Table 1. List of variables/terms and their explanations.

Variables and Terms	Definitions
M	number of bins used for discretization of observations
k	number of bins an observation can be assigned to at the same time.
n	number of observed metabolites
t	knot vector that is used to define the shapes of B-spline curves
	the probability associated with the i th B-spline curve for the given z value and for a specific k
P	population of individuals
s	an individual in the population
mj	j th observed metabolite
s[mj]	the observed value for j th metabolite for individual s
	transformed value for s[mj] given the max and min values for mj
	probability of assigning s[mj] to bin i.
H(X)	entropy of the random variable X.
I(X;Y)	mutual information of random variables X and Y.
Sub	a subset of the observed metabolites
	random variable that represents all combinations of the binned metabolite observations for Sub
C	random variable that represents the class variable (e.g. WT and CF)
ps(o)	probability of observing the bin combination o for individual s
p(o)	probability of observing the bin combination o in population P
	marginal mutual information obtained from the bin combination o
o[mj]	the bin associated with the j th metabolite in the bin combination array o
	random variable that contains all bin combinations for metabolites in Sub that are class C -specific.
	expected bins for metabolites in Sub for class C
	expected bin for metabolite j for class C found using the subset of metabolites Subj
	expected bin for metabolite j for class C found after aggregating results for different subsets