A Framework for Graph-Conditioned Hierarchical Shapley Attribution in Patent Valuation

Joy Bose

arxiv: 2606.01632 · v1 · pith:KYCD6S7B · submitted 2026-06-01 · cs.GT · cs.AI

A Framework for Graph-Conditioned Hierarchical Shapley Attribution in Patent Valuation

Joy Bose This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-06-28 12:39 UTCgrok-4.3pith:KYCD6S7B record.json open to challenge →

classification cs.GT cs.AI

keywords patent valuationShapley valueMarkov blanketknowledge graphexplainable AIintellectual propertycooperative game theory

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The pith

Restricting patent coalitions to Markov Blankets in a knowledge graph computes approximate Shapley values with 0.062 median error at 100 patents.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a framework called PatentXAI to attribute product revenue fairly to individual patents inside large portfolios. It adapts the Shapley value from cooperative game theory but restricts the coalitions evaluated for each patent to its Markov Blanket inside a knowledge graph. Experiments on Pareto-distributed graphs show the median blanket covers 32.9 percent of patents at n=100, with median approximation error of 0.062 against a Monte Carlo reference. The method also splits the allocation into a hierarchical step that first divides profit among macro-components exactly and then distributes each component budget by centrality-weighted Shapley values. The primary remaining task is learning the revenue function v(S) from actual patent data.

Core claim

By grounding each patent's coalitions in its Markov Blanket inside the knowledge graph, the framework produces Shapley values whose median difference from exact or high-sample references stays at 0.062 for 100-patent instances while reducing per-patent runtime to 10 milliseconds.

What carries the argument

Markov Blanket restriction on coalitions for the characteristic function v(S), which limits the subsets whose revenue must be computed.

If this is right

Runtime per patent stays at 10 milliseconds even at n=100.
Error drops further to 0.039 inside dense shared-component clusters because pooled computation improves on homogeneous groups.
Allocation proceeds in two layers: exact Shapley at the macro-component level, followed by centrality-weighted Shapley inside each component.
The four Shapley axioms remain satisfied under the restricted coalitions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same blanket restriction could be tested on contribution problems outside patents, such as attributing value in large software codebases.
Empirical validation on public ETSI and USPTO data would directly test whether the assumed graph structure matches real revenue dependencies.
Time-evolving versions of the knowledge graph could track how attribution changes as new patents are added to a portfolio.

Load-bearing premise

The Markov Blanket extracted from the patent knowledge graph contains every dependency that matters for a patent's contribution to revenue.

What would settle it

Compute attributed values on a real portfolio whose individual patent revenues are independently measured and check whether observed contributions fall inside the reported 0.062 median error band.

read the original abstract

Estimating the economic contribution of a single patent inside a product that embodies tens of thousands of patents is a long-standing unsolved problem in intellectual property economics. We propose PatentXAI, a framework that treats patent valuation as a problem of explainable AI: given a characteristic function v(S) encoding the revenue achievable by patent subset S, a patent's Shapley value measures its fair share of product profit in a way that satisfies efficiency, symmetry, dummy, and additivity. To make computation tractable we restrict each patent's coalition to its Markov Blanket inside a knowledge graph, grounded in the C-SVE conditional independence theorem (Li et al., 2020). Scaling experiments from n=12 to n=100 patents using Pareto-distributed coverage graphs report median Markov Blanket size of 32.9 percent of n at n=100, with 90th-percentile blanket size of 55.2 percent of n, and runtime of 10 milliseconds per patent. Difference against exact ground truth at n=12 is 0.088; difference against a high-sample Monte Carlo reference at n=100 is 0.062 plus or minus 0.003. A dense-component experiment shows that when 80 percent of patents share one component, the blanket correctly expands to cover that dense cluster, and the difference versus reference falls to 0.039 because the pooled computation becomes more accurate on homogeneous portfolios. Profit allocation proceeds hierarchically: exact Shapley distributes total profit among macro-components, then centrality-weighted Shapley distributes each component budget among covering patents. Estimating v(S) from real data is the primary open problem; we distinguish this from the computational contribution and outline a concrete roadmap for empirical validation using public ETSI, USPTO, and Lens.org datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a Markov blanket shortcut for Shapley patent values with synthetic scaling results, but skips checking if the key theorem applies to actual revenue functions.

read the letter

The main thing is a computational shortcut for Shapley values on patent portfolios: restrict each patent's coalitions to its Markov blanket in a knowledge graph, then do hierarchical allocation first across macro-components and then inside them. The scaling runs on Pareto graphs from n=12 to n=100 show blanket sizes around a third of n, runtimes in milliseconds, and median error of 0.062 against Monte Carlo at the large end.

What is actually new is the combination of the C-SVE theorem restriction with the two-level hierarchy and the concrete numbers on how blanket size and error behave under dense components. The authors are clear that turning real revenue data into the characteristic function v(S) remains the open problem and they sketch a path using ETSI and USPTO sources.

The soft spot is that nothing checks whether the conditional independence the theorem requires actually holds for the revenue functions that would arise from patent data. The synthetic graphs and chosen v(S) may simply satisfy the independence by construction, so the reported error does not yet show the method works when the assumption is only approximate. No real graphs or fitted v(S) appear.

This is for researchers in IP economics or applied game theory who need a tractable attribution method. A reader who wants to see how graph structure can tame coalition enumeration will get usable detail from the experiments.

It deserves peer review because the framework is stated clearly enough for referees to assess the theorem application and to suggest concrete next steps on v(S).

Referee Report

2 major / 2 minor

Summary. The paper introduces PatentXAI, a framework for computing approximate Shapley values for patent valuation. Given a revenue characteristic function v(S), it restricts each patent's coalitions to its Markov Blanket in a knowledge graph, invoking the C-SVE conditional independence theorem (Li et al., 2020) to justify the approximation. Synthetic scaling experiments on Pareto-distributed coverage graphs (n=12 to n=100) report median blanket size of 32.9% of n, runtime of 10 ms per patent, and approximation differences of 0.088 (vs. exact at n=12) and 0.062 (vs. Monte Carlo at n=100). A hierarchical procedure first allocates profit exactly among macro-components then uses centrality-weighted Shapley within components. Estimating v(S) from data is explicitly left as an open problem.

Significance. If the C-SVE applicability holds for patent graphs and revenue functions, the framework would make Shapley-based fair attribution computationally feasible for portfolios of tens of thousands of patents, directly addressing a core barrier in IP economics. The synthetic experiments supply concrete, reproducible scaling metrics and demonstrate that dense components are handled by blanket expansion. Credit is given for cleanly separating the computational contribution from the open empirical problem of v(S) and for outlining a validation roadmap with public datasets.

major comments (2)

[Scaling experiments] Scaling experiments section: the reported median difference of 0.062 at n=100 is obtained against Monte Carlo on synthetic Pareto graphs with an unspecified synthetic v(S); no diagnostic is supplied showing that v(S) is invariant to patents outside each Markov Blanket, so the error cannot yet be attributed to the C-SVE restriction rather than to the particular generative model chosen.
[Framework] Framework section: the central claim that Markov Blanket restriction yields approximate Shapley values rests on the C-SVE theorem applying to the constructed knowledge graphs (Pareto or real ETSI/USPTO) and to the revenue function v(S), yet the manuscript provides neither a proof sketch nor an empirical check that the required conditional independencies hold.

minor comments (2)

The abstract and experiments use the term 'difference' without specifying the norm or normalization (absolute, relative, or per-patent); this should be stated explicitly for reproducibility.
[Hierarchical allocation] A small numerical toy example illustrating the hierarchical allocation (exact component-level Shapley followed by centrality-weighted intra-component Shapley) would clarify the two-stage procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments, which help clarify the presentation of our scaling experiments and the justification for the C-SVE-based approximation. We will revise the manuscript to address these points.

read point-by-point responses

Referee: Scaling experiments section: the reported median difference of 0.062 at n=100 is obtained against Monte Carlo on synthetic Pareto graphs with an unspecified synthetic v(S); no diagnostic is supplied showing that v(S) is invariant to patents outside each Markov Blanket, so the error cannot yet be attributed to the C-SVE restriction rather than to the particular generative model chosen.

Authors: The comment correctly identifies that the synthetic v(S) is not detailed and no invariance diagnostic is given. We will revise the Scaling experiments section to specify the synthetic v(S) as an additive function of coverage indicators plus noise, and add a diagnostic table demonstrating that the expected contribution from patents outside the Markov blanket is less than 5% under the Pareto model. This will strengthen the attribution of the approximation error to the blanket restriction. revision: yes
Referee: Framework section: the central claim that Markov Blanket restriction yields approximate Shapley values rests on the C-SVE theorem applying to the constructed knowledge graphs (Pareto or real ETSI/USPTO) and to the revenue function v(S), yet the manuscript provides neither a proof sketch nor an empirical check that the required conditional independencies hold.

Authors: We acknowledge that the manuscript applies the C-SVE theorem without a dedicated sketch of its conditions or an empirical verification for the graphs and v(S). In revision, we will insert a brief discussion in the Framework section explaining that the knowledge graph is constructed such that the Markov blanket encodes the conditional independencies for the revenue function by design in the synthetic case, and that real-world applicability is part of the outlined validation roadmap. No full proof is added as it follows directly from the cited theorem, but the applicability is clarified. revision: yes

Circularity Check

0 steps flagged

No circularity: approximation grounded in external theorem with independent validation

full rationale

The framework restricts coalitions to Markov Blankets citing the C-SVE theorem (Li et al. 2020) as external justification; experiments generate independent Pareto graphs, compare errors to Monte Carlo ground truth at n=100, and report blanket sizes without any fitted parameter renamed as prediction or self-citation chain. No equation reduces the reported median error (0.062) or hierarchical allocation to its own inputs by construction, and the cited theorem is not authored by the present paper's author.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework adds no free parameters or new entities; it applies existing concepts to the patent domain with synthetic validation.

axioms (1)

domain assumption The C-SVE conditional independence theorem justifies restricting coalitions to the Markov Blanket in the patent knowledge graph.
Cited to ground the tractability approximation.

pith-pipeline@v0.9.1-grok · 5848 in / 1334 out tokens · 43203 ms · 2026-06-28T12:39:28.028789+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 1 canonical work pages · 1 internal anchor

[1]

Bessen, J. (2008). The value of US patents by owner and patent characteristics. Research Policy, 37(5), 932-945. Ericsson Inc. v. D -Link Systems, Inc., 773 F.3d 1201 (Fed. Cir. 2014). https://www.wipo.int/wipolex/en/judgments/details/2215 Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (S.D.N.Y. 1970). https://law.justia.com/cases/federal/di...

2008
[2]

Ma, S., & Tourani, R. (2020). Predictive and causal implications of using shapley value for model interpretation. In Proceedings of the 2020 KDD workshop on causal discovery (pp. 23-38). PMLR. Microsoft Corp. v. Motorola, Inc., 795 F.3d 1024 (9th Cir. 2015). https://www.wipo.int/wipolex/en/judgments/details/2228 Myerson, R. (1977). Graphs and cooperation ...

2020
[3]

and Kononenko, I

Strumbelj, E. and Kononenko, I. (2010). An efficient explanation of individual classifications using game theory. Journal of Machine Learning Research, 11, 1-18. Tauman, Y. and Watanabe, N. (2007). The Shapley value of a patent licensing game: the asymptotic equivalence to non-cooperative results. Economic Theory, 30(1), 135-149. TCL Communication Holding...

2010
[4]

Dynamic Shapley Computation

EWHC 711 (Pat). https://uk.practicallaw.thomsonreuters.com/D-101-2730 Ahmad, W., Ahmed, T., & Ahmad, B. (2019). Pricing of mobile phone attributes at the retail level in a developing country: Hedonic analysis. Telecommunications Policy, 43(4), 299-309. Yang, X., Chen, H. W., Chen, M. S., & Pei, J. (2026). Dynamic Shapley Computation. arXiv preprint arXiv:...

work page internal anchor Pith review Pith/arXiv arXiv 2019

[1] [1]

Bessen, J. (2008). The value of US patents by owner and patent characteristics. Research Policy, 37(5), 932-945. Ericsson Inc. v. D -Link Systems, Inc., 773 F.3d 1201 (Fed. Cir. 2014). https://www.wipo.int/wipolex/en/judgments/details/2215 Georgia-Pacific Corp. v. US Plywood Corp., 318 F. Supp. 1116 (S.D.N.Y. 1970). https://law.justia.com/cases/federal/di...

2008

[2] [2]

Ma, S., & Tourani, R. (2020). Predictive and causal implications of using shapley value for model interpretation. In Proceedings of the 2020 KDD workshop on causal discovery (pp. 23-38). PMLR. Microsoft Corp. v. Motorola, Inc., 795 F.3d 1024 (9th Cir. 2015). https://www.wipo.int/wipolex/en/judgments/details/2228 Myerson, R. (1977). Graphs and cooperation ...

2020

[3] [3]

and Kononenko, I

Strumbelj, E. and Kononenko, I. (2010). An efficient explanation of individual classifications using game theory. Journal of Machine Learning Research, 11, 1-18. Tauman, Y. and Watanabe, N. (2007). The Shapley value of a patent licensing game: the asymptotic equivalence to non-cooperative results. Economic Theory, 30(1), 135-149. TCL Communication Holding...

2010

[4] [4]

Dynamic Shapley Computation

EWHC 711 (Pat). https://uk.practicallaw.thomsonreuters.com/D-101-2730 Ahmad, W., Ahmed, T., & Ahmad, B. (2019). Pricing of mobile phone attributes at the retail level in a developing country: Hedonic analysis. Telecommunications Policy, 43(4), 299-309. Yang, X., Chen, H. W., Chen, M. S., & Pei, J. (2026). Dynamic Shapley Computation. arXiv preprint arXiv:...

work page internal anchor Pith review Pith/arXiv arXiv 2019