Interaction-Aware Feature Importance

• Interaction-aware feature importance techniques are approaches that measure both individual predictive contributions and interdependencies, capturing unique, redundant, and synergistic effects.
• They utilize diverse methodologies such as additive game-theoretic methods, permutation tests, and neural network models with attention mechanisms to isolate interaction effects.
• Empirical evaluations using visualizations like swarm plots and directed graphs confirm that these methods improve model explainability and support robust feature selection.

Interaction-Aware Feature Importance

Interaction-aware feature importance refers to any quantification of feature relevance that explicitly incorporates effects arising from dependencies or interactions between multiple input features, rather than attributing predictive influence to features solely on an additive or marginal basis. A broad literature distinguishes between feature importance measures that are oblivious to interaction structure and those that, either by design or post hoc analysis, seek to isolate main effects, synergistic contributions, redundancies, and higher-order cooperative phenomena. This article surveys foundational definitions, families of methods, theoretical properties, algorithmic realizations, and empirical benchmarks for interaction-aware feature importance.

1. Formal Definitions and Theoretical Foundations

Interaction-aware importance departs from classical marginal paradigms by quantifying not just the predictive power of individual features but also the unique, redundant, and synergistic contributions of sets of features.

• Non-additive/statistical interaction: Given a prediction function $f(x)$, there is a non-additive interaction among features in $I\subset \{1,\dots,p\}$ if $f(x)$ cannot be decomposed as $\sum_{i\in I} f_i(x_{-i})$; see (Tsang et al., 2021).
• Interaction score (Rashomon/FIS): For model $f$, set $I$, and loss $L$, the feature interaction score is

$$\mathrm{FIS}_I(f) = E[L(f(X_{-I}),y)] - E[L(f(X),y)] - \sum_{i\in I} (E[L(f(X_{-i}),y)] - E[L(f(X),y)]).$$

This isolates non-additive contributions by comparing the effect of ablating all features in $I$ together versus separately (Li et al., 2023).

• Partial information decomposition (PID): For random variables $X_1, X_2, Y$, PID decomposes $I\subset \{1,\dots,p\}$0 into unique information $I\subset \{1,\dots,p\}$1, redundant information $I\subset \{1,\dots,p\}$2, and synergistic information $I\subset \{1,\dots,p\}$3, formally using conditional mutual information and greedy search for maximizing/minimizing context sets (Lazic et al., 6 Jul 2025).

Interaction-aware importance thus subsumes both main and context-specific effects and provides a conceptual bridge between feature selection, statistical interaction, and interpretability.

2. Methodological Taxonomy

Numerous algorithmic families exist, each with different operationalizations of interaction-aware importance:

• Additive game-theoretic approaches: SAGE computes global feature importance via Shapley values over predictive power, inherently allocating importance according to main and interactive effects; the individual score for $I\subset \{1,\dots,p\}$4 is the expected incremental decrease in model loss when feature $I\subset \{1,\dots,p\}$5 is added to all possible subsets, thereby accounting for all higher-order redundancies and synergies (Covert et al., 2020).
• Permutation and conditional ablation: CAPFI assesses the drop in performance within disjoint context subsets when a feature is permuted, revealing context- and interaction-specific effects, especially when context divides are granular and meaningful for the task (Azarmi et al., 2024).
• Hierarchical significance and forward selection: SFIT uses a non-asymptotic, model-free test to select both main effects and higher-order feature interactions in a data-adaptive, efficient manner (Horel et al., 2019).
• Model structure and attention: Interaction-aware FM (IFM and extensions), GNN designs (FI-GNN, EFI-GNN), and explicitly structured neural methods induce and extract interaction-aware importance via attentions, gates, or explicit parameterizations of interaction terms, providing per-instance or per-node fine-grained attributions (Hong et al., 2019, Ding et al., 2019, Kim et al., 2022).
• Hybrid pipelines: Frameworks combining LIME for local linear explainability and NID for neural weight-based interaction screening realize importance at both marginal and higher-order levels, iteratively refining the feature set based on detected interactions (Ma et al., 2024).
• High-order mutual information: PID/Hi-Fi decomposes the total class-predictive mutual information into unique, redundant, and synergistic terms, leveraging nonparametric kNN-CMI estimators and greedy context search (Lazic et al., 6 Jul 2025).
• LOCO decomposition and extensions: Adaptive LOCO maximizes and minimizes the LOCO score with respect to feature subsets, separating the unique, redundant, and synergistic predictive contributions of a feature (Ontivero-Ortega et al., 2024); iLOCO generalizes this further to allow distribution-free inference and valid CIs for feature-pair (and higher) interactions using ensemble-based estimation (Little et al., 10 Feb 2025).

3. Model Architectures for Interaction-Aware Importance

Several modeling approaches build interaction-awareness directly into prediction architectures.

• Feature Refinement Network (FRNet): For click-through rate prediction, FRNet learns context- and interaction-aware bit-level importance weights $I\subset \{1,\dots,p\}$6 for each embedding dimension, via a dual IEU + CSGate structure (cross-attention, context aggregation, and adaptive bitwise gating), resulting in refined embeddings $I\subset \{1,\dots,p\}$7 (Wang et al., 2022). The $I\subset \{1,\dots,p\}$8 scores can be interpreted as high-resolution, instance-specific importance for each feature dimension, controlled by cross-feature relationships. Empirical ablations show that bit-level gates and context aggregation are essential for interaction sensitivity.
• Feature Interaction-aware GNNs (FI-GNN, EFI-GNN): FI-GNN augments node representations with attention-weighted pairwise feature interactions, assigning per-node $I\subset \{1,\dots,p\}$9 importance scores to each pair $f(x)$0; EFI-GNN builds explicit, fully transparent higher-order feature cross-terms at each layer, providing exact decomposition of class logits into first-, second-, etc., order contributions (Ding et al., 2019, Kim et al., 2022).
• Interaction-aware FMs (IFM, INN, DeepIFM): IFM introduces learned attention and field-based similarity terms ($f(x)$1, $f(x)$2) to modulate each feature-pair within the FM structure, thus learning flexible, stratified, interaction-aware importances (Hong et al., 2019).

4. Statistical Properties, Unique vs. Redundant vs. Synergistic Effects

Recent work emphasizes disentangling the unique, redundant, and synergistic importance components:

• PID/Hi-Fi: For each feature $f(x)$3, the unique information $f(x)$4, redundancy $f(x)$5, and synergy $f(x)$6, where $f(x)$7 are adaptively selected subsets minimizing/maximizing CMI (Lazic et al., 6 Jul 2025). This decomposition isolates which features have predictive value only jointly (synergy), singly (unique), or as overlap (redundant).
• Adaptive LOCO: By searching for the background subset $f(x)$8 (achieving minimal marginal importance; i.e., maximal redundancy) and $f(x)$9 (maximal synergy), LOCO decomposes each feature’s achievable importance into $\sum_{i\in I} f_i(x_{-i})$0 (unique/two-body), $\sum_{i\in I} f_i(x_{-i})$1 (redundant), and $\sum_{i\in I} f_i(x_{-i})$2 (synergistic) components (Ontivero-Ortega et al., 2024).
• SAGE: By averaging increments in predictive power across all possible subsets (via Shapley), SAGE distributes total importance fairly, so marginal gains for features in the presence of redundant/synergistic partners are proportionally down- or up-weighted (Covert et al., 2020).

5. Visualization, Interpretation, and Empirical Findings

Quantitative and qualitative assessments of interaction-aware importance rely on appropriate benchmarking and visualization tools.

• Swarm and Halo Plots: For a Rashomon set of high-performing models, swarm plots display the cloud of FIS scores for each interaction, revealing robustness or model-dependence; halo plots visualize joint effects with fixed sums of main effects (Li et al., 2023).
• Directed graphs from Shapley-interaction values: Bivariate explanations (e.g., BivShap-S, BivShap-K) construct directed graphs encoding the directionality and redundancy of feature-pair contributions; strongly connected components correspond to interchangeable groups, and PageRank scores capture global influence (Masoomi et al., 2023).
• Model and context-specific breakouts: CAPFI highlights how, across multiple neural architectures and context slices, utility of perceptual cues (bbox, speed, local context, pose) varies, and how interaction features (e.g., proximity-change-rate) reduce context-induced prediction bias (Azarmi et al., 2024).
• Ablation and attribution: Experiments consistently show that accounting for interaction-aware importance, whether by adding detected pairs to the feature set or adapting network architecture, improves predictive accuracy, calibrates attribution, and reduces over-reliance on spurious main effects (Wang et al., 2022, Hong et al., 2019, Ding et al., 2019, Ma et al., 2024).

6. Algorithmic and Computational Considerations

The combinatorial nature of interaction analysis introduces substantial computational burden, which is addressed by sampling, structure-exploiting encodings, and inference-efficient estimators.

• Mask- and patch-based approximation: Rashomon set exploration uses greedy mask updating; iLOCO and adaptive LOCO leverage minipatch ensemble methods or forward-greedy subset construction to obtain fast, statistically valid interaction scores and confidence intervals (Li et al., 2023, Little et al., 10 Feb 2025, Ontivero-Ortega et al., 2024).
• Dimension reduction for interactions: Interaction Pursuit (IP) employs marginal squared-correlation screening to restrict the candidate interaction set to manageable size before regularized selection (Fan et al., 2016).
• Context subdivision and permutation schemes: CAPFI reduces variance and bias in permutation-based scores by only shuffling features within homogeneous context groups, rather than globally (Azarmi et al., 2024).
• Metaheuristics: Evolutionary frameworks such as MMI-FS maintain and update global significance vectors and interaction matrices to favor non-redundant, complementary feature combinations, yielding improved Pareto fronts and hypervolume metrics (Namakin et al., 2022).

7. Implications, Limitations, and Best Practices

Interaction-aware feature importance fundamentally expands the toolkit for model explanation, selection, and design, but it is not without theoretical and practical caveats.

• Model dependence: Interaction patterns are not necessarily stable across all equally accurate models; the Rashomon set analysis reveals that the sign and magnitude of FISs can vary substantially, requiring caution in interpretability or feature selection (Li et al., 2023).
• Interpretability-complexity trade-off: Many approaches are computationally demanding for high-order interactions or large feature spaces, necessitating sampling, pre-screening, or focus on low-order terms (Covert et al., 2020, Fan et al., 2016).
• Axiomatic guarantees: Methods that rely on Shapley, path-integral, or CMI/PID-based decompositions enjoy strong axiomatic properties; fast surrogate-based or purely architectural approaches (e.g., attention) may not satisfy all such guarantees (Tsang et al., 2021).
• Recommendations:
  • Restrict search and reporting to pairwise or a handful of salient higher-order interactions unless sample size and context knowledge permit more.
  • Visually present both unique and interactive importance via bar plots, heatmaps, and interaction networks.
  • Where possible, benchmark interaction-aware importance against ablation or retraining loss to validate attribution.
  • Use context-aware and data-driven baselines, as choice of reference for masking or permutation can strongly influence scores (Azarmi et al., 2024, Masoomi et al., 2023).
  • For workflow integration, combine global (SAGE/PID/LOCO) with local (attention/bivariate SHAP/CAPFI) interaction-aware analyses, and employ inference tools (iLOCO) for statistical validity (Little et al., 10 Feb 2025).
  • In industry or automated machine learning, employ interaction-aware search (e.g., MMI-FS), then prune or regularize by stability and cross-validation (Namakin et al., 2022).

Interaction-aware feature importance, by leveraging statistical, information-theoretic, and model-driven perspectives, now forms a central pillar for interpretability and robust variable selection across deep, tabular, and graph-structured learning settings.