Statistics and machine learning toolbox

To determine which changes in the value of the direction recognition index between particular measurement situations should be considered significant, we completed a statistical analysis of the obtained data. For this purpose, a Wilcoxon test (equivalent to the Mann-Whitney U test) was used. The calculations were performed using MATLAB R2017b (version 9.3) with the Statistics and Machine Learning Toolbox (MathWorks Inc., Natick, MA, USA).

We trained an ensemble of 100 decision trees using the fitcensemble function from the Statistics and Machine Learning Toolbox from MathWorks. Decision tree models are simple, highly interpretable, and can be displayed graphically (James et al., 2013 ). Consequently, the decision process of the classifier can be easily interrogated. However, decision tree models have two key disadvantages: (1) mediocre prediction performance (Caruana and Niculescu-Mizil, 2006 ) and (2) high variance due to overfitting (James et al., 2013 ). Both disadvantages can be mitigated by aggregating an ensemble of decision trees. Empirical comparison of classification models shows that ensembles of decision trees outperform other classification algorithms across a variety of problem sets (Caruana and Niculescu-Mizil, 2006 ).
We used a bootstrap aggregation (bag) method for constructing the ensembles. Each tree in the ensemble is trained on a boot-strapped replica of the data—each replica is a random selection of the data with replacement. The predictions from the ensemble model are determined by a majority vote from each individual tree prediction. We trained the ensemble to learn the stimulus labels (TNF, Pam3CSK4, CpG, LPS, and poly(I:C)) from either the entire set of predictors (all 918 metrics, Table S6A) or a subset of predictors termed “signaling codons” (Table S6B).

Within the manuscript, convergent validity, and test-retest reliability for the CGN_ICA test is shown with Pearson’s Correlation. P-values for Pearson’s correlation are based on a Student’s t distribution. Calculations are done using MathWorks’ statistics and machine learning toolbox (https://www.mathworks.com/help/stats/index.html).
To measure dependency of the cognitive tests with level of education, we used explained variance, defined as the square of Pearson’s Correlation between participants’ cognitive score and their level of education (i.e. number of years). Here the statistical significance was obtained by a permutation test (10,000 permutations of participants). To formally assess statistical independence, we used a non-parametric independence test, proposed by Gretton and Gyorfi⁶² , based on 10,000 bootstrap resampling of participants.
Finally, we used a single factor analysis of variance (ANOVA) to compare average CGN_ICA scores for participants who had taken the CGN_ICA test every other day for two weeks. The goal was to see if the mean CGN_ICA scores are significantly different at any given day.