Algorithm 3.

Q-Finder’s iterative top-k selection based on subgroups’ intensions

Input: k maximum number of selected subgroups,

$G_{ranked}$ set of ranked generated subgroups, with complexities ranging from $C_{min}$ to $C_{max}$

${\delta }_{ES}$ minimum delta to consider that a subgroup has a higher effect size11

$G_{split}=$ splitByComplexity$\left(G_{ranked}\right)$ # split $G_{ranked}$ by subgroup complexity ($G_{split}\left[1\right]$ corresponds to complexity 1, $G_{split}\left[2\right]$ to complexity 2, …)

$S_k=\left\{\right\}$ # Initialize $S_k$, the set of top candidate subgroups

For $c=C_{min}$ to $C_{max}$ do

For g in $G_{split}\left[c\right]$ do # g: candidate subgroup

If p-value(g) $>$ max(p-values($S_k$)) and size$\left(S_k\right)==k$ then continue to next c

For s in $S_k$ do # s: subgroup in the top-k

If redundant($g,s$) then

If complexity(g) $==$ complexity(s) then

continue to next g

If complexity(g) $>$ complexity(s) then

If EffectSize(g) $\le$ EffectSize($s){\delta }_{ES}$ then

continue to next g

For s in $S_k$ do

If redundant($g,s$) and complexity(g) $>$ complexity(s) and

EffectSize(g) $>$ EffectSize($s){\delta }_{ES}$ and p-value(g) $<$ p-value(s) then

$S_k=S_k\backslash \left\{s\right\}$

$S_k=S_k{{\displaystyle \cup }}^{\text{}}\left\{g\right\}$

while size($S_k)$ > k do

$S_k=S_k\backslash \{$subgroup from $S_k$ with the highest p-value$\}$

Output: $S_k$ # top-k best candidate subgroups