# Probabilistic Shapley Value Modeling and Inference

arXiv: https://arxiv.org/abs/2402.04211 · HTML: https://mlsanity.com/paper/2402.04211/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [On the Tractability of SHAP Explanations](https://mlsanity.com/paper/2009.08634/) (2020)
- [TorchRL: A data-driven decision-making library for PyTorch](https://mlsanity.com/paper/2306.00577/) (2023)
- [Post hoc Explanations may be Ineffective for Detecting Unknown Spurious Correlation](https://mlsanity.com/paper/2212.04629/) (2022)
- [Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions](https://mlsanity.com/paper/2007.13481/) (2020)
- [Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift](https://mlsanity.com/paper/2006.14988/) (2020)
- [Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models](https://mlsanity.com/paper/2305.15167/) (2023)
- [Robust Recursive Partitioning for Heterogeneous Treatment Effects with Uncertainty Quantification](https://mlsanity.com/paper/2006.07917/) (2020)

## Abstract (arXiv)

We propose probabilistic Shapley inference (PSI), a novel probabilistic framework to model and infer sufficient statistics of feature attributions in flexible predictive models, via latent random variables whose mean recovers Shapley values. PSI enables efficient, scalable inference over input-to-output attributions, and their uncertainty, via a variational objective that jointly trains a predictive (regression or classification) model and its attribution distributions. To address the challenge of marginalizing over variable-length input feature subsets in Shapley value calculation, we introduce a masking-based neural network architecture, with a modular training and inference procedure. We evaluate PSI on synthetic and real-world datasets, showing that it achieves competitive predictive performance compared to strong baselines, while learning feature attribution distributions -- centered at Shapley values -- that reveal meaningful attribution uncertainty across data modalities.