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Investigating the Parameter Space of A T-Cell Cross Regulation Binary
ClassifierIan Wood
4/25/13I690, Prof. Flammini
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T-Cell Cross Regulation
Image From: J. Carneiro, et al., “When three is not a crowd: a Crossregulation model of the dynamics and repertoire selection of regulatory CD4+ T cells.,” Immunological Reviews, vol. 216, pp. 48–68, 2007.
𝑑𝐸𝑑𝑡
=𝑝𝐸 𝐸𝐴−𝑑𝐸 𝐸
𝑑𝑅𝑑𝑡
=𝑝𝑅 𝑅𝐴−𝑑𝑅 𝑅
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T-Cell Cross Regulation for Machine Classification
Image From: A. Abi-Haidar and L. M. Rocha, “Collective Classification of Textual Documents by Guided Self-Organization in T-Cell Cross-Regulation Dynamics,” Evolutionary Intelligence, p. In press, 2011.
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Machine Classification IssuesBenefits:
Temporal dynamics could allow the system to adapt to changes over time (concept drift)
Possibly useful for classifying unbalanced setsProblems:
Agent-based models take timeLarge parameter space is difficult to explore
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A Large Parameter SpaceNslot – The number of antigens to produce for each feature
DE – Death rate for unbound effectors
DR – Death rate for unbound regulators
E0- - Initial effector population for Nonself documents
E0+ - Initial effector population for Self documents
E0u - Initial effector population for Unlabeled documents
R0- - Initial regulator population for Nonself documents
R0+ - Initial regulator population for Self documents
R0u - Initial regulator population for Unlabeled documents
This doesn’t include variations in the algorithm!
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Finished Work
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Top Parameter Configurations So Far
nslot eself rself
enself
rnself eunlab runlab
edrate
rdrate cond condi precision
accuracy recall
mcc f1 tpos tneg
fpos fneg
12 3 9 8 2 6 3 1 1 2 1 0.74 0.8 0.930.62
0.82 28 20 10 2
13 3 9 8 2 5 3 1 1 2 1 0.95 0.78 0.60.61
0.73 18 29 1 12
12 3 9 8 2 5 3 2 2 2 1 0.84 0.78 0.70.57
0.76 21 26 4 9
20 8 12 12 8 8 8 25 25 2 2 1 0.57 0.130.2
7 0.24 4 30 0 26
20 12 24 12 10 12 10 2 2 1 2 0.58 0.63 10.3
9 0.73 30 8 22 0
20 8 12 12 8 8 8 25 25 5 2 0.58 0.63 10.3
9 0.73 30 8 22 0
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Features Over Time
nslot eself rself
enself
rnself
eunself runself
edrate
rdrate cond
condi
precision
accuracy
recall mcc f1 tpos tneg
fpos fneg
12 3 9 8 2 6 3 1 1 2 1 0.74 0.80.9
30.620.8
2 28 20 10 2
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ApproachSee how distributions of cosine scores
correspond to parametersThe system should be able to correct itself, so
I want to see how parameters allow sensitivity to changes in co-occurrence frequencyInvestigate artificial datasets for simple casesInvestigate mathematical relationships in
simple cases
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Distribution of TCells
nslot eself rself
enself
rnself
eunself runself
edrate
rdrate cond
condi
precision
accuracy
recall mcc f1 tpos tneg
fpos fneg
12 3 9 8 2 6 3 1 1 2 1 0.74 0.80.9
30.620.8
2 28 20 10 2
nslot eself rself
enself
rnself
eunself runself
edrate
rdrate cond
condi
precision
accuracy
recall mcc f1 tpos tneg
fpos fneg
12 3 9 8 2 6 3 1 1 2 1 0.74 0.80.9
30.620.8
2 28 20 10 2
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Distribution of Tcells cont.
nslot eself rself
enself
rnself
eunself runself
edrate
rdrate cond
condi
precision
accuracy
recall mcc f1 tpos tneg
fpos fneg
14 3 8 3 7 3 7 1 2 5 1 0 0.38 0 -0.36 -1 0 23 7 30
20 4 6 6 4 4 4 1 1 6 1 0 0.5 0 0 0 0 30 0 30
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Artificial Datasets10 documents of 100 words eachWords are randomly generated and unique to
each documentOne word, “lambda”, is present in every
document, but initially biased incorrectlySet 1 – First document is labeled Self, the rest
NonselfSet 2 – First document is labeled Nonself, the
rest SelfSet 3 – First 5 = Self, Last 5 = NonselfSet 4 – First 5 = Nonself, Last 5 = Self
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Parameter ConfigurationsParameter Values, Step
Nslot [10, 13], 1
DE 0.1
DR 0.1
E0- =E0
+
E0+ [5, 14], 1
E0u =E0
+
R0- [1, 6], 1
R0+ [6, 16], 1
R0u =R0
-
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Set1Appropriate Behavior Inappropriate Behavior
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Set2Appropriate Behavior Inappropriate Behavior
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Appropriate Behavior in Sets 1 & 2
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Appropriate ConfigurationsNslot E0
+ R0+ E0
- R0- E0
u R0u DE DR
10 5 12 5 3 5 3 .1 .1
10 6 12 6 2 6 2 .1 .1
10 7 13 7 1 7 1 .1 .1
10 8 10 8 5 8 5 .1 .1
11 11 11 11 2 11 2 .1 .1
12 6 12 6 3 6 3 .1 .1
12 7 10 7 4 7 4 .1 .1
12 9 11 9 3 9 3 .1 .1
13 5 14 5 4 5 4 .1 .1
13 6 15 6 3 6 3 .1 .1
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Future DirectionsMathematical Analysis
I tried to write equations for the expected change in the lambda population between the first and second documents, but I either assumed too much or made errors.
Larger SearchSimple artificial dataset runs much faster than an actual
corpusRun on Sets 3 and 4More variation in the artificial data (lambda should not
be the only common feature)More precision in distribution data (only looks at
mean, over-emphasizes features that appear only once)
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References J. Carneiro, et al., “When three is not a crowd: a Crossregulation
model of the dynamics and repertoire selection of regulatory CD4+ T cells.,” Immunological Reviews, vol. 216, pp. 48–68, 2007.
A. Abi-Haidar and L. M. Rocha, “Collective Classification of Textual Documents by Guided Self-Organization in T-Cell Cross-Regulation Dynamics,” Evolutionary Intelligence, p. In press, 2011.