# Synthesizing Explainability Across Multiple ML Models for Structured Data
## 3 Proposed Method: Weighted Importance Score and Frequency Count (WISFC)
### Integrating WIS and FC for Feature Ranking  
A simplified overview of WISFC is depicted in Figure 1. The figure illustrates how feature importance is extracted from multiple XML models, aggregated via Weighted Importance Score and Frequency Count, and combined into a final feature ranking.  
Applying WISFC produces a feature table annotated with _WIS_ and _FC_. To derive a final importance ranking or identify robust predictors, consider the following strategies:  
* **Joint criteria:** We can set thresholds on both _WIS_ and _FC_. For example, we might decide that a feature is robust if it has \(FC\geq 50\%\) (appeared in at least half of the models) and is in the top quartile of _WIS_ scores. This ensures we keep features that are not only frequent but also relatively highly ranked on average. Features meeting both criteria would be our high-confidence predictors. This approach is useful for binary decisions (selecting a subset of features for downstream use, e.g., in a final model or for reporting to stakeholders).
* **Composite score:** Alternatively, we could combine _WIS_ and _FC_ into a single composite importance metric. For instance, one might multiply a feature's average importance by a factor related to its frequency (somewhat like a weighted scoring). A simple composite could be \[C(f)=WIS(f)\,\frac{FC(f)}{N},\] effectively penalizing features that are not consistently found. However, interpreting this composite can be less intuitive, so often, it is clearer to keep _WIS_ and _FC_ separate and use them in tandem.
* **Ranking by WIS, tie-break by FC:** Another practical method is to primarily sort features by _WIS_ (which gives an overall ranking from most important to least) and use _FC_ as a secondary sort or a filter. For example, one can list features by descending _WIS_ and then highlight those that have high _FC_ as well (these would be the top stable features). Features with high _WIS_ but low _FC_ might be noted as \"model-specific importance\" and scrutinized further before trusting.  
If we consider two features evaluated by five models:  
* Blood Pressure ranks: [1, 2, 4, 1, 3] WIS \approx\) approx 2.2 (consistently high) FC = 1.0 (top-3 in all models)  
Figure 1: Simplified overview of WISFC method.  
Cholesterol ranks: [1, 8, 2, 15, 1]  
WIS \approxprox 5.4 (more variable)  
FC = 0.8 (top-3 in four models)  
A simple top-\(k\) overlap would treat both as majority-selected, but WISFC reveals that Blood Pressure never falls below fourth place and is thus more robust, whereas cholesterol's low rank in one model lowers its consistency.  
WISFC is model-agnostic and reproducible: any feature-importance output (e.g., SHAP, coefficients, permutation scores) can be normalized, scored, and aggregated. Researchers can replicate the procedure to verify _WIS_ and _FC_ values, ensuring transparent \"consensus\" selection. While extensions, such as tracking sign agreements across models, are straightforward, we focus on core rank-based aggregation. This framework directly addresses our research questions by enabling brute-force model synthesis and by offering a rigorous, quantitative alternative to ad hoc overlap methods. The next section applies WISFC to real data, illustrating its ability to surface stable predictors.