Look into AIC curves and alternative L-curve plots to compare and evaluate different sized networks

[kdahlquist]

When looking at the L-curve results #351 today, we saw some interesting behavior with regards to the step-down from the 15-gene, 28-edge network to the 3-gene, 4-edge network.

@bengfitzpatrick suggested the following:

• plotting LSE versus number of parameters instead of the magnitude of the parameters (penalty)
• using AIC curves to come up with a measure for how much a gene or an edge contributes to the model error

We noted that there was a jump (discontinuity?) in the L-curves when ACE2 was removed from the network.

[bklein7]

Plots showing LSE vs. number of parameters and AIC vs. number of genes in the network were generated for the db5 step-down experiment. These plots were included after the related L-curves in the following presentation: https://github.com/kdahlquist/DahlquistLab/blob/master/documents/L-Curve-Analysis_Varied-Optimization-Data-Size_BK20170909.pptx.

The associated Excel file used to generate these plots can be found here: https://github.com/kdahlquist/DahlquistLab/blob/master/data/Fall2017/db5-step-down-exp_calculations_BK20170928.xlsx.

Note: The calculation we decided to use for computing AIC (2xLSE + 2xparameter-number) weighs parameter number far more heavily than LSE, likely moreso than is intended. Thus, the AIC plot is not particularly informative. We may want to use different constants to account for this issue.