[Paper Review] Priority-Aware Shapley Value

Kiljae Lee, Ziqi Liu+2 more|arXiv (Cornell University)|Feb 10, 2026

Data Quality and Management0 citations

TL;DR

PASV integrates hard precedence constraints with soft, contributor-specific priority weights to produce structure-faithful data valuation and feature attribution, with scalable Monte Carlo estimation and a sensitivity tool called priority sweeping.

ABSTRACT

Shapley values are widely used for model-agnostic data valuation and feature attribution, yet they implicitly assume contributors are interchangeable. This can be problematic when contributors are dependent (e.g., reused/augmented data or causal feature orderings) or when contributions should be adjusted by factors such as trust or risk. We propose Priority-Aware Shapley Value (PASV), which incorporates both hard precedence constraints and soft, contributor-specific priority weights. PASV is applicable to general precedence structures, recovers precedence-only and weight-only Shapley variants as special cases, and is uniquely characterized by natural axioms. We develop an efficient adjacent-swap Metropolis-Hastings sampler for scalable Monte Carlo estimation and analyze limiting regimes induced by extreme priority weights. Experiments on data valuation (MNIST/CIFAR10) and feature attribution (Census Income) demonstrate more structure-faithful allocations and a practical sensitivity analysis via our proposed "priority sweeping".

Motivation & Objective

• Motivate the need for valuation methods that respect dependency and precedence among contributors.
• Define a unified Shapley-type value that combines hard precedence constraints with soft, contributor-specific priorities.
• Develop a scalable MCMC-based estimator for sampling precedence-feasible orders under non-uniform weighting.
• Provide axiomatic characterization that uniquely identifies PASV and explain limiting regimes under extreme priorities.
• Offer a practical diagnostic tool (priority sweeping) for robustness analysis of valuations.

Proposed method

• Formulate PASV as a random-order value with p^(preceq, lambda) that respects general precedence and weights.
• Show that PASV reduces to PSV when all weights are equal and to WSV under ordered partitions.
• Provide an SCF (state–choice factorization) representation to enable Plackett–Luce–style sampling under precedence constraints.
• Develop an adjacent-swap Metropolis–Hastings sampler to approximate the PASV distribution efficiently.
• Derive theoretical results on limiting regimes where extreme weights translate into modified precedence structures.
• Introduce priority sweeping as a diagnostic to assess valuation sensitivity to weights.

Figure 5 : MNIST results. Top: Provider-level values (summed value for each provider (Lee et al. , 2025 ) ; $10$ repetitions, report mean & $\pm 1$ std. bars; Middle: Marginal contributions: $\mathbb{E}[U(\pi^{i}\cup\{i\})-U(\pi^{i})||\pi^{i}|=s]$ vs $s$ , c.f. ( 1 ), $p:=$ Uniform $(\Pi^{\preceq})$

Experimental results

Research questions

• RQ1 How can Shapley-type attributions incorporate both hard precedence constraints and soft, per-player priorities?
• RQ2 Does PASV unify existing precedence-based and weight-based Shapley variants and under what conditions are these reductions exact?
• RQ3 How can we efficiently compute PASV for large sets of players with general DAGs?
• RQ4 What are the limiting effects of extreme priority weights on the underlying precedence structure?
• RQ5 Can PASV provide actionable sensitivity analysis for data valuation and feature attribution?

Key findings

• PASV provides a unified distribution over precedence-feasible orders that combines hard precedence with soft priority weights.
• PASV reduces to PSV when all weights are equal and reduces to WSV for DAGs that are ordered partitions.
• An SCF form supports scalable Monte Carlo estimation and retains interpretability of weights as soft priorities.
• An adjacent-swap Metropolis–Hastings sampler enables efficient sampling from the PASV distribution.
• Extreme weights can induce effective changes to the precedence structure without altering the original DAG, via limiting behavior analyzed in the paper.
• Experiments on data valuation (MNIST/CIFAR10) and feature attribution (Census Income) demonstrate more structure-faithful allocations and practical sensitivity analysis through priority sweeping.

(a) Ordered Partition