Computational Intelligence - November 2012 - 38

4 predictive attributes, where only two
attributes were predictive within a respective subset of the data. Additionally, each
data set contained 16 randomly generated,
non-predictive attributes, with minor allele
frequencies randomly selected from a uniform distribution ranging from 0.05 to 0.5.
In this study we demonstrated the efficacy of our analysis
pipeline using one of these aforementioned datasets that concurrently models epistasis and heterogeneity. Minor allele frequencies of all 4 predictive attributes were 0.2, heritabilities for
both underlying models were 0.4, relative model architecture
difficulty was "Easy," the ratio of samples representative of
either model was 50:50, and the dataset sample size was 1600.
The heritability of a model indicates the proportion of variation that can be attributed to the attributes in the model. Any
model heritability less than 1 indicates the presence of noise
(i.e., lower heritability corresponds to greater noise). This dataset offers a reasonable approximation of how a complex disease
association pattern might appear within a balanced dataset
comprised of sick and healthy subjects. Evaluation of this dataset in [12], with an implementation of the UCS algorithm,
yielded significant power to detect the underlying predictive
attributes. This dataset was chosen to provide a clear example of
this pipeline analysis. If this were a real biological investigation,
our goal would be the identification of predictive attributes,
without making any assumptions about the number of attributes involved or knowing whether their association followed
patterns of epistasis or heterogeneity. Genetic or environmental
attributes identified in this manner would be investigated further to determine whether they are causal variants or merely
markers of disease.
As a negative control for this study, we repeated the pipeline
analysis on a second dataset within which all attributes were
non-predictive. Specifically, this dataset is a class-permuted
version of the dataset described above.

All datasets were generated using a pair of distinct,
two-locus epistatic interaction models, both utilized to
generate instances (i.e., case and control individuals)
within a respective subset of each data set.
drive the discovery of better rules. For a complete LCS introduction and review, see [1].
UCS, or the sUpervised Classifier System [28], is based
largely on the very successful XCS algorithm [17], but replaces
reinforcement learning with supervised learning, encouraging
the formation of best action maps and altering the way in
which accuracy, and thus fitness, is computed. UCS was
designed specifically to address single-step problem domains
such as classification and data mining, where delayed reward is
not a concern. The implementation of UCS applied in this
study is the same as the one used in [12] upon which we had
previously performed a parameter sweep in an attempt to optimize major run parameters. With this as our basis, we adopted
mostly default parameters with the exception of 200,000 learning iterations, a population size of 2000, tournament selection,
uniform crossover, subsumption, and a v of 1. v has been
described as a "constant set by the user that determines the
strength [of ] pressure toward accurate classifiers'' [29], and is
typically set to 10 by default. A low v was used to place less
emphasis on high accuracy in this type of noisy problem
domain, where 100% accuracy is only indicative of over-fitting.
Also, as in [12], we employ a quaternary rule representation,
where for each SNP attribute, a rule can specify genotype as (0,
1, or 2), or instead generalize with "#," a character that implies
that the rule does not care about the state of that particular
attribute. Note that when evaluating UCS over the entire
training or testing datasets, discovery mechanisms were disabled
such that the rule population remained constant.
2.2 Simulated Dataset

In both [12] and [13], datasets were generated that concur2.3 Manual Inspection
rently modeled epistasis and heterogeneity as they might
To highlight the need for our proposed analysis pipeline we
simultaneously occur in a single nucleotide polymorphism
began with an example of manual inspection within the
(SNP) genetic association
study. All datasets were
Table 1 Manual rule inspection of our UCS rule population trained on the entire simulated dataset.
generated using a pair of
Rules (R's) are ordered by numerosity (Num.). To save space we have left out SNPs (X's) which were
distinct, two-locus epistatic
generalized over these top 10 rules. The accuracy of each rule listed in the table was 100%.
interaction models, both
utilized to generate
x0
x1
x2
x3
x4
x6
x7
x8
x10
x11
x15
x18
ClaSS
Num.
R1
#
#
0
1
#
#
1
#
#
#
#
1
1
10
instances (i.e., case and
R2
1
0
1
0
#
#
#
#
#
#
#
#
1
9
control individuals) within
R3
#
0
1
1
#
#
#
#
0
#
1
#
0
9
a respective subset of each
R4
2
1
#
#
#
#
1
#
#
#
#
#
1
6
data set. Two-locus epistatR5
1
1
#
#
2
#
#
#
#
0
#
#
0
6
ic models were simulated
R6
0
1
0
1
#
#
#
#
#
#
#
#
1
6
without Mendelian/main
R7
#
#
1
0
#
0
#
#
0
#
1
#
1
6
effects, as penetrance
R8
1
0
#
#
#
#
#
2
#
#
#
#
1
5
R9
#
#
1
1
#
0
#
#
0
#
#
1
0
5
tables. In total, each simuR10 #
#
1
1
#
#
#
#
0
#
2
#
0
5
lated data set contained

IEEE ComputatIonal IntEllIgEnCE magazInE | noVEmBER 2012

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