Utku
Sirin
a
,
Utku
Erdogdu
a
,
Faruk
Polat
a
,
Mehmet
Tan
b
, and
Reda
Alhajj
c
a
Department of Computer Engineering
Middle East Technical University
Ankara, Turkey
b
Department of Computer Engineering
TOBB University of Economics and Technology
Ankara, Turkey
c
Department of Computer Science
University of Calgary
Alberta, Canada
IEEE 11
th
International Conference on Machine Learning and Applications
December 13
th
, 2012
Outline
Background and Motivation
Multi

Model Framework & Evaluation Metrics
Generative Models
Probabilistic Boolean Networks
Ordinary Differential Equations
Experimental Evaluation
Conclusion & Future Works
Background & Motivation
Gene expression data is the main source of
information for many applications in computational
systems biology
However, the datasets suffer from the problem of
skewed data matrices
There are thousands of genes and just several tens of
samples
So few samples lower the confidence level of any
computational method significantly
Background & Motivation
How to enrich available gene expression datasets confidently ?
There are several tools generating synthetic gene expression
samples, such as
GeneNetWeaver
(
Schaffter
et. al., 2011)
or
SynTReN
(
Bulcke
et. al.,2006)
However, all of them use single model such as ordinary
differential/stochastic equations or
boolean
networks, which
makes them to model gene regulation restrictively
Our idea is to integrate different machine learning
techniques into single unified multi

model framework so
that we can benefit from different models concurrently
Thereby, we aimed to generate synthetic gene expression samples
more confidently and mitigate the low sample size problem for
gene expression datasets by producing high qualitative data
Multi

Model Gene Regulation Model
Construct different gene
regulation models from
available gene expression
samples
Sample from each of them
equally and pool the generated
samples
Select the
best
samples from
the pool and output them
Each model contributes its own
characteristics and we utilize
all of them concurrently
How to select
the best
samples?
Original Gene Expression Data
Model 1
Model N
…
k Samples
k Samples
Multi

Objective Selection
…
k Samples
Evaluation Metrics
After having generated samples from each model, it is very important to select the most qualitative
samples to output. Otherwise our method would be impractical
To decide on the quality of generated samples, we defined three metrics measuring quality of the
generated samples from different aspects:
Compatibility, Diversity and Coverage.
Compatibility
How much close the generated samples to the original samples?
To assure that the generated samples are similar to the original samples
Mean of the
euclidean
distances of each generated sample to the original samples
Diversity
How much different the generated samples from the original samples?
To assure that the generated samples are not the
duplicate
of the original samples but carry
always new information
We calculate the entropy value of each sample in the dataset and sum the differences. For each
sample, we add the new sample to the original dataset and again sum the differences of entropy
values. The diversity value is the ratio of the latter value to the former value for that sample
Coverage
How much the generated samples cover the sample space?
To assure to cover the sample space as much as possible
Mean of the
euclidean
distances of each generated sample to the already generated samples
Evaluation Metrics, Multi

Objective Selection
After calculating three metric values, we have a vector of metric results
for each sample
To select the best samples among the generated samples we applied
multi

objective selection mechanism to the vector of metric results
using strict dominance rule
Strict dominance rule: A sample is more qualitative than some other
sample, if all of its metric results are greater than that specific sample.
We sort all of the generated samples multi

objectively and select the
best
k
ones to output
Non

dominant samples are grouped together and selected randomly
Generative Models
In our framework there may be any number of gene
regulation models
The important point is the models should be least
dependent so that the generated gene expression samples
cover different parts of sample space
In this study we representatively select two generative
models for our multi

model data generation framework
Probabilistic Boolean Networks (PBNs)
(
Shmulevich
et. al.,
2002)
Ordinary Differential Equations (ODEs)
(Bansal et. al., 2006)
Probabilistic Boolean Networks (PBNs)
Probabilistic versions of Boolean Networks (
Kauffman
,
1993
)
Each gene is either ON of OFF (Binary Values)
Each gene is associated with a set of
boolean
functions
and each
boolean
function is associated with a set of
genes (variables)
Each set of
boolean
function is also associated with a
probability distribution so that each time step the
value of each gene is determined by a
boolean
function
which is selected according to its probability value
Probabilistic Boolean Networks (PBNs)
g
n
g
1
g
2
…
g
n
g
1
g
2
…
Time t
Time t+1
2
3
1
2
5
4
1
1
g
g
g
f
g
g
g
f
}
30
.
0
,
45
.
0
,
25
.
0
{
},
,
,
{
1
3
2
1
1
P
f
f
f
F
6
4
2
3
g
g
g
f
We construct the PBNs by adapting the MATLAB PBN Toolbox
Then, we run the PBN and generate synthetic gene expression
samples to feed into our multi

model framework
Ordinary Differential Equations (ODEs)
One of the oldest methods to model gene regulation
Each gene’s expression value is associated with other gene’
s
expression values through a
regulation matrix presented as A below
The differentiation of each gene expression value is determined by a linear combination
of the expression values of all other genes
There are many algorithms modeling gene regulation with ODEs
“Network Identification by Multiple Regression” (NIR), applying multiple linear regression
(
Gardner
et. al., 2003)
“Differential Equation

based Local Dynamic Bayesian Network” (DELDBN), combining
differential equations and dynamic
bayesian
networks
(
Li
et. al., 2011)
In our study, we use the algorithm “Time Series Network Identification” (TSNI) due to its
prevailing properties to the other methods
(Bansal et. al., 2006)
It can handle both time series and steady state gene expression
data
sets
It can easily be applied to large datasets due to its utilization of principal component
analysis
It can determine external perturbation automatically from the data
Ax
dt
dx
Ordinary Differential Equations (ODEs)
)
(
)
(
.
k
k
t
U
B
t
X
A
X
The only unknowns are A and B matrices
If we write the equation by concatanating the known and unknown matrices
Differentiation
Term
Regulation
Matrix
Perturbation
Matrix
Expression
Values
Perturbation
Values
KNOWN !
UNKNOWN
Ordinary Differential Equations (ODEs)
It is easy to find the unknown matrix H in
this schema
However, the number of equations should
be greater than the number of variables,
which may not hold always.
At this point, TSNI applies Principal
Component Analysis (PCA) to the Y matrix
and reduce the dimension of the matrix Y
and solve the equation.
Then, the unknown matrices A and B can
be obtained easily
By running the ODE model we generated,
it is easy to produce synthetic gene
expression samples to feed into our multi

model framework
U
X
Y
B
A
H
Y
H
X
]
[
.
Experimental Evaluation, Datasets
We evaluated our framework using three different real life
biological datasets
The first dataset is the gene expression profile of metastatic
melanoma
cells (Bittner
et. al.
, 2000
)
It originally includes 8067 genes and 31 samples. We have used its
reduced from composed of 7 most important genes and 31 samples
(
Datta
et. al., 2003
)
The second dataset is the gene expression data set of
yeast
cell cycle (
Spellman
et. al., 1998
)
It includes 25 genes and 77 samples
The third dataset is
siRNA
disruptant
dataset in human
umbilical vein endothelial cells (
HUVECs
) (
Hurley
et. al.,
2011
)
It includes 379 genes and
400 samples
Newly published very useful source for our model
Experimental Evaluation, Results
We evaluated our framework based on the
three
metrics we defined in
two different settings
In the first setting, we used the melanoma and yeast datasets without
partitioning the datasets into training and testing sets
This is because the melanoma and yeast datasets have relatively less
number of samples such that dividing them into training and testing
sets would be meaningless
Then, we used the yeast and HUVECs datasets by partitioning them
into training and testing datasets in the second setting. Here, we have
enough number of samples to divide. HUVECs dataset has
400
samples
.
In the first set of experiments, the results are always suspicious since
training and testing sets are same. The second set of experiments
provides to see the picture clearer and increase the confidence level of
our framework
Note that because yeast dataset is middle

sized, we used it both in our
first and second sets of experiments to see the results comparatively
Figure 2: Diversity
In this set of experiments, we increased the number of generated samples as 10, 20, …, 500 by our
framework and checked the mean of the metric results
w.r.t
training samples.
Figure 1 and 2 shows the compatibility and diversity results. Compatibility results show that the
data generated by our framework converges to the original dataset since it gets closer and closer
to original dataset
The diversity results on the other
hand say
that although generated samples are getting closer to
the original dataset, they always carry new information with respect to the original dataset.
That means, our multi

model gene expression data generation framework always produces
qualitative samples which are both very close to the original dataset and bringing new
information
For melanoma dataset, newly generated samples bring almost % 30 new information , which is a
very good result
Experimental Evaluation, Results, Setting #1
Figure 1: Compatibility
Experimental Evaluation, Results, Setting #1
Coverage results concludes our first set of experiments
As seen from Figure 3, coverage results are decreasing for both datasets. This is
consistent with the compatibility results. Because system converges to generate
similar results to the original dataset, hence to each other also.
Figure 3: Coverage
In the previous experiments the testing and training
datasets were same due to low sample sizes, which lowers
the confidence level of the experimental results
In this set of experiments, we divide the yeast and HUVECs
datasets into training and testing sets. We constructed our
generative models based on training samples and checked
the metric results based on testing samples
Note that we also found the metric results based on training
samples to compare the results
We used first 50 samples for training and last 27 samples
for testing in yeast dataset
We used first 300 samples for training and last 100 samples
for testing in HUVECs dataset
Experimental Evaluation, Results, Setting #2
Experimental Evaluation, Results, Setting #2
Figure 4: Compatibility for Yeast
Figure 5: Diversity for Yeast
First we generate 50 samples and checked the metric results for each generated sample
separately
Figure 4 and 5 shows the results for yeast dataset in terms of compatibility and diversity
They verify our concern on low confidence level of first set of experiments. Because we
see that the generated data is less close to the original samples and more diverse than the
original samples when it is evaluated
w.r.t
testing data
Experimental Evaluation, Results, Setting #2
Figure 6: Compatibility for HUVECs
Figure 7: Diversity for HUVECs
Figure 6 and 7 shows the results for HUVECs dataset in terms of compatibility and
diversity
They again verify our concern on low confidence level of first set of experiments. Because
we see that the generated data is less close to the original samples and more diverse than
the original samples when it is evaluated
w.r.t
testing data
So, we can say that our generated samples are actually more qualitative than it is shown in
the first set of experiments. Because, we still have a very good compatibility values
around % 93, and the diversity values are greater than their previous values
Experimental Evaluation, Results, Setting #2
Now we know that our generated data is less close and
more diverse
w.r.t
to the original dataset
So what happens when we generate large number of
samples? To understand this, we generate 10, 20, …,
500 samples and checked the difference of the mean of
the metric results
w.r.t
testing and training
That is, for each generated sample set, we evaluate
them
w.r.t
testing dataset and
w.r.t
training dataset and
we
plot the difference
Results
w.r.t
training comprise a baseline for us and we
try to understand how the metric results
w.r.t
testing
samples change relatively
Experimental Evaluation, Results, Setting #2
Figure 8 and 9 show the results for Yeast dataset
These results show that our generated samples are very close to the original dataset
because there is only % 5 percentage difference between compatibility values
Moreover, they always carry new information because the diversity values are always
greater than zero
Nonetheless, the results for yeast dataset is not promising, because as we generate more
and more samples they do not pose a regular pattern
Figure 8: Compatibility for Yeast
Figure 9: Diversity for Yeast
Experimental Evaluation, Results, Setting #2
Figure 10 and 11 show the results for HUVECs dataset
Now, we actually see much better results. First of all the compatibility difference is less than that of
yeast. We have only % 2 percent value , which is a very good result
Secondly and more importantly, the diversity values are always increasing. That means, as we generate
more and more samples, our generated samples are not only very close to the original dataset but also
bring always new, even more and more information to the original dataset
It is a very important result, actually. Because we see that computationally we can generate gene
expression samples just like generating original samples. Hence, the complex internal dynamics of
gene regulation can successfully be simulated by superposing different methods and generating data
as if it were generated originally by the complex internal dynamics itself.
We think the reason for this result is the number of training samples we have in HUVECs dataset
It does not only show the power of computational methods but also provide practically very valuable
result of generating highly qualified gene expression data
Figure 10: Compatibility for HUVECs
Figure 11: Diversity for HUVECs
Conclusion & Future Work
By integrating different machine learning methods we can
simulate complex gene regulation system successfully
System always produces samples that are both similar to the
original gene expression dataset and carrying new information
Our system can be used as a preprocessor for any computational
approach requiring gene expression data
As future work;
The framework can be extended by integrating more models
Moreover, the produced samples may be studied under a pre

determined analysis task verifying the effectiveness of our system
Furthermore, a bound can be determined for number of required
samples to train our multi

model framework
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silico
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Any Question o
r
Comment?
This research is partially supported by The Scientific and Technological
Research Council of Turkey (TUBITAK), with project #110E179.
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