# Synthesizing Explainability Across Multiple ML Models for Structured Data
## 3 Proposed Method: Weighted Importance Score and Frequency Count (WISFC)
### Measuring Consistency (Frequency Count)  
Aggregating scores into _WIS_ addresses how important, on average, a feature is, but it does not directly capture how many models concur in citing that feature. A feature could attain a high _WIS_ if it had extreme importance in a few models, even if half the models ignored it. For greater transparency, WISFC, therefore, includes a second metric: Frequency Count (_FC_). The Frequency Count \(FC(f)\) is essentially the number of models (out of \(N\)) for which feature \(f\) was deemed important by some criterion. There are a few ways to define \"deemed important\": one practical way is to set a rank threshold (e.g., was \(f\) in the top 10 important features for model \(j\)?) or a score threshold (e.g., did \(f\)'s importance exceed 0.01 in normalized importance for model \(j\)?). The threshold can be tuned based on how many features one expects to be important in the problem. By default, using top-\(k\) lists is convenient--for instance, \(FC(f)\) could count in how many models \(f\) appeared in the top-\(k\) ranking (say \(k=10\)). If \(FC(f)=N\), that means every single model considered \(f\) to be among the most important features; if \(FC(f)=1\), only one model found \(f\) important (and the rest did not rank it in top-\(k\)). We can also express this as a percentage:  
\[FC\%(f)\ =\ \frac{FC(f)}{N}\times 100\%.\]  
This frequency-based view aligns with the intuitive practice researchers follow of checking how often a feature appears across different methods. Indeed, one of the alignment metrics in explainer disagreement research is exactly the top-\(k\) feature overlap between explainers [14]. Our \(FC(f)\) generalizes that concept to \(N\) models: it effectively measures the overlap of \(f\) across all model lists. A high \(FC\) is a sign of consensus. In the context of stability, \(FC\) relates to the concept of selection stability--for example, stability selection procedures [17] select features that appear in a high fraction of bootstrapped lasso models. Similarly, in ensemble feature selection, the frequency of a feature being selected is a key indicator of robustness [18]. Our use of \(FC\) is grounded in these ideas. It provides an easy-to-interpret number: if \(FC(f)=8\) out of 10 models, one can straightforwardly explain that \"eight different models independently found this feature important\", which can be persuasive for domain experts looking for reliable signals.  
It is worth noting that \(FC\) by itself could be gamed (e.g., a feature might appear barely at rank \(k\) in many models but never high). That is why _WIS_ and \(FC\) are complementary. Wesuggest using _FC_ with a reasonably high \(k\) (so that we are counting fairly strong evidence of importance) or even combining it with a secondary condition (like \"feature is in top-\(k\) and has a positive impact on outcome\" if considering sign). _FC_ directly measures consistency: features consistently identified across models yield high _FC_, whereas those important to only one model receive low _FC_, highlighting potential model-specific effects.