lin, NTU
Creator: Yaser Abu-Mostafa - LFD Leture 18
19/23
Course sta
Carlos Gonzalez (Head TA)
Ron Appel
Costis Sideris
Doris Xin
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Creator: Yaser Abu-Mostafa - LFD Leture 18
20/23
Filming, prodution, and infrastruture
Leslie Maxeld and the AMT sta
Rih Fagen and the IMSS sta
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Creator: Yaser Abu-Mostafa - LFD Leture 18
21/23
Calteh support
IST -
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Mathieu Desbrun
E&AS Division -
Ares Rosakis
Provost's Oe -
Ed Stolper
Creator: Yaser Abu-Mostafa - LFD Leture 18
and
and
Mani Chandy
Melany Hunt
22/23
Many others
Calteh TA's and sta members
Calteh alumni and Alumni Assoiation
Colleagues all over the world
AM
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Creator: Yaser Abu-Mostafa - LFD Leture 18
23/23
To the fond memory of
Faiza A. Ibrahim
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