TABLE 1.

Mathematical formulation for three regression models.

Model	Regularization	Optimization problem	Hyperparameters
Linear	Elastic net	$\underset{\mathit{\beta }, {\beta }_0}{\min }\left[\frac{1}{N}\sum _{i=1}^N{\left({\mathit{\beta }}^T{\mathit{x}}_i+{\beta }_0-y_i\right)}^2+\lambda \left(\sum _{j=1}^p\frac{1}{2}{\beta }_j^2+\left|{\beta }_j\right|\right)\right]$	$\lambda =0.128$
SVM	L2 norm	$\underset{\mathit{\beta }, {\beta }_0,\mathit{s}}{\min }\left[\sum _{j=1}^p\frac{1}{2}{\beta }_j^2+C\sum _{i=1}^N{s}_i\right]$ such that $\left|\left({\mathit{\beta }}^T{\mathit{x}}_i\right)a+{\beta }_0-y_i\right|\le ϵ+s_i$ and $s_i\ge 0$	$C=0.001$ $ϵ=0.005$ $a=2.699$
Logistic	Elastic net	$\underset{\mathit{\beta }, {\beta }_0}{\min }\left[\frac{1}{N}\left(\sum _{i=1}^N-y_i\ln \left(f\right)-\left(1-y_i\right)\ln \left(1-f\right)\right)+\lambda \left(\sum _{j=1}^p\frac{1}{2}{\beta }_j^2+\left|{\beta }_j\right|\right)\right]$ where $f={\left(1+e^{-{\mathit{\beta }}^T{\mathit{x}}_i-{\beta }_0}\right)}^{-1}$	$\lambda =0.013$

SVM, support vector machine; $\mathit{\beta }=\left[{\beta }_1 {\beta }_2\dots {\beta }_{12}\right]$, vector of model parameters; ${\beta }_0$, model intercept term; N=56, number of observations in training data set; x, vector of electrically-evoked compound action potential (eCAP) parameters; y, output vector; λ, regularization parameter; p=12, number of eCAP parameters; s, vector of slack parameters; C, box constraint; ϵ, error margin; a, kernel scaling factor.