Investigating the Parameter Space of A T-Cell Cross Regulation Binary

ClassifierIan Wood

4/25/13I690, Prof. Flammini

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

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.

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

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!

Finished Work

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

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

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

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

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

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

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

-

Set1Appropriate Behavior Inappropriate Behavior

Set2Appropriate Behavior Inappropriate Behavior

Appropriate Behavior in Sets 1 & 2

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

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)

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.