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RoSHAP: A Distributional Framework and Robust Metric for Stable Feature Attribution

This paper introduces RoSHAP, a distributional framework that leverages bootstrap resampling and asymptotic Gaussianity to create a robust feature attribution metric, thereby improving the stability and interpretability of machine learning models by identifying features that are consistently active, strong, and reliable across varying data splits and model configurations.

Original authors: Lanxin Xiang, Liang Shi, Youhui Ye, Boyu Jiang, Dawei Zhou, Feng Guo

Published 2026-05-15

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CC BY 4.0

Original authors: Lanxin Xiang, Liang Shi, Youhui Ye, Boyu Jiang, Dawei Zhou, Feng Guo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to figure out which ingredients in a giant soup are actually responsible for its delicious taste. You ask a food critic (the machine learning model) to taste it and tell you which ingredients matter most.

The problem is, if you ask the critic to taste the soup five different times, they might give you five different answers. One time they say "It's the salt!" The next time, "No, it's the garlic!" This happens because the critic might taste a slightly different spoonful each time, or their mood changes slightly. In the world of data science, this is called stochastic variation—the results change just because of random luck in how the data is split or how the model is built.

This paper introduces a new tool called RoSHAP to solve this "unreliable critic" problem. Here is how it works, using simple analogies:

1. The Problem: The "One-and-Done" Critic

Usually, data scientists ask the model to give an answer just once. They split the data, train the model, and get a list of "top features" (the most important ingredients).

The Issue: As shown in the paper's examples (like analyzing cancer genes), if you run the same analysis twice with slightly different random settings, the "top 3" ingredients can change completely. Relying on just one run is like trusting a single coin flip to decide the winner of a race.

2. The Solution: The "Crowdsourced" Critic (Bootstrap)

Instead of asking the critic once, the authors say: "Ask them 1,000 times!"

The Method: They use a technique called bootstrapping. Imagine taking a bag of marbles (your data), pulling out a handful to make a soup, asking the critic, putting the marbles back, and doing it all over again. You do this hundreds of times.
The Result: Instead of getting one single answer, you get a distribution (a whole range of answers). You can see which ingredients the critic consistently praises and which ones they only mention by accident.

3. The Shortcut: The "Gaussian" Guess

Doing this 1,000 times takes a lot of computer power. The authors discovered a clever trick:

The Analogy: If you ask enough people (or run enough simulations), the answers tend to form a perfect "bell curve" (a Gaussian distribution).
The Benefit: Once you know the shape is a bell curve, you don't need to ask 1,000 times. You can just ask 10 times and mathematically "guess" the rest. This saves a massive amount of time while keeping the accuracy high.

4. The New Score: RoSHAP

The paper creates a new score called RoSHAP (Robust SHAP) to rank the ingredients. It doesn't just look at how strong an ingredient is; it looks at three things:

Activity: Does the ingredient show up often? (Is it active in the soup, or does it disappear half the time?)
Strength: When it does show up, is it a big flavor or a tiny whisper?
Stability: Is the critic consistent? (If the critic says "Salt!" 99 times and "Garlic!" 1 time, Salt wins. If they flip-flop every time, neither wins.)

RoSHAP combines these into a single number that rewards ingredients that are active, strong, and stable.

5. What the Experiments Showed

The authors tested this on real-world data, including:

Genes: Finding which genes cause cancer (where previous methods picked different genes every time).
Molecules: Distinguishing between "musk" and "non-musk" smells.
WiFi Signals: Figuring out your location based on signal strength.
Images: Looking at pictures of ships and cars to see which pixels the computer is actually "looking at."

The Findings:

Better Stability: RoSHAP picked the same "top ingredients" every time, whereas the old methods changed their minds constantly.
Smarter Selection: Models built using only the RoSHAP-selected features worked just as well as models using all the features. This means you can throw away the "noise" (the useless ingredients) without losing the flavor.
Image Insight: In the image experiments, RoSHAP helped show that sometimes a model is "hallucinating" (looking at the sky instead of the car). The new method revealed these errors by showing that the model's focus was unstable.

Summary

Think of RoSHAP as a way to stop trusting a single, fickle opinion and start trusting a consistent consensus. It filters out the random noise and highlights the features that truly matter, making machine learning models more reliable and easier to understand.

Technical Summary: RoSHAP – A Distributional Framework and Robust Metric for Stable Feature Attribution

1. Problem Statement

Feature attribution is essential for interpreting machine learning models and supporting data-driven decisions. However, standard attribution measures (e.g., SHAP, LIME) often exhibit significant stochastic variation. Factors such as random train–test splits, random seeds, and stochastic optimization procedures can lead to substantially different attribution values and feature rankings. This instability is particularly problematic in high-dimensional, noisy, or correlated settings (e.g., genomics), where unreliable rankings can misguide scientific conclusions and costly downstream experiments. Existing methods typically focus on average attribution magnitudes or rankings but fail to account for the full empirical distribution of attribution scores across resampling runs.

2. Methodology

The paper proposes RoSHAP (Robust SHAP), a framework that treats feature attribution as a distributional problem rather than a point estimate. The methodology consists of three main components:

Bootstrap-Based Distribution Estimation:
The framework repeatedly resamples the training data (bootstrap), refits the model, and recomputes attribution scores (specifically SHAP values) for each feature. This generates an empirical distribution of attribution scores for every feature, capturing both the magnitude of contribution and its variability.
- Algorithm: For $B$ bootstrap iterations, the model is fitted on a resampled dataset, and out-of-bag (OOB) SHAP values are computed. These values are aggregated to form the distribution of feature-level attribution.
Zero-Inflated Modeling and Gaussian Approximation:
Since SHAP values (especially in tree-based models) often contain exact zeros, the authors model the sample-feature SHAP value $T_{ij}$ as a zero-inflated mixture:
$T_{ij} \sim w_{ij} \delta_0 + (1 - w_{ij}) G_{ij}$
where $\delta_0$ is a point mass at zero, $w_{ij}$ is the probability of zero attribution, and $G_{ij}$ is the nonzero component.
The feature-level aggregated magnitude is defined as $U_j = \sum |T_{ij}|$ . Under mild regularity conditions (specifically, a Lyapunov condition ensuring the aggregate is driven by many small terms rather than a few dominant ones), the distribution of $U_j$ is shown to be asymptotically Gaussian. This allows the distribution to be summarized by its mean and standard deviation, significantly reducing the computational cost of bootstrapping compared to non-parametric kernel density estimation (KDE) for large $B$ .
The RoSHAP Metric:
RoSHAP synthesizes the estimated distribution into a single robust ranking criterion that rewards features based on three properties:
1. Activity: The proportion of non-zero attributions ( $1 - P_{0j}$ , where $P_{0j} = \text{Pr}(U_j = 0)$ ).
2. Strength: The median magnitude of nonzero attributions ( $m_j$ ).
3. Stability: The inverse of the standard deviation ( $1/s_j$ ), representing the signal-to-noise ratio.
The metric is defined as:
$\text{RoSHAP}_j := (1 - P_{0j}) \frac{m_j^2}{s_j}$
This formulation prioritizes features that are consistently active, have strong contributions, and exhibit low variability across resampling runs.

3. Key Contributions

Distributional Framework: Shifts the paradigm from point-estimate attribution to modeling the full distribution of attribution scores via bootstrapping and KDE.
Theoretical Justification: Proves that under regularity conditions, the aggregated feature attribution score is asymptotically Gaussian, justifying the use of mean-variance summaries to reduce computational burden.
Robust Metric (RoSHAP): Introduces a composite metric that explicitly penalizes instability and inactivity, addressing the limitations of standard magnitude-based ranking.
Empirical Validation: Demonstrates the framework's effectiveness across diverse data modalities (tabular, molecular, spatial, and image data) and model types (XGBoost, LightGBM, CatBoost, Neural Networks, ViT).

4. Results

Simulation Studies:
In a binary classification simulation with 1,000 features (10 true signals), RoSHAP successfully identified 8 out of 10 signal features within the top 12 rankings using 1000 bootstrap runs. Even with only 10 bootstrap runs, it recovered 8 signals in the top 12. In contrast, standard single-run SHAP identified only 4 signals in the top 12 and assigned near-zero importance to the strongest signal feature ( $x_1$ ). Other metrics like Information Gain and LIME also showed unstable rankings.
- Gaussian Approximation: The empirical distributions of robust importance estimates were found to be approximately Gaussian, validating the theoretical reduction in required bootstrap repetitions.
Real-World Experiments:
- Golub (Genomics): In a high-dimensional, small-sample setting (7,129 genes), RoSHAP provided a clearer summary of consistently important genes compared to seed-specific SHAP. Models trained on RoSHAP-selected features achieved performance comparable to full-feature models while using fewer predictors.
- Musk (Molecular): RoSHAP handled imbalanced data and distributed signals effectively, showing comparable performance to other methods but with more stable feature selection.
- UJIIndoorLoc (Regression): In a high-dimensional regression task (WiFi fingerprinting), RoSHAP achieved competitive and stable performance across RMSE, MAE, and MAPE metrics.
- CIFAR-10 (Image): Applied to Vision Transformers (ViT), the framework revealed that single-run image explanations are sensitive to training randomness (e.g., attribution shifting from water to ship body across runs). The aggregated RoSHAP map provided a stable, interpretable focus on the correct object regions, helping to diagnose prediction errors where models attended to irrelevant background regions.

5. Significance and Claims

The paper claims that RoSHAP improves the stability and interpretability of machine learning models by providing a reliable basis for feature ranking that accounts for stochastic variation.

Reliability: It enables consistent insights for analysis, reducing the risk of drawing conclusions from artifacts of random data splits or seeds.
Efficiency: The Gaussian approximation allows for substantial computational savings (reducing bootstrap runs from 1,000 to 10) while maintaining robust performance.
Practical Impact: Models built using RoSHAP-selected features achieve predictive performance comparable to full-feature models but with substantially fewer predictors, facilitating more efficient and interpretable downstream applications.

The authors position RoSHAP not as a replacement for existing attribution methods, but as a robust complement that addresses the critical gap of attribution instability, particularly in high-stakes or high-dimensional domains.