Antithetic and Monte Carlo kernel estimators for partial rankings

Lomelí, María; Rowland, Mark; Gretton, Arthur; Ghahramani, Zoubin

doi:10.1007/s11222-019-09859-z

Cited by 11 publications

(12 citation statements)

References 31 publications

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“…Note that Equation (13) totally ignores the influence of non-contributive features j ∈ U \S i \{i} to the value function, which leads to sub-optimal solutions. To address this problem but without extra calculation, SHEAR employs the antithetical sampling (AS) (Lomeli et al, 2019) to fix the preceding difference in Equation ( 13) to promote the estimation. Specifically, following the enumeration of S ⊆ S i in Equation ( 13) where…”

Section: Antithetical Samplingmentioning

confidence: 99%

“…Baseline Methods: SHEAR is compared with five stateof-the-art baseline methods of Shapley value estimation, including Kernel-SHAP (KS) (Lundberg & Lee, 2017), Kernel-SHAP with Welford algorithm (KS-WF) (Covert & Lee, 2021), Kernel-SHAP with Pair Sampling (KS-Pair) (Covert & Lee, 2021), Permutation Sampling (PS) (Mitchell et al, 2021) and Antithetical Permutation Sam-pling (APS) (Lomeli et al, 2019). More details about the baseline methods are provided in Appendix G.…”

Section: Datasetmentioning

confidence: 99%

See 1 more Smart Citation

Accelerating Shapley Explanation via Contributive Cooperator Selection

Guanchu¹,

Yu-Neng²,

Du³

et al. 2022

Preprint

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Even though Shapley value provides an effective explanation for a DNN model prediction, the computation relies on the enumeration of all possible input feature coalitions, which leads to the exponentially growing complexity. To address this problem, we propose a novel method SHEAR to significantly accelerate the Shapley explanation for DNN models, where only a few coalitions of input features are involved in the computation. The selection of the feature coalitions follows our proposed Shapley chain rule to minimize the absolute error from the ground-truth Shapley values, such that the computation can be both efficient and accurate. To demonstrate the effectiveness, we comprehensively evaluate SHEAR across multiple metrics including the absolute error from the ground-truth Shapley value, the faithfulness of the explanations, and running speed. 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. The source code is available at https: //github.com/guanchuwang/SHEAR.

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Section: Antithetical Samplingmentioning

confidence: 99%

Section: Datasetmentioning

confidence: 99%

Accelerating Shapley Explanation via Contributive Cooperator Selection

Guanchu¹,

Yu-Neng²,

Du³

et al. 2022

Preprint

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“…A common choice for sampling on the unit cube is X ∼ U (0, 1) d with Y i = 1 − X i . Antithetic sampling for functions of permutations is discussed in Lomeli et al (2019), with a simple strategy being to take permutations and their reverse. We implement this sampling strategy in our experiments with antithetic sampling.…”

Section: Antithetic Samplingmentioning

confidence: 99%

Sampling Permutations for Shapley Value Estimation

Mitchell¹,

Cooper²,

Frank³

et al. 2021

Preprint

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Game-theoretic attribution techniques based on Shapley values are used extensively 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 sophisticated quasi Monte Carlo methods are not well defined on the space of permutations. To address this, we investigate new approaches based on two classes of approximation methods and compare them empirically. First, we demonstrate quadrature techniques in a RKHS containing functions of permutations, using the Mallows kernel to obtain explicit convergence rates of O(1/n), improving on O(1/ √ n) for plain Monte Carlo. The RKHS perspective also leads to quasi Monte Carlo type error bounds, with a tractable discrepancy measure defined on permutations. Second, we exploit connections between the hypersphere S d−2 and permutations to create practical algorithms for generating permutation samples with good properties. Experiments show the above techniques provide significant improvements for Shapley value estimates over existing methods, converging to a smaller RMSE in the same number of model evaluations.

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“…Indeed, we have to sum over |E R ||E R | permutations. Several works aim to reduce the computation cost of this kernel (see [28,30,31]). However, its efficient computation remains an issue.…”

Section: 1 a New Kernel On Partial Rankingsmentioning

confidence: 99%

Gaussian field on the symmetric group: Prediction and learning

Bachoc¹,

Broto²,

Gamboa³

et al. 2020

Electron. J. Statist.

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In the framework of the supervised learning of a real function defined on an abstract space X , Gaussian processes are widely used. The Euclidean case for X is well known and has been widely studied. In this paper, we explore the less classical case where X is the non commutative finite group of permutations (namely the so-called symmetric group S N ). We provide an application to Gaussian process based optimization of Latin Hypercube Designs. We also extend our results to the case of partial rankings.

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Antithetic and Monte Carlo kernel estimators for partial rankings

Cited by 11 publications

References 31 publications

Accelerating Shapley Explanation via Contributive Cooperator Selection

Accelerating Shapley Explanation via Contributive Cooperator Selection

Sampling Permutations for Shapley Value Estimation

Gaussian field on the symmetric group: Prediction and learning

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