# Artificial Neural Networks 2

AI and Robotics

Oct 19, 2013 (4 years and 8 months ago)

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Artificial

Neural Networks 2

Morten Nielsen

Depertment

of Systems
Biology
,

DTU

Outline

Optimization procedures

Network training

back propagation

cross
-
validation

Over
-
fitting

examples

Neural network. Error estimate

I
1

I
2

w
1

w
2

Linear function

o

Neural networks

Gradient descent is based on the observation that
if the real
-
valued function F(x) is defined and
differentiable in a neighborhood of a point
a
, then
F(x) decreases fastest if one goes from
a

in the
direction of the negative gradient of F at
a
.

It follows that, if

for

> 0 a small enough number,

then F(b)<F(a)

Weights are changed in the opposite direction of the

I
1

I
2

w
1

w
2

Linear function

o

Hidden to output layer

Hidden to output layer

Hidden to output layer

Input to hidden layer

Input to hidden layer

Input to hidden layer

Summary

Or

Or

I
i
=X[0][k]

H
j
=X[1][j]

O
i
=X[2][i]

Can you do it your self?

v
22
=1

v
12
=1

v
11
=1

v
21
=
-
1

w
1
=
-
1

w
2
=1

h
2

H
2

h
1

H
1

o

O

I
1
=1

I
2
=1

What is the output (O) from the network?

What are the

w
ij

and

v
jk

values if the
target value is 0 and

=0.5?

Can you do it your self (

=0.5).

Has the error decreased?

v
22
=1

v
12
=1

v
11
=1

v
21
=
-
1

w
1
=
-
1

w
2
=1

h
2
=

H
2
=

h
1=

H
1
=

o=

O=

I
1
=1

I
2
=1

v
22
=
.

v
12
=

V
11
=

v
21
=

w
1
=

w
2
=

h
2
=

H
2
=

h
1
=

H
1
=

o=

O=

I
1
=1

I
2
=1

Before

After

Sequence encoding

Change in weight is linearly dependent on
input value

True

sparse encoding is therefore
highly inefficient

Sparse is most often encoded as

+1/
-
1 or 0.9/0.05

Training and error reduction

Training and error reduction

Training and error reduction

Size matters

A Network contains a very large
set of parameters

A network with 5 hidden
neurons predicting binding for
9meric peptides has more than
9x20x5=900 weights

Over fitting is a problem

Stop training when test
performance is optimal

Neural network training

years

Temperature

What is going on?

years

Temperature

Examples

Train on 500 A0201 and 60 A0101 binding data

Evaluate on 1266 A0201 peptides

NH=1: PCC = 0.77

NH=5: PCC = 0.72

Neural network training. Cross validation

Cross validation

Train on 4/5 of data

Test on 1/5

=>

Produce 5 different
neural networks each
with a different
prediction focus

Neural network training curve

Maximum test set performance

Most cable of generalizing

5 fold training

Which network to choose
?

5 fold training

How many folds?

Cross validation is always good!, but how
many folds?

Few folds
-
> small training data sets

Many folds
-
> small test data sets

Example from Tuesdays exercise

560 peptides for training

50 fold (10 peptides per test set, few data to stop
training)

2 fold (280 peptides per test set, few data to
train)

5 fold (110 peptide per test set, 450 per training
set)

Problems with 5fold cross validation

Use test set to stop training, and test set
performance to evaluate training

Over
-
fitting?

If test set is small yes

If test set is large no

Confirm using

true

5 fold cross
validation

1/5 for evaluation

4/5 for 4 fold cross
-
validation

Conventional 5 fold cross validation

True

5 fold cross validation

When to be careful

When data is scarce, the performance
obtained used

conventional

versus

true

cross validation can be very large

When data is abundant the difference is
small, and

true

cross validation might
even be higher than

conventional

cross
validation due to the ensemble aspect of
the

true

cross validation approach

Do hidden neurons matter?

The environment
matters

NetMHCpan

Context matters

FMIDWILDA YFAMYGE
KV
AHT
HVD
TLY
VR
YH
Y
YTWA
V
L
A
Y
TW
Y 0.89 A0201

FMIDWILDA YFAMYQE
NM
AHT
DAN
TLY
II
YR
D
YTWV
A
R
V
Y
RG
Y 0.08 A0101

DSDGSFFLY YFAMYGE
KV
AHT
HVD
TLY
VR
YH
Y
YTWA
V
L
A
Y
TW
Y 0.08 A0201

DSDGSFFLY YFAMYQE
NM
AHT
DAN
TLY
II
YR
D
YTWV
A
R
V
Y
RG
Y 0.85 A0101

Example

Summary

Gradient decent is used to determine the
updates for the synapses in the neural network

Some relatively simple math defines the

Networks without hidden layers can be solved on the
back of an envelope (SMM exercise)

Hidden layers are a bit more complex, but still ok

Always train networks using a test set to stop
training

Be careful when reporting predictive performance

Use

true

cross
-
validation for small data sets

And hidden neurons do matter (sometimes)

And some more stuff for the long
cold winter nights

Can it might be made differently?

Predicting accuracy

Reliability

Identification of position specific
receptor ligand interactions by use of
artificial neural network decomposition.
An investigation of interactions in the
MHC:peptide

system

Master these by
Frederik

Otzen

Bagger

Making sense of ANN weights

Making sense of ANN weights

Making sense of ANN weights

Making sense of ANN weights

Making sense of ANN weights

Making sense of ANN weights

Making sense of ANN weights