# Sampling Permutations for Shapley Value Estimation

@article{Mitchell2022SamplingPF, title={Sampling Permutations for Shapley Value Estimation}, author={Rory Mitchell and Joshua N. Cooper and Eibe Frank and Geoffrey Holmes}, journal={ArXiv}, year={2022}, volume={abs/2104.12199} }

Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more…

## Figures and Tables from this paper

## 19 Citations

### Algorithms to estimate Shapley value feature attributions

- Computer ScienceArXiv
- 2022

This work describes the multiple types of Shapley value feature attributions and methods to calculate each one and describes two distinct families of approaches: model-agnostic and model-speciﬁc approximations.

### Accelerating Shapley Explanation via Contributive Cooperator Selection

- Computer ScienceICML
- 2022

The experimental results indicate SHEAR consistently outperforms state-of-the-art baseline methods across different evaluation metrics, which demonstrates its potentials in real-world applications where the computational resource is limited.

### PDD-SHAP: Fast Approximations for Shapley Values using Functional Decomposition

- Computer ScienceArXiv
- 2022

PDD-SHAP is proposed, an algorithm that uses an ANOVA-based functional decomposition model to approximate the black-box model being explained, which allows it to cal-culate Shapley values orders of magnitude faster than existing methods for large datasets.

### FastSHAP: Real-Time Shapley Value Estimation

- Economics, Computer ScienceICLR
- 2022

FastSHAP is introduced, a method for estimating Shapley values in a single forward pass using a learned explainer model that amortizes the cost of explaining many inputs via a learning approach inspired by the Shapley value’s weighted least squares characterization.

### Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features

- Computer ScienceArXiv
- 2021

This paper uses a variational autoencoder with arbitrary conditioning (VAEAC) to model all feature dependencies simultaneously and demonstrates that this approach to Shapley value estimation outperforms the state-of-the-art methods for a wide range of settings for both continuous and mixed dependent features.

### Joint Shapley values: a measure of joint feature importance

- EconomicsArXiv
- 2021

Deriving joint Shapley values in ML attribution problems gives the first measure of the joint effect of sets of features on model predictions, and presents a presence-adjusted method for calculating global values that retains the efficiency property.

### Variable importance without impossible data

- Computer ScienceArXiv
- 2022

Cohort Shapley is advocated, a Bayesian bootstrap is proposed to quantify uncertainty in both individual and aggregate Shapley values, and it is illustrated on an algorithmic fairness problem where it is essential to attribute importance to protected variables that the model was not trained on.

### Edinburgh Research Explorer The Shapley Value in Machine Learning

- Computer Science, Economics
- 2022

An overview of the most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation.

### The Shapley Value in Machine Learning

- Computer Science, EconomicsIJCAI
- 2022

The most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation are given.

### PredDiff: Explanations and Interactions from Conditional Expectations

- Computer ScienceArtificial Intelligence
- 2022

## References

SHOWING 1-10 OF 55 REFERENCES

### A Multilinear Sampling Algorithm to Estimate Shapley Values

- Computer Science, Economics2020 25th International Conference on Pattern Recognition (ICPR)
- 2021

This work proposes a new sampling method based on a multilinear extension technique as applied in game theory that is applicable to any machine learning model, in particular for either multiclass classifications or regression problems.

### Antithetic and Monte Carlo kernel estimators for partial rankings

- Computer ScienceStat. Comput.
- 2019

A novel way to extend kernel methods for complete rankings to partial rankings, via consistent Monte Carlo estimators for Gram matrices: matrices of kernel values between pairs of observations, is presented.

### Addressing the computational issues of the Shapley value with applications in the smart grid

- Computer Science
- 2015

An improved error bound for approximating the Shapley value using simple random sampling (SRS), which can be used in any superadditive game, and the use of stratified sampling, which can lead to smaller standard errors.

### Improving polynomial estimation of the Shapley value by stratified random sampling with optimum allocation

- Computer ScienceComput. Oper. Res.
- 2017

### On kernel methods for covariates that are rankings

- Computer Science
- 2016

This paper studies the use of reproducing kernel Hilbert space methods for learning from permutation-valued features, and describes both the feature spaces and spectral properties associated with two kernels for rankings, the Kendall and Mallows kernels.

### Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration

- Computer Science
- 2010

This comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research.

### A Value for n-person Games

- Economics
- 1988

Introduction At the foundation of the theory of games is the assumption that the players of a game can evaluate, in their utility scales, every “prospect” that might arise as a result of a play. In…

### Feature Selection via Coalitional Game Theory

- Computer ScienceNeural Computation
- 2007

Empirical comparison with several other existing feature selection methods shows that the backward elimination variant of CSA leads to the most accurate classification results on an array of data sets.

### Permutations as Angular Data: Efficient Inference in Factorial Spaces

- Mathematics, Computer Science2010 IEEE International Conference on Data Mining
- 2010

This work proposes an embedding of all $n!$ permutations for a given $n$ in a surface of a hyper sphere defined in $\mathbbm{R}^{(n-1)}$ and acquires ability to define continuous distributions over ahyper sphere with all the benefits of directional statistics.

### On the Complexity of Cooperative Solution Concepts

- EconomicsMath. Oper. Res.
- 1994

The von Neumann-Morgenstern solution is pointed out that its existence may not even be decidable, and many of these results generalize to the case in which the game is presented by a hypergraph with edges of size k > 2.