RankSHAP: Shapley Value Based Feature Attributions for Learning to Rank
Authors: Tanya Chowdhury
Yair Zick
James Allan
Venue: ICLR 2025 Poster (2025)
Keywords: Feature attributions
Shapley values
Information Retrieval
Passage Reranking
Primary area: interpretability and explainable AI
TL;DR: Shapley value based feature attributions for Ranking tasks

Abstract: Numerous works propose post-hoc, model-agnostic explanations for learning to rank, focusing on ordering entities by their relevance to a query through feature attribution methods. However, these attributions often weakly correlate or contradict each other, confusing end users.  We adopt an axiomatic game-theoretic approach, popular in the feature attribution community, to identify a set of fundamental axioms that every ranking-based feature attribution method should satisfy. We then introduce Rank-SHAP, extending classical Shapley values to ranking. We evaluate the RankSHAP framework through extensive experiments on two datasets, multiple ranking methods and evaluation metrics. Additionally, a user study confirms RankSHAP’s alignment with human intuition. We also perform an axiomatic analysis of existing rank attribution algorithms to determine their compliance with our proposed axioms. Ultimately, our aim is to equip practitioners with a set of axiomatically backed feature attribution methods for studying IR ranking models, that ensure generality as well as consistency.

Published as a conference paper at ICLR 2025
RANKSHAP: SHAPLEY VALUE BASED FEATURE AT- TRIBUTIONS FOR LEARNING TO RANK
Tanya Chowdhury, Yair Zick, James Allan Manning College of Information and Computer Sciences University of Massachusetts Amherst (tchowdhury, yzick, a allan) ecs. uww.s. edu
ABSTRACT
Numerous works propose post-hoc, model-agnostic explanations for learning to rank, focusing on ordering entities by their relevance to a query through feature attribution methods. However, these attributions often weakly correlate con- tradict each other, confusing end users. We adopt an axiomatic game-theoretic approach, popular in the feature attribution community, to identify set of funda- mental axioms that every ranking- based feature attribution method should satisfy. We then introduce Rank-SHAN extending classical Shapley values to ranking. We evaluate the RankSHAP framework through extensive experiments on two datasets, multiple ranking methods and evaluation metries. Additionally, a user study con- firms RankSHAP's alignment with human intuition. We also perform an axiomatic analysis of existing rank attribution algorithms determine their compliance with our proposed axioms. Ultimately, our aim is to equip practitioners with a set of axiomatically backed feature attribution methods for studying IR ranking models, that ensure generality as well as consistency.
INTRODUCTION
A user submits a query to a search engine, wanting to know, say, what is the best car to purchase. The search engine processes the query and outputs a ranked list of documents (web pages) in response to the query. How did the search engine decide on the order in which the documents are presented? The task of ranking entails query 7 and set of documents 1) as input to a ranking model fn, which in turn generates an ordering of these documents. We assume that the ranking model is available only as a black-box which can be queried using an API. For a particular query, we wish to understand the logic behind the generated ordering, to verify the functionality of the model as well as to help end users. Ranking feature attributions are critical for building trust in systems which are used for high stakes decision making (Anand et al.] 2022 Chowdhhuy al.) (023)). Such feature attributions are also useful in ruling out prejudices in widely used web search, product search and recommendation
systems (Singh & Anand 2019 (Singh et al. 2020).
Additive feature attributions have become a well studied topic in recent years, especially for regression and classification tasks. To maintain consistency between different feature attribution methods, various authors (Lundberg & Lee 2017 Datta et al. 2016) proposed unique solution based on the Shapley value (Shapley) 1953) This solution is considered the reference standard of feature attributions because of the several fundamental axioms it uniquely satisfies. Different approximations such KernelSHAP (Lundberg & Lee (017)) and DeepSHAP (Lundberg & Leel 2017 Shrikumar et al. 2017) are used for popular real-world applications.
Quite few attempts have been made to generate feature attributions for ranking tasks, often by extending attribution methods from classification/regrsssi
EXS (Singh & Anand (219)) and Rank-LIME (Chowdhury et al.) 2023) extend LIME in different manners to obtain ranking feature attributions. However, these attributions contradict each other across the different settings in the very same algorithm. Fernando et al. (0019) also generate explanations for ranking models using DeepSHAP and report little correlation between the attributions generated by different reference values for the very same query. This shows us that extensions of popular feature attribution methods for classification and regression are not good attribution candidates for ranking. More recently,

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RankingSHAP (Heuss et al. 2024) extend Shapley values to generate feature attributions for ordered lists. However, we show that even their proposed- proposed-framewort. framework does not satisfy fundamental properties like monotonicity and efficiency. Consequently, establishing robust reference standard for ranking feature attributions is imperative. Such a framework will significantly benefit a wide range of stakeholders, from end users seeking more reliable search results researchers and practitioners aiming to gain deeper insights into model behavior.
Our Contributions. We present a set of fundamental axioms for Information Retrieval (IR) value (unctions-Relevancce Sensitivity and Position Sensitiviry- along with Shapley properties specific to ranking: Rank-Efi Efficieni,,,,y, these axioms are essential for any ranking feature attribution method to uphold without sacrificing generality. To address this need, we introduce RankSHAP, an extension of the Shapley value that satisfies all the aforementioned axioms. We discuss computationally feasible approximations using KerneISHAP to make RankSHAP practical for real-world applications. We conduct extensive experiments on two datasets MS MARCO and Robust04 using multiple document re-ranking models based on BERT, T5, and LLAMA2. Our results demonstrate that RankSHAP outperforms existing ranking feature attribution methods, surpassing the best baseline by 25.78% in Fidelity and 19.68% weighted Fidelity (wFidelity). Additionally, we carry out an IRB-approved user study assess how well the proposed axioms align with human intuition. We also provide an axiomatic analysis of existing rank attribution methods-EXX RankLIME, and RankingSHAPP-O determine whether they satisfy the fundamental axioms. Ultimately, we advocate for practitioners to adopt SonkSHAP-basee axiomatically grounded feature attribution methods as the reference standard for their IR explanation needs. Once the work accepted, we plan to release our code as a python library.
Missiiiissnsssss, Rank- Sonnk-ymmeetry and connkooonotoicctty We believe,
BACKGROUND
We start by briefly describing the Shapley value, used for credit assignment in coalitional game theory, and its consequent use in feature attributions for machine learning models. Following this, outline some basic properties of information retrieval systems and discuss evaluation metrics for ordered document lists.
2.1 BASIC AXIOMS AND THE SHAPLEY VALUE
The Shapley axioms for feature attributions have been borrowed from coalitional game theory, where they are foundational constraints, used to fairly distribute costs/rewards among a set of players. In the context of feature attributions for ML models, we can think of each feature as a player contributing to the model's output. Thus, given any model f. that has scalar output, the feature attribution of feature in the decision made by f towards the model input is represented by (f, 5). Let us assume there are total of m features. For a feature attribution (s f $) to be sound, it is necessary for it to satisfy certain basic axioms, namely: Efficiency, Missingness, Symmetry and Monotonicity (Appendix [B).
The Shapley value (Yunng 1985 Shapley 1953) uniquely satisfies the four axioms above and has been widely adopted in feature attribution for regression/classiicatioon tasks. It is defined as:
1m 27 1)! [f(²) - f(E) i)
(I)
m!!
SC
where C represents all binary vectors where the non-zero entries correspond to a subset of the non-zero entries in 8. Essentially, E indicates which features are included (non-zero) and which are excluded (zero) in a particular subset; |=] the number of non-zero entries in ž; z' i denotes the vector Z with the i-th feature removed (set to zero/replaced by bascline value); f(ā) denotes the output of the model f when the input features corresponding to the non-zero entries in ă are set to their values in 5, and the remaining features set to baseline value (e.g., zero).
Satisfying these basic axioms ensures that a feature attribution method fair and consistent, and as a result, trustworthy for end users. The classical Shapley framework cannot be directly applied to the ranking feature attribution task as in the ranking scenario, the model output f ()) is not scalar, but an ordering of documents.
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2.2 DOCUMENT RELEVANCE AND IR EVALUATION METRICS
In Information Retrieval (IR), the concept of relevance is fundamental to understanding how search systems operate. Relevance rel de) quantifies how well document d; matches user's query q For simplicity, the relevance score of particular document d can be denoted rely. These scores can be binary (relevant or not relevant) or numerical values indicating varying degrees of relevance, with higher scores representing better matches. Assigning relevance scores allows IR systems to prioritize the most pertinent documents in search results, enhancing the user's ability to find useful information quickly.
Evaluating the quality of an ordered list of documents (e.g., web pages) is crucial for assessing how effectively an system meets users' needs. Given an ordered list, we need determine how well this arrangement serves the user compared to other possible orderings. Several evaluation metrics are commonly used for this purpose. Precision measures the proportion of retrieved documents that are relevant. Mean Average Precision (MAP) calculates the average precision across multiple queries, considering the rank positions of all relevant documents. Discounted Cumulative Gain (DCG) takes into account both the relevance of documents and their positions in the ranked list. It applies logarithmic discount factor to penalize relevant documents that appear lower in the list. Normalized Discounted Cumulative Gain (NDCG) (Jrvelln & Kekäläinen 2002) is normalized version of DCG that scales the scores between 0 and 1. This allows for fair comparison across different queries and systems.
Among these metrics, NDCG has become the standard and is almost universally used to evaluate the effectiveness of ranked lists (Yining et al. 2013). Due to its ability effectively account for both the relevance and the position of documents, NDCG extensively adopted in modern IR systems, search engines, and recommendation platforms to assess and compare the performance of different ranking algorithms (Appendix
3 THE RANKSHAP FRAMEWORK
We first define the feature attribution problem for ranking models in Section 3.1 We then define
the Shapley axioms for the ranking task in Section [3.2] Next, in Section 3.3 we discuss ideal
properties of ordered list value functions and propose Generalized Ranking Effectiveness Metric (GREM). Finally, in Section 3.4 we present the unique solution that satisfies the Shapley and GREM constraints for the ranking feature attribution task. In Section 3.5] we discuss computationally feasible approximations of the RankSHAP expression, making it suitable for practical use cases.
3.1 THE RANKING ATTRIBUTION PROBLEM
Let fR represent ranking model, acessible to us only as a black-box. Given query q and a set of documents D = {di...., ). fR computes an ordering of documents D, i.e. fa(ī, D). Let the query and set of documents (Ø, D) jointly form the instance (ø). The goal is to generate post-hoc feature attributions ( J7, to understand the ranking model's decision corresponding to
We assume that there are documents in D, and that there are features of interest. ΦR(RR- 7) is thus a m- dimensional vector where each element represents the contribution a particular feature to the ranking decision. The query and documents here can be represented in any manner, for example: bag of words, human engineered features, vectors in some embedding space, etc.
3.2 SHAPLEY AXIOMS FOR RANKING
Let the set of features being studied be represented by M = (1, 2, m] and let Vn be a function that assigns real-valued effectiveness score to each ordering of documents. The effectiveness score reflects the quality the ranking based on the relevance of the documents to the query. We refer to the mean value of feature across the dataset being studied as its baseline value. Using these, we re-write the Shapley axioms for the ranking task as follows:
Rank-Effie :fnn-Efffcieenc:: The sum total of all feature attributions for a particular ordering should be equal the difference between the effectiveness scores of the orderings obtained when all features
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included and when all features replaced by their baseline values.
Σ
= -
where fR()) represents the model's output when all features are replaced by their baseline values.
Bank-Missinggnss:: If the inclusion of feature does not change the effectiveness score for any ordering as compared when the feature is replaced by its baseline value, must be assigned an attribution of O.
More formally, if for all S S M {i} have Vn(Jn(S U 1, Vn)(n(S,3)) then (RRRR. H, 0.
Two features i,j M are called symmetric if they produce equal effectiveness scores when added individually to every possible feature coalition excluding them. The Rank- symmetry axiom requires that assign equal attributions symmetric features.
Cank-Symmetryy
for all S M (i.j} we have VR(JR(S U i, = VR(SR(S j,ā)), then ØR(FR, 2, = (R(FR.
Gank-Monotonicity: For input E and two ranking models fR and fh. if for all coalitions where S S MM {i). the marginal effectiveness gain of adding i to S in fR. is greater than equal to the marginal effectiveness gain of adding to S in f'. the attribution of in fn has to be greater in fn compared f'k.
for all S Mi) have then Φn( Z, i) 2 Φn(sk. i)
V
3.3 A GENERALIZED RANKING EFFECTIVENESS METRIC (GREM)
In this section, we study the desired properties for the ordering effectiveness score VR. The IR evaluation community uses number of measures to evaluate the effectiveness of a search engine's ranking system. Different measures focus on different aspects of the retrieval and different needs of users (Gupta et al., 2019). key part of all measures is the relationship between document's rank and the relevance score: they are expected to be consist with each other. Summarizing most work on evaluation leads us to two high-level properties that we expect any metric quanitifying effectiveness of a ranking to provide.
Given a query q. set of documents D [d], d2 d2...., del. human-generatee relevance value rely associated with each document dj. and a metric value GREM,, determined from the set of query-document pairs, consider the ordered list fn(Āī D). For an evaluation of the ordering. is ideal for the metric (GREM,, to satisfy the following axioms:
Relevance Sensitivity: If the relevance score of any document increases, while the relevance scores of all other documents remain the same, the metric value GREM, should not decrease. Formally, rel', > rel, for some j, and rel' = rel, for all i + j. then GREM,, 2 GREM,,, where GREM,, is the metric computed with the updated relevance scores (rellreely,
rel))
Position Sensitivity: two documents d, and d, are swapped in the ranking, moving the document with the higher relevance score higher (better) rank, the metric value GREM,, should not decrease.
Formally, let be the original ordering, and o' be the ordering where only d; and d, are swapped. rel, rel, and (d,) > (d)), then GREM", Z GREM,, where GREM", is the metric computed with the new ordering o'.
Relevance Sensitivity intuitively captures the principle that more relevant documents should enhance the overall effectiveness, while Position Sensitivity reflects that users prefer find relevant information earlier in the ranking. These axioms are fundamental to any rank effectiveness metric because they align with the core goal of retrieval systems: to present the most relevant information prominently, thereby maximizing user satisfaction and system effectiveness.
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Theorem 3.1. An ordered list evaluation metric satisfies the axioms of Relevance Sensitivity and Position Sensitivity if and only if it can be represented as
GREM, Σ g(rel)) h(5).
where g(rel}) is non-decreusing function of the relevance score rel, (gain function), and h(j) is non-negative, non con-increasinng function of the rank position j (discount function).
Proof of Theorem 3.1 sketched Appendix Examples of gain functions g(rel)) include linear gain rely and exponential gain 2rely 1. Examples of discount functions h(j) include no
discount h(j) 1, logarithmic discount h(j) 1og, and reciprocal discount h(j) J. Most widely-used IR metrics like CG, DCG, NDCG, reciprocal rank, precision @ k belong to the GREM, framework.
3.4 RANKSHAP ATTRIBUTIONS
Building upon the Shapley axioms adapted for ranking tasks (Section 3.2 and the characterization of ordering effectiveness metrics (Theorem 3.1), we conclude the following:
Theorem 3.2. Let VR ranking effectiveness metric that belongs to GREM,, as characterized in Theorem 3.7 Then, the Shapley value OR computed with respect to VR is the unique feature
attribution method that satisfies the axioms of Bank-Efficiert and Rank- Sonk-Monotonicity.
Missingssing,,ss, Lank-Symmerry
Specifically, the attribution for feature is given by:
|S| (m |S] 1)!
2,1
Σ
(i)()((SU()).)) - -Va((a(5,))
m
SCMVO
where the sum over all subsets S of M \ (t), [S] is the cardinality of S, and m is the total number of features.
Proof. The proof is direct application of Shapley's 's theorem (Shapley 1953) in the context of ranking models. By adapting the classical Shapley axioms to the ranking task (as detailed in Section 3.2), establish a set of axioms (Rank-Eftt Sfank-Efficieecy, Rank- Bank--Msssiggness, tailored to ranking feature attributions. Given that VR satisfies Relevance Sensitivity and Position Sensitivity (as per Theorem 3.II), it ensures that VR is appropriate for evaluating the effectiveness of document rankings in response to feature subsets.
Symmmerry,, Rank-Monotonicity)
unique method that satisfies the axioms of Efficiency, Null Player (Missingness), Symmetry, and Additivity (which corresponds to Monotonicity in our context). By applying this theorem to the ranking scenario with our adapted axioms, we conclude that the Shapley value on is the unique feature attribution method satisfying all the specified axioms. Therefore, the attributions computed using the Shapley value formula provide a fair and consistent distribution of the total ranking effectiveness among the features, reflecting each feature's contribution to the ranking decision.
Shapley's theorem states that the Shapley value
Hence, recommend practitioners RankSHAP for their ranking attribution needs due to its adherence to set fundamental properties.
3.5 APPROXIMATING RANKSHAP
Among the metrics in GREM, we use NDCG in further experiments due to its appealing properties discussed in Appendix C Computing the exact Shapley value is NP-Hard (Shapley 1953) because it grows exponentially with the number features. Additionally, NDCG computation for each subset increases the complexity by O(n log n). Relevance labels, necessary for ranking value functions, are often unavailable. Here we discuss how we approximate the RankSHAP solution for practical applications.
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The NDCG score relies knowing the relevance scores for each document, ideally obtained from ground truth labels in a human human-annotatee annotated dataset, which are often unavailable. Several neural rankers (c.g., BERT NNgueira & Cho 2019) assign similarity score to each query- document pair, which can infer relevance and compute NDCG. In the absence of similarity scores, relevance can be indirectly inferred using methods such click-through rate, time spent on page, bounce rate, scroll depth, bookmarking, and social media shares (Zoeter et al. 2008) or via heuristic based relevance measures such BM25.
Inferring NDCG:
Cernel-RankSHAPP While the Shapley value itself is NP-hard compute, KernelSHAP (Lund- berg & Lee| 2017) leverages a kernel based model to faithfully approximate the Shapley value. It is linear approximation of the ranking model fR at instance H, which extends the LIME optimization function with a defined kernel and loss function. Below we write it for ranking attributions and name Kernel-RankSHAP. Let G be the class of all linear additive attribu- tions. OR(FR, i. arg mingeG L(fR. T&) where L(fR, 9. RT) = (DCG((((())) NDCG (E)) and (z) (T =I)
QII vs Kernel-SHAP: Another popular way to approximate Shapley values is to sampling based QII (Datta et al. 2016) in place of kemelss. The decision to use kernels rather than sampling in high-dimensional feature spaces is computationally motivated. Sampling
introduce significant noise, reducing the reliability of estimates. Kernels, however, can more effectively approximate feature contributions without the extensive computation and noise associated with random sampling, especially in large feature spaces.
4 AXIOMATIC ANALYSIS OF RANK FEATURE ATTRIBUTION ALGORITHMS
Previously, we discussed the importance of feature attribution methods satisfying the foundational Shapley axioms be considered effective for IR feature attributions. Here, we mathematically formalize existing ranking feature attribution methods and analyze them axiomatically to determine they fulfill Shapley criteria.
Table 1: Analysis of Ranking Feature Attribution algorithms EXS, RankLIME, RankingSHAP and RankSHAP for axiomatic compliance of Rank- Saanleh axioms.
Algorithm Rank-Efficiency
Rank Lank-Missingness
Rank Lank-Symmetry
Rank-Monotonicity
EXS
X
X
RankLIME
X
X
RankingSHAP
X
X
RankSHAP
V
V
4.1
OPTIMIZATION FUNCTION
In order to study these feature attribution algorithms individually, we write their KernelSHAP optimization function and use them to analyze the algorithms satisfy the axioms of Rank- Ffficieei, Rank-Missingness,, Rank- Cank-Symmetry and Kank-Monotonicity:
LRANKLIME (fR, T.) =
Σ AApro2N Tz(2)
ZEZ
(RANKINGSHAP(FRR..... RT)
Σ
(T((f(2), T=(2)
BEZ
TRANKSHAP((R. Σ ZEZ
TT(E)
Here, fR is the original ranking model, y is the surrogate model used for explanation, TH is the KernelSHAP weighting kernel, is the set all possible coalitions (subsets of features), 7 is
Kendall's 's tau rank correlation coefficient, and ApproxNDCG is approximation of the Normalized Discounted Cumulative Gain (NDCG). The details the axiomatic analysis are presented in Appendix
The results summarized in Table T Our analysis reveals that RankSHAP is the only method

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that have decomposable and additive value function and result satisfies the fundamental Shapley axioms, making it reliable to use for ranking feature attributions.
Table 2:
Comparing performance between different feature attribution methods (Random, EXS, RankLIME, RankingSHAP and RankSHAP) for ooken-based explanations of textual rankers (BM25, BERT. T5 and LLAMA2) based on model fidelity (Fidelity) and weighted-fidelin (wFidelity) with ranking models fine tuned on the MS MARCO (MM) and TREC ROBUST 2004 (R04) datasets. For these experiments, we generate feature attributions for each ranking models with the 10, 20 and 100
most relevant documents for particular query respectively.
Ranker +
Top-10
Top-20
Top- 100
Metric
Fidelity
wFidelity
Fidelity
wFidelity
Fidelity
wFidelity
Random
0.08
0.04
-0.05
0.01
-0.09
0.00
EXS
0.39
0.34
0.31
0.29
0.24
0.17
MM/BM25
RankLIME
0.45
0.37
0.37
0.29
0.26
0.20
Ranking SHAP
0.52
0.41
0.45
0.33
0.31
0.24
RankSHAP
0.63
0.48
0.54
0.40
0.47
0.33
Random
0.12
0.02
-0.09
0.01
-0.12
0,00
EXS
0.36
0.21
0.28
0.18
0.11
0.08
MM/BERT
RankLIME
0.41
0.24
0.32
0.24
0.23
0.18
RankingSHHP
0.45
0.29
0.38
0.27
0.28
0,24
RankSHAP
0.59
0.41
0,45
0.38
0.39
0.29
Random
0.05
0.03
-0.11
0.01
-0.04
0.00
EXS
0.36
0.21
0.30
0.17
0.11
0.06
MM/T5
RankLIME
0.35
0.24
0.35
0.20
0.27
0.17
RankingSHAP
0.41
0.30
0.38
0.32
0.31
0.22
RankSHAP
0.56
0.39
0.43
0.37
0.36
0.29
Random
0.04
0.01
-0.2
0.0
0,02
0.1
EXS
0.39
0.20
0.32
0.15
0.17
0,05
MM/LLAMA2
RankLIME
0.35
0.24
0.35
0.20
0.27
0.17
RankingSHAP
0.44
0.33
0.37
0.23
0.31
0.22
RankSHAP
0.60
0.42
0,45
0.39
0.39
0.32
Random
0.08
0.04
-0.04
0,00
-0.07
0.00
EXS
0.37
0.33
0.30
0.26
0.22
0.18
R04/BM25
RankLIME
0.43
0.36
0.36
0.25
0.25
0.18
RankingSHAP
0.45
0.35
0.37
0.29
0.26
0,24
RankSHAP
0.61
0.44
0.52
0,38
0.45
0.31
Random
0.12
0.02
-0.09
0.01
-0.12
0.00
EXS
0.35
0,20
0.27
0.16
0.10
0.07
R04/BERT
RankLIME
0.40
0.22
0.31
0.23
0.23
0.17
STIA
0.43
0.26
0.36
0.28
0.28
0.23
RankSHAP
0.59
0.41
0.45
0.38
0.39
0.29
Random
0.05
0.03
-0.11
0.01
-0.04
0,00
EXS
0.38
0.21
0.32
0.17
0.13
0,06
R04/T5
RankLIME
0.38
0.24
0.35
0.20
0.28
0.17
RankingSHAP
0.41
0.31
0.38
0.24
0.32
0,24
RankSHAP
0.56
0.39
0,43
0.37
0.36
0.29
5
COMPUTATIONAL AND HUMAN EVALUATION STUDIES
In this section, we first describe our experimental design. Next we evaluate the performance of our attribution algorithm based various metrics. Lastly we conduct user study to investigate how well different attribution algorithms align with human intuition for the ranking task.
5.1 EXPERIMENTAL SETTINGS
Dataset: We test our hypothesis on two datsets (i) the MS MARCO mmsm
2016 passage reranking
dataset (ii) the TREC 2004 Robust track dataset (Robust04, (Voorhees al. 2003 MS MARCO is a large-scale dataset aggregated from anonymized Bing search queries containing > 8.M passages from diverse text sources. The average length of passage in the MS MARCO dataset is 1 1131
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words. Similarly, Robust04 is aggregated from News Articles and Descriptions serve its queries. It contains over 528,000 news articles, 250 queries and binary human-annotateed relevance judgements.
Ranking models: For our ranking models, we use the classic BM25 ranker (Robertson & Spärck Jones 1994) as well as models based on the BERT (Devlin al., 2019). T5 (Raffel et al. 2020) and Llama2 (Tovrron et al. 2023) large language models. We in particular use the versions of these LLMs fine-tuned on the MS MARCO and Robust04 datasets for the document re-ranking task, released by various authors (Nogueira & Cho 2019 Nogueira et al. 2020 Ma et al. 2023). All the above ranking approaches are score based rankers, i. they return a relevance score corresponding to each document. This makes relevance score estimation straightforward for NDCG computation, as discussed previously, in Section 2
Experimental Settings: sets of the MS MARCO and Robust04 datasets, retrieving the 100 highest scoring documents for each query. Using these query-document sets, we apply the ranking models to obtain an ordered list of documents. We then generate feature attributions for the top-10, top-20, and top-100 documents. Stemmed tokens from the vocabulary of the query-document sets as bag of words make up the features for which we generate attributions. Binary feature values are assigned based on their presence or absence. Le if feature (token) is excluded from a coalition, all occurrences of that token are omitted from the query and documents for that pass of the model (Ribeiro et al.] 2016).
Similar to related works, we randomly sample 250 queries from the test
Competing Systems: We generate feature attributions for each query and corresponding ordered- document set using EXS (Singh & Anand, 2019), RankLIME (Chowdhury al. (002), Ranking- SHAP (Heuss et al. 2024). and our proposed method, RankSHAP. For EXS, we utilize the rank-based setting to allow direct comparison with RankSHAP. For RankLIME, compute attributions using the NeuraINDDGG loss function in the single-pertie panteeperturbbtion setting. In the case of RankingSHAP we employ Kendall's Tau to calculate the marginal contributions. To ensure consistency across all methods, we extend KernelSHAP for implementation and apply the same masking techniques as used in LIME. Each algorithm is limited 5,000 neighborhood samples per decision. For evaluation, we process only the top most significant features produced by each algorithm, adhering to human comprehension limits (Chowdhury et al., 2023).
We also evaluate the performance of RankSHAP using alternative value functions that satisfy GREM, including MAP, CG, and DCG. Additionally, we compare the performance RankSHAP when using explicit relevance labels to its performance when employing heuristic-basse -based relevance labels, such as those derived from BM25.
Apart from human evaluations, feature attributions can evaluated using either fidelity-based based metries via reference-basee metrics. Since ground truth attributions are not available in this case, we stick to fidelity- metrics, which measure the degree to which an attribution algorithm is successful in recreating the underlying model decision (Anand al. 2022, [hoowdhury et al. 2023). For this, we use the metrics Fidelity and its weighted version wFidelity. Given feature attribution and set of documents, we reconstruct the attribution ordering by sorting linearly-combing document features multiplied with their attributions. For Fidelity, we report the simplified unweighted Kendall's Tau between the original ranking model's ordering and ordering. For wFidelity, we penalize each swap in passages found in
Evaluation Metries:
the ceribution-reconstreee the reconstructed ordering by the difference in their positions. More formally, let Ofn fā) be the ranking output by Sn. and let og be the ranking of documents by their total importance according to some feature attribution method di that is, each document F is given a score of EM @n(RR, ē. i) x I;. Given two rankings a and b, let [a[d] be the rank of the i-th element in a. We set r(,, b) be the Kendall's tau distance between and b, i.e.
2 n(n - 1)
Σ
sgn(rald] - rabi)) sgn(ro[t] roli))
and let (a, b) be the weighted Kendall's Tau distance:
Eies way (sgn(rali) rali)) sgn(roli] ro(o))
Eien Waj
Here, w;; is |r, [ rr [i]l- Fidelity is defined as T(os, f. and WFidelity is set to be Tw ofn)
(Kendall 1938
Vigna 2015). The range of both Fidelity and wFidelity is (-1, 1).
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5.2 EXPERIMENTAL RESULTS
The results of the above experiments can be seen in Table 2 We discuss them below.
Across competing Systems: RankSHAP surpasses the top-performing competitor by 25.78% on Fidelity and 19.68% on weighted Fidelity, averaged across all ranking models, datasets, and document settings. This demonstrates that RankSHAP is most effective at recovering the original ranking model's order. RankingSHAP (Heuss et al. 2024) follows closely. All evaluated methods, except for Random, show positive correlation between the original and reconstructed rankings.
Impact of the number of documents: Both metries decline the number of documents in the ordered set for which we generate attributions increases. Specifically, there is a 20% average performance drop between attributions for 10 documents and attributions for 20 documents, and further 14.6% average decrease in Fidelity between 20 and 100 documents for RankSHAP, suggesting performance reduction that scales with the logarithm of the number of documents. Notably, while EXS and RankLIME demonstrate similar Fidelity when generating attributions for 10 and 20 documents, EXS performs significantly worse in the 100 document setting.
Across datasets: We observe that, average, our ranking systems perform 5.7% worse the Robust04 dataset compared to the MS MARCO dataset, considering all systems, ranking methods, and metrics. This slightly lower performance on Robust04 can be attributed to its smaller size, which hinders convergence during fine-tuning, Notably, the neural ranking models used in the Robust04 experiments were initially fine-tuned on the MS MARCO dataset, which may further explain the performance difference.
Across ranking models: BM25 is a heuristic-based ranking model, while BERT, T5, and LLAMA2 are large neural models. RankSHAP exhibits similar performance on BERT and T5, which is on average 13.3% and 14.7% lower on Fidelity than it's performance on BM25. RankSHAP performs slightly better when explaining ILAMA2 as compared to when explaining BERT and T5. No experiments were conducted with an LLAMA2 ranker on the Robust(4 data set due to the lack of publicly available fine-tuned model for that data set.
Across RankSHAP variants: The results of RankSHAP performance with different value functions within GREM are discussed in Appendix [ and Table The results of RankSHAP performance with different value functions paired with explicit vs heuristic relevance measures are discussed in Appendix D and and Table 5
5.3
USER STUDY
The goal of developing RankSHAP is to help humans understand why a model ranks items in specific order. Towards this, we conduct a user study with 30 participants to assess if RankSHAP aids human understanding. Following Institutional Review Board (IRB) approval each participant is shown sets of 5 short passages along with feature attributions from one of the competing systems, displayed as bar charts (see Figure I in Appendix Gp. Participants 5 documents from most to least important, and (ii) infer what the query might have been based on the attributions. The first task assesses which algorithm best aligns with human intuition, while the second evaluates how well the attributions explain the ranking task. We sampled query- query-document sets from the MS MARCO dataset and used BERT to rank the documents. Each participant was shown 10 such passage sets, with attributions randomly selected from one of Random, EXS, RankL RankingSHAP, and RankSHAP. At the end, the Kendall's Tau score (Fidelity) between the original ordering and the predicted ordering was used to identify the algorithm that better reconstructed the underlying model decision. text- based semantic similarity measuring LLM was used to assess the quality of the queries estimated by the participants. The similarity metric returned scores in the range [0,1], with indicating the estimated query was most similar the original query. The results of this study are presented in Table 3
then asked to (i) re-order the
Results. Initially, we observe that the randomly generated feature attributions achieve a concordance score of 0.23 on Task 1, which exceeds their metric-evaluated value (Table 2 Top-10 Fidelity Random). This suggests that participants may rely on preconceived notions about the topics while performing the study. The inter-annotator agreement for participants shown the same feature attribution in Task averaged 0.65 (Kendall's 's Tau). RankSHAP outperformed the strongest baseline by 19.1%. 19, following similar trends as reported in Table 2 In Task 2, some query estimates produced

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Table 3: Table demonstrating the user study results for (i)the passage reordering task, measured using Kendall's ' Tau (Fidelity) (ii) the query estimation task, measured using GPT-4 similarity (μ) for feature attributions generated using Random, EXS, RankLIME, RankingSHAP and RankSHAP feature attribution algorithms.
Random
EXS
RankLIME
RankingSHAP
RankSHAP
QI (T) Q2 (1)
0.23
0.43
0.47
0.52
0.56
0.3
0.48
0.52
0.58
0.69
by all algorithms were off-topic, and we observed substantial variance in the queries generated by different participants for the same set of documents and feature attributions. However, participants shown RankSHAP attributions performed least 30.9% better than those shown other attributions, indicating that RankSHAP enhances the effectiveness of ranking feature attributions in real-world scenarios.
RELATED WORK
In this section, we discuss additional related works that have not yet been covered in the paper so far. Fernando et al. (2019) extend the DeepSHAP algorithm (Lundberg & Lee, 2017 Shrikumar et al. 2017) from clasifiiction/reeression to propose a set of model-intrinsic feature aftributions for neural ranking models. Recently, ShaRP (Pliatsika et al. 2024) generates feature attributions to explain a particular document's score, its rank, and its presence within the top-k documents, by extending QII (Datta al. 2016). Since ShaRP does not generate attributions for entire ranked lists, it is challenging to integrate it within the RankSHAP framework. Völske et al. (2021) attempt to explain the performance of neural ranking models using axioms from statistical IR like term frequency and document length (Fang et al. 2004), lower bounding term frequency (Lv & Zhai] (201)) 1). and query aspects (Wu& & Fang. 2012), among others. Singh al. (2020) introduce the axioms of validity and completeness as means to measure the effectiveness of ranking explanations and propose an algorithm to suggest a small set of features sufficient explain ranking decision. LRIME (Vermal & Ganguly 2019) proposes a set of heuristics to improve regression/classifiatiii -basdd feature attribution methods for information retrieval, such as choosing a diverse set of perturbation samples and parameters. Ranking GAMs (Zhuang et al., 2020) offer an inherently interpretable structure that can be distilled into a set of compact piece-wise linear functions with minimal accuracy loss. Anand et al. (2022) provide comprehensive summary of explanation methods proposed for the IR ranking task, also exploring free-text explanations (Rahimi et al.) (02I], adversarial example- based explanations (Raval & Vermal 2020 Wu et al./ (2023). probing the representation space (Choi et al.) 2022), rationale-based explanations (Zhang et al. 2021 Wojtas & Chen 2020), and more. Our work focuses on generating attributions for cooperative ranking systems, which differs from generating attributions for competitive ranking systems (Hu et al. 2022 Anahidch & Johabbati-Kalejal 2022]
Gale & Marian 2020). The two frameworks differ mainly that in cooperative ranking, entities are ranked based on their inherent attributes (c.g., relevance to a query) without direct competition against each other. contrast, in competitive rankings, entities (e.g., participants in a chess tournament) are ranked against each other based on their performance or scores.
7 CONCLUSION AND LIMITATIONS
We proposed RankSHAP, a valid feature attribution framework for ranking problems. We introduced axioms that valid feature attribution algorithm should satisfy and provided a solution that meets these criteria. Additionally, we presented a computationally efficient approximation of RankSHAP that outperformed competing systems and conducted an user study to demonstrate its alignment with human intuition. We analyzed existing ranking feature attribution algorithms, to assess their adherence to fundamental axioms. Our work faces typical limitations associated with Shapley values, primarily the assumption of feature independence, which may not hold in practical applications. Moreover, our ranking value functions depend on the availability of relevance scores for each query-document pair. When relevance labels are inferred implicitly, such through click rates in recommendation systems, RankSHAP can capture biases present in the logs, including recency bias. KernelSHAP is a perturbation-bar based approach, and the results may be influenced by sampling density.
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ACKNOWLEDGMENTS
This work was supported in part by the Center for Intelligent Information Retrieval. Any opinions. findings and conclusions or recommendations expressed in this material are those of the authors and do necessarily reflect those of the sponsor.
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A RANKING AXIOMS
Given a query T. set of n. documents D = [d1, rel, associated with each document dj. and a metric value GREM, determined from the set of query-document pairs, consider the ordered list fn(Ā. D). For an evaluation of the ordering, it is ideal for the metric (GREM,) to satisfy the following axioms:
dg), human-generated relevance value
Relevance Sensitivity: If the relevance score of any document increases, while the relevance scores of all other documents remain the same, the metric value GREM, should not decrease.
Formally, ret", > rel, for some j, and rel' = rel, for all + j, then GREM,, 2 GREM,,. where GREM", is the metric computed with the updated relevance scores (rel', rell re
Position Sensitivity: If two documents d, and d, are swapped in the ranking, moving the document with the higher relevance score higher (better) rank, the metric value GREM,, should not decrease.
Formally, let be the original ordering, and o' be the ordering where only de and d, are swapped. If rel; 2 rely and (d,) > rank,(d,), (dz), then GREM, 2 GREM,, where GREM", is the metric computed with the ordering d'
Theorem A.1. An ordered list evaluation metric satisfies the axioms of Relevance Sensitivity and Position Sensitivity if and only if it can be represented as
GREM, = Σ ( h()).
where g(relz) is a non-decreasing function of the relevance score rely (gain function), and h(f) is negative, non-increasing function of the rank position, (discount function).
Proof. We split the proof into two parts:
(i) If the metric satisfies the axioms, then can be represented in the specified form.
(ii) If the metric is in the specified form, then it satisfies the axioms.
Necessity Assume that the metric
GREM, @((re1,, 1), (rel2, 2)..... (reln, n))
satisfies Relevance Sensitivity and Position Sensitivity. addition, assume that é continuously differentiable in each of its relevance arguments. We will show that under these conditions, there exist functions y and l such that
GREM, Σ g(rel,) h()).
with y non-decreasing and /i non-increasing.
Step Additive Separability.
For any fixed indices + j. fix the relevance values for all documents except those in positions and j. and define the two-variable function
F(a, b) @ ((reh, 1),... (a, (a, ..... (b.j). .... (rela, n))-
By Relevance Sensitivity, F is non-decreasing each argument. addition, by Position Sensitivity, the marginal impact of changing the relevance at ranked position (i.e., with lower index) is at least as great as that for lower-ranker one. particular, < then for all a and b,
0F
aF
(a, b) 2
(a, b).
Da
ab
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Now, consider the mixed partial derivative
0 Örel,drely
If this mixed partial were nonzero, then the effect of changing rel; would depend the value of rely, introducing an interaction between the two positions. However, such an interaction would conflict with the following observation: by Relevance Sensitivity, increasing rel; (or relj) while holding the others fixed must always lead to a non-decrease in GREM,, regardless of the value of the other variable. A nonzero mixed partial would allow for situations where the marginal effect of changing one relevance value depends on the other, potentially violating the axiom when documents are swapped. Therefore, we conclude that
8
drel,ürel, for +
standard result from multivariable calculus (see, e.g., results on additivity or the "Cauchy equation" in several variables) then implies that di is additively separable in the relevance scores. That is, there exist functions [n, one for each rank j. such that
n1
((reh, .)....
...., (reln; n1) Σ fy(relz).
==1
Step 2. Factorization into and h.
Next, we leverage the Position Sensitivity axiom. For any two positions and j with consider fixed relevance value r. Define
(r(()) = -f()))
Since swapping document from position with at (when both have the same relevance r) should not improve the metric (indeed, the higher position should be at least as valuable), we must have
f(() 2 fr( for all r.
Thus, the functions { are ordered by rank in a manner that depends only on the position. In other words, the only difference among the fy should be multiplicative "weight" reflecting the importance of the position.
In light of this, choose an arbitrary position (say, 1) and define the gain function
g(r) fr()..
Then for each position j. define
fr(
h(j) g(r)
for any r for which g(r) > O. (A short continuity and monotonicity argument shows that this ratio is independent of the choice of r.) By the properties of the fy and the axioms. follows that g(r) is non-decreasing in (by Relevance Sensitivity) and h(j) is non-increasing in j (by Position Sensitiviry). Thus, for every position we have
f,(r) g()) h(j)-
Conclusion.
Substituting back into the separable form, we obtain
GREM, = Σ fr(ll))) = Σ g(rel)) h(j),
j=1
which is the desired representation.
This completes the proof of necessity. (ii) Sufficiency
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Assume that the metric is defined
GREM, Σ
g(rel)) h(),,
1=1
where g(relz) is non-decreasing in rely and h(j) is non-increasing in j. We will show that GREM, satisfies both axioms.
Relevance Sensitivity
If relly > rel, for some j. and relk = rel, for all i + j. then
GREM, GREM,, = [g(ret)) - g(rel,)] h(j) 2 0,
since s(rel)) 2 g(rel)) and l(() 2 O. Thus, GREM, 2 GREM,.
Position Sensitivity
Suppose we swap d, and d where >> j and rel; 2 relj. The change in the metric is AGREM, Ig(rel)) h()) + g(rel,) h(i)] (g(re4) -h(i) + s(rel,) h())l = g(reli) [h(j) h(i)) + g(rel)) [h(i) - h())
(g(reli) - gg(ell))] -())-
Since re4, rely, g(rel,) 2 g(rel)). Also, since j h(j) 2 h(i). Therefore, AGREM, 2 0.
Thus, swapping documents to place the higher relevance document higher in rank does not decrease GREM,
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B BASIC SHAPLEY AXIOMS AND THE SHAPLEY VALUE
The Shapley axioms for feature attributions have been borrowed from coalitional game theory, where they are used fairly distribute costs/rewards among of players. We are given dlasificationnreegrssiin model f. The feature attribution of feature (can be words, human engineered features etc. in the decision made by f. towards the model input š is represented by (c(f. S).
We adopt Young's characterization of the Shapley value, also used by Datta et al. (0166). Let us assume there are total of features. For feature attribution @. s) be considered valid, is necessary for it to satisfy certain axioms. We briefly describe the axioms below:
The sum of feature attributions over set of features should be equal to the dif- ference between the model output containing all features and the output containing no features. (==,,15,3 (() f(ő).
Efficiency:
Missingness: If for every subset of features S s.t features & S, f(S U s) is equal to f(S, $), then o.(f.) must be given an attribution of f(S. s) represents the case where features not in S, have been replaced by their reference value, and model input 5" has been reconstructed.
Symmetry: for every subset of features S s.t features i. & S, the effects of adding to S is equal the effect of adding j S, then features and should be assigned equal attribution towards f
Monotonicity:
Given two models f and f', if for all feature coalitions S, & S, fSSU, 5) fSS, 5) is greater than or equal to ('(S U, - f'(S, 8), then (J, 8) is greater than or equal to (J' 8).
The Shapley value (Young 1985 Shapley 1953) uniquely satisfies the four axioms above, and has been widely adopted in feature attribution for regressionnclassiffcttiin tasks. is defined as:
| | - 1)! m!
de (s
where 2 is the number of non-zero entries in ह and 5' S rrrereeentt all 2 vectors where the non-zero entries are subset of the non-zero entries in s.
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C
THE NDCG METRIC
Normalized Discounted Cumulative Gain (NDCG) (Järvelin & Kekäläinen 2002) is an extremely popular metric evaluate the effectiveness of ordering, often used search engines and commerce. It assumes that some relevance score rel, for each document dj is known, and that in an effective ordering highly relevant documents appear at the beginning of the list. For an ordered list of documents, the Discounted Cumulative Gain is computed as:
relj
DCG, Σ
loga (j + 1)
The above expression is dependent on the number of documents in the set being evaluated. This metric is thus difficult to use as-is, when comparing document lists of different lengths. As result, we normalize it by dividing it with the maximum possible DCG,, score, also known as Ideal-DCG, DCi--- (IDCC,, This is obtained by sorting documents decreasing order of relevance and computing DCG,, using the so obtained ideal ordering. To compute NDCG,, we simply normalize DCG... Note that NDCG, E [0, 1]. and that the higher the value, the more effective the ranking. In situations where document relevance scores rely are unknown, they can be estimated using implicit measures such clicks, views the time spent page via heuristic measures such as BM25.
DCG,: NDCG, IDCG,
NDCG is better choice for the value function compared to other rank evaluation metrics because of numerous reasons. NDCG discounts the relevance a document based on its position logarithmically. Unlike metrics that depend on binary relevance (precision, recall, F1), NDCG accommodates smooth relevance function. NDCG is also more effective in measuring the quality of a large ranked list. Lastly, large number of product search e-commerce and recommendation systems (which might be trying to explain) already use NDCG to evaluate the quality their orderings. It is the single most popular metric evaluate the quality of ranked list and has been used by most major search engines and e-commerce websites at some point.
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D RANKING FEATURE ATTRIBUTION ALGORITHMS
D.1 FEATURE ATTRIBUTION METHODS FOR RANKING TASKS
The following solutions have been proposed address the ranking attribution problem described above:
EXS EXS, EXS,,Singh & Anand first use LIME (Ribeiro et al. 2016) to generate feature attributions for each query- query-document pair individually. In order to compute LIME attributions, they perturb documents and assign a binary relevance label to each perturbation, assigning a positive label if the rank of the perturbed document is higher than k. The authors then add the LIME attributions of top-k: documents to assign a feature attribution to the entire query-document set.
RankLIME (Chowdhury et al. (2023) extend LIME listwise manner, replacing the Lg loss function in LIME with differentiable ordering distance metric. This enables them to directly compute LIME feature attributions from ranked lists. Two of the loss functions used by them, which lead the best results, are ApproxNDCG (Qin al. 20TO) and NeuraINDCG (Pobrotyn & Bialobrzeski 2021), both differentiable alternatives to NDCG, with all relevance scores set to I.
RankingSHAP Heuss et al. (2024) propose using the Shapley value along with ordered list distance metrics to compute feature attributions for listwise ranking models. Specifically, they calculate the marginal contribution of particular feature by determining Kendall's Tau of the ranking model output with and without that feature.
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E ANALYSIS OF KERNELSHAP OPTIMIZATION ALGORITHMS AND SHAPLEY AXIOMS
In this section, provide detailed analysis of whether the algorithms using the following Ker- neISHAP optimization objectives approximate the Shapley axioms. We examine each algorithm's 'ss loss function and discuss whether satisfies the fundamental properties of the Shapley value.
The optimization objectives for the algorithms are:
LF = ApproNNDCG(fA(O).(()) (
BEZ
(FANKINGSHAPP(RRR.)))
Σ (r(fa(3). TT)))
SEZ
TRANKSHAP(/Rn.)
Σ (NDCG(fn(E)
NDCG m
Here, fR the original ranking model, g is the surrogate model used for explanation, `T is the KernelSHAP weighting kernel, Z is the set of all possible coalitions (subsets of features), 7 is Kendall's tau rank correlation coefficient, and ApproXNDCG is an approximation of the Normalized Discounted Cumulative Gain (NDCG).
E.1 ANALYSIS OF RANKLIME
Efficiency. The Efficiency axiom requires that the total attribution should equal the overall dif- ference between the model output with all features and that with none. In RANKLIME, the loss minimizes an approximation етrоr measured by ApproxNDCG. However, ApproxNDCC is not an additive measure. In other words, even one could decompose NDCG over individual documents or features, its approximation may not retain this additivity.
Intuitive Counter Example: Suppose that for given coalition the true NDCG decomposes as
NDCG ((re)))) h(j).
the approximation introduces nonlinearities (e-g., due to smoothing or rounding), then for two features i and j. the marginal effects
ApproxNDDC and AppproXNDDC
need not sum to the total change. Thus, even if feature and feature j are the only contributors, one might have
ApAproxNDDC ApAproXNDCCG * Total change,
thereby violating Efficiency.
Symmetry. Symmetry requires that if two features yield the same change in the model output in all coalitions, they should have equal attributions. However, the approximation in ApproxNDCG can be sensitive ranking positions.
Intuitive Counter Example: Consider two features, and b, which individually yield identical changes in relevance scores. given coalition, due to subtle ranking reordering. the approximation may assign a slightly higher weight to the contribution of than to (or vice versa), because the ranking order determines the discount factors. Thus, even though and b are symmetric effect, the approximate metric may break the symmetry, leading to different attributions.
Dummy (Missingnesss) For feature that does not affect the model output (a dummy feature), the Shapley axiom requires that its contribution be zero. In RANKLIME, even non non- non-influential feature might change the ordering in the surrogate model (due to interactions with other features or the way missing features treated in the approximation).
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feature do not Published as a conference paper at ICLR 2025
Intuitive Counter Example: If feature does not change any document's relevance in fR. one would expect its contribution to vanish. However, when is added to coalition, the computation of ApproxNDCG might slightly alter the ranking order (because the algorithm may treat missing features a nontrivial manner), resulting in a small non-zero attribution. Hence, the Dummy axiom may be violated.
Monotonicity. Monotonicity implics that if the marginal contribution a feature increases in every coalition, its attribution should not decrease. Since ApproxNDCG is non-linear function of ranking order and not a linear combination of contributions, increases in the relevance translate in a straightforward way increases the approximate score.
Imagine a situation where increasing the relevance of a document moves it from a borderline position (with high discount factor) to the top of the list, but due the nonlinear nature of ApproXNDCG, the gain saturates. This means that further increases in relevance might have a negligible effect on the ApproxNDCG, even though the true marginal contribution should be larger. Consequently, the attributions computed by minimizing the loss may not increase monotonically, thereby violating the Monotonicity axiom.
Intuitive Explanation:
E.2 ANALYSIS OF RANKINGSHAP
Efficiency. RANKINGSHAM minimizes the squared difference of Kendall's tau (7) between the rankings of fn and g. Kendall's tau measures the rank correlation, not the absolute difference in scores. Thus, even if two coalitions have similar values, the overall difference in model output might not be captured.
Intuitive Counter Example: Suppose the full model output changes by a large amount when all features present, but two different coalitions yield rankings that are highly correlated (i.e., high T). In this case, the loss may be small despite there being a significant change in the absolute values, meaning that the sum of the computed contributions (derived indirectly from r) does not match the total change. This discrepancy violates the Efficiency axiom.
Symmetry. Kendall's tau is based on pairwise comparisons of ranking orders. Two features that are symmetric in their true impact may, however, influence the ranking order differently due to interactions with other features. This can lead different changes when each is perturbed.
Intuitive Explanation: If features and b are swapped in some coalitions, even though they are truly symmetric, the way counts pairwise disagreements might favor one ordering over the other. Thus, when minimizing the squared difference in the attributions computed for and b might differ, thereby violating Symmetry.
Dummy (Null Player). A feature that does not affect the ranking should contribute zero to However, due the permutation- based nature Kendall's tau, even a dummy feature may change the number of concordant or discordant pairs in subtle ways.
Intuitive Counter Example: Imagine feature d that is irrelevant to the ranking. When d added to coalition, if it is randomly inserted, the overall number of pairwise comparisons changes. Even though the feature does not affect the true ranking, this insertion can alter r by a small amount, leading to nonzero squared difference in the loss and thus nonzero attribution.
Since the loss in RANKINGSHAP non-linear (squaring the difference in T), even if feature's 's true marginal contribution increases, the resulting change in Kendall's tau may not increase proportionally.
Monotonicity.
Consider two coalitions where, in one, increasing the relevance of feature causes a small improvement in т. and in another, a larger improvement. If these changes do not align linearly with the changes in the model output (because is rank statistic), the attribution derived from minimizing the squared differences might not reflect a monotonic increase the true marginal effect. Hence, the Monotonicity axiom is not well approximated.
Intuitive Explanation:
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E.3 ANALYSIS OF RANKSHAP
RANKSHAP uses the loss function
LRANKSHAp (fn: Tz)
NDCG(fu(E) (NDCG(()))) TT(E)). BEZ
(DCG
Because Normalized Discounted Cumulative Gain (NDCG) can be decomposed into a sum over documents, it admits additive formulation:
NDCG = greel) h(5),
3=1
where is a non-decreasing gain function and h is a non-increasing discount function. This additivity precisely what is needed for the Shapley axioms.
Efficiency. Since NDCG is additive, the difference in NDCG between two coalitions is the sum of the individual differences. Thus, the attributions computed by RANKSHAP naturally sum to the total difference in the model outputs, satisfying the Efficiency axiom.
Intuitive Proof: If we denote the individual contribution of document j by g(rel,) h(()), then the total effect of including set of features is the sum over these contributions. The loss function directly minimizes the squared error between the true and surrogate NDCG scores. doing so, it forces the surrogate model to distribute the total difference (the "explanation budget") among features in way that respects additivity, which is the core idea behind the Shapley value.
Symmetry. When two features affect the ranking in an identical manner, the corresponding changes in each document's ' gain function are the same. Since NDCG is additive and each document's s contribution is determined independently by its position, symmetric features will receive equal contributions. Thus, the Symmetry axiom is satisfied.
Dummy (Null Player). If feature is dummy (i.e., it has no impact any document's 's relevance), then its inclusion does not change the per-docunne documeemtnt gain values. Consequently, its marginal contribu- tion NDCG zero, and the corresponding attribution will be zero, agreement with the Dummy axiom.
Monotonicity. Because an increase in the relevance score of any document leads to an increase in its gain g(relz) and thus in its weighted contribution g(rel,) h()), the additivity of NDCG ensures that the surrogate model's attributions increase monotonically with the true marginal contributions. This is in line with the Monotonicity axiom.
E.4 CONCLUSION
RANKLIME:
The use of ApproxNDCG leads to loss function that is not fully additive over features, and its sensitivity to ranking order may produce counter-intuitive attributions. Intuitive counter examples show that Efficiency, Symmetry. Dummy, and Monotonicity can be violated.
By relying on Kendall's tau, which is a rank correlation measure, the loss function fails to capture absolute changes and linear contributions. This results in potential violations of Efficiency (since the sum of contributions does not match the total change), as well as Symmetry, Dummy, and Monotonicity violations due to nonlinear and permuutaioon-eensitiv behavior.
RANKINGSHAP:
RANKSHAP: In contrast, by using NDCG-which can be decomposed additively into gain and discount ComponentS-RNNKSHEE reasoning shows that the additivity inherent in NDCG ensures that Efficiency, Symmetry, Dummy, and Monotonicity are satisfied.
aligns well with the Shapley axioms. Intuitive
Thus, only RANKSHAP, with its loss function based on the additive properties of NDCG, pro- duces explanations that fully approximate the fundamental Shapley axioms, while RANKLIME and RANKINGSHAP fall short due their reliance non-additive, non-linear measures.
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F RANK COMPARISON METRICS
The following rank comparison metrics are popularly used in literature:
Kendall's Tau: Measures the number of pairs of alternatives over which two rankings disagree. Equivalently, it is also the minimum number of swaps of adjacent alternatives required to convert one ranking into another.
2. Spearman's Footrule Distance: Measures the total displacement of all alternatives between two rankings, i.e., the sum of the absolute differences between their positions in two rankings.
3. Maximum Displacement Distance (MD): Measures the maximum of the displacements of all alternatives between rankings.
4. Cayley Distance: Measures the minimum number of swaps (not necessarily of adjacent alternatives) required to convert one ranking into another.
5. Copeland's Method: Copeland's s method is an algorithm to assign scores to candidates in Ranked choice voting. Quoting Wikipedia, each voter is asked to rank candidates in order preference. A candidate A is said to have majority preference over another candidate B if more voters prefer A to B than prefer B to A; if the numbers a preference tie. The Copeland score for a candidate is the number of other candidates over whom he she has a majority preference plus half the number of candidates with whom he or she has preference tie. The winner of the election under Copeland's method is the candidate with the highest Copeland score; under Condorcet's method this candidate wins only if he or she has the maximum possible score of n I where n is the number of candidates.
equal then there is
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G USER STUDY INSTANCE
Honey
Sugar
Supersaturated
Nutritional
Calories
Nectar
Versatility
P1 So while raw honey and sugar both contain glucose and fructose, our raw liquid gold is nutrient dense food. Just as good grey sea salt is healthier that iodized table salt, raw honey beats the buzz off of regular white sugar in both nutritional content and effects the body.
P2 Agave nectar has a taste and appearance similar to honey, making it popular substitute for strict vegans and others who avoid honey. There are two kinds of agave nectar: dark agave nectar and light. Though the two can be used interchangeably. dark agave nectar has a stronger taste.
P3 Clover honey named so because it's produced from the nectar clover blossoms. has mild flavor and sweetness and is favored in the United States for its abundance and versatility. When honey labeled "pure," means it has no additives such as sugar, corn syrup, or flavorings.
P4 Energy Source. According Therefore, it is used by many people as a source of energy. On the other hand, one tablespoon of sugar will give you about 15 calories.
the USDAA, honey contains about 64 calories per tablespoon.
P5 Honey crystallizes because it is supersaturated solution. 2 This supersaturated state occurs because there is so much sugar in honey (more than 70%) relative to the water content (often less than 20%).
Actual Query: Is honey as a substitute for sugar healthier?
Figure I: A user study instance, depicting passages and a corresponding feature attribution. Words that influenced the ranking decision positively are shown in green, whereas those that influenced negatively were shown red. Participants were asked re-rank documents based on the feature attribution to try and estimate the query.
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Question 2: Read following passaçes briefly
1. The cheetah is capable of speed. 72 mph (114 km/h) and ma intain thie speed over average prey chase 3.5 miles.. m/s. The cheetah (Acinonyx jubatus) is one the fastest mammals found in the animal kingdom today. The maximum speed of cheetah is documented with the speed of about 30 m/s (70 mph).
2 While accelerating time c1, cheelah travels distance of. The cheetah then travels c2 400 that the total distance travelled the cheetah de 452.5 The gazelle starts initial speed vig m/s and accelerates fg= 70 km/h 19.4 m/s time. fastest land mammal, the cheetah, able accelerate from standing start 96 km/h just three seconds, which corresponds acceleration 8.9 m/s
speed of
3. The cheetah accelerate from 0 km/h km/h in seconds, this gives acceleration of 8.9 m/s 2. has top speed v 100 km/h 30.6 The time reach its speed from 400 given bythe land mammal, the cheetah,
is. The time to travel speed
for distance able to accelerate from standing start km/h in just three seconds, which corresponds acceleration m/s 2.
EMG Electromyography function FMG testing provide your doctor with information ahout the extent and type and muscle disease/injury and can determine the location injury and give some indication whether the damage is reversible.
that used study the and muscle
5. is the paper monitor normally prints
of the same factors apply. height and in width. Large squares = in width. You require this knowledge because when assessing the 12-lead ECG you will
Small squares
height and
Figure 2: User Study Passage Snapshot
H USER STUDY DETAILS
H.1 ANONYMIZED INSTRUCTIONS
For each question, you will be shown 5 short passages related to a web search query in no particular order, and bar chart of important words explanation depicting unknown ranking model's rationale for ordering those answers. You have to briefly read the passages and then using your intuition (i) reorder the passages from most relevant to least relevant based on the explanation (ii) guess the query/question that led to this particular ordering.
word in the bar chart explanation, with positive or negative values, indicate whether they affected the order of documents that contain them, positively or negatively. Your response, which would be of the form (3.1.2.5,4) and a short text phrase/question would be recorded. This would just be used to understand how well the explanations aid in human understanding of an unknown model's intent.
This session has 10 such questions and should take longer than 30 minutes. We don't 't recommend spending more than 3 minutes question. You would be completed within Cash cards worth $10 on successful completion of a session.
H.2 USER STUDY SNAPSHIOT
Snapshots from the User study for particular query- query-document set, by study participants shown in Figures 23 The study was conducted via Google Forms.
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Explanation
0.4
0.3
0.2
0
-0.1
-02
Cheetah
speed
accelation
time
top speed
diseace
monitor
Based the explanation and your intuition, rearder the above documents from most important to leas: important.
Your answer
Based your intuition, guess the query that led the ordering.
Your answer
Figure 3: User Study Bar Chart and questions snapshot
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I RANKSHAP PERFORMANCE WITH DIFFERENT VALUE FUNCTIONS
We run experiments comparing the performance of the RankSHAP framework with different value functions, namely Mean Average Precision (MAP), Cumulative Gain (CG), Discounted Cumulative Gain (DCG) and Normalized Discounted Cumulative Gain (NDCG) in Table 4 Below we discuss the same.
1.1 COMPARATIVE ANALYSIS OF RANKSHAP VARIANTS
RankSHAP, employing different value functions (CG, MAP, DCG, and NDCG), exhibits clear performance distinctions across datasets, rankers, and query-document configurations. Among these, RankSHAP(NDCG) consistently achieves the highest fidelity and weighted fidelity (wFi- delity) scores, outperforming the other RankSHAP variants. Aggregating across all configurations, RankSHAP(NDDG) delivers average fidelity improvement of 8.3% 11.5% over RankSHAP(MAP), and 13.8% over RankSHAP(CG), The performance edge of NDCG stems from its logarithmic discounting of ranks, which effectively prioritizes highly relevant docu- ments, making it particularly suited for tasks where top-ranked items have disproportionate impact on the evaluation.
RankSHAP(DCC)),
Interestingly, the gains achieved by RankSHAP(NDDG) are most pronounced in the Top- 10 setting, where surpasses RankSHAP(CG) by an average of 17.4% fidelity and 15.8% in wFidelity. In contrast, the improvements diminish slightly for Yop-100, where NDCG maintains an edge of approximately 7.9% over DCG and 10.4% % over MAP. These trends suggest that while all RankSHAP variants benefit from the Shapley-based attribution framework, those incorporating normalized or discounted value functions, like NDCG and DCG, are better suited for ranking tasks that emphasize relevance. Meanwhile, CG and MAP exhibit competitive yet slightly lower fidelity scores, likely because they lack the nuanced scaling necessary to capture differences in document importance effectively. Overall, RankSHAP(NDCG) emerges as the most robust and versatile variant, maintaining high fidelity across diverse scenarios.
1.2 COMPARISON OF RANKSHAP VARIANTS WITH BASELINES
When compared to baseline methods such Random, EXS, RankLIME, and RankingSHAP, all RankSHAP variants demonstrate significantly higher fidelity and weighted fidelity (wFidelity) scores across rankers and datasets. Among the baselines, RankingSHAP generally performs better, but RankSHAP(NDCG) consistently outperforms it with average fidelity gain of 16.7% % across all settings, highlighting the advantage incorporating axiomatic value functions like NDCG into the Shapley framework. For instance, in the Top- 10 setting with the BM25 ranker the MS MARCO dataset, RanKSHAP(NDCG)) achieves fidelity scores that are 21.2% higher than RankingSHAP, showcasing its superior ability identify and attribute relevant features accurately.
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J RANKSHAP WITH EXPLICIT VS IMPLICIT RELEVANCE JUDGEMENTS
In scenarios where absolute relevance judgments are not available, we propose generating synthetic relevance labels based on predefined rules or heuristic relevance functions. This approach involves leveraging document features such as term frequency. topic overlap, or query-document embeddings to approximate relevance proxies. Specifically, we recommend using BM25, a widely adopted baseline relevance measure in information retrieval tasks. BM25 is computationally efficient and scales well for large document collections. effectively balances term frequency (TF) saturation and inverse document frequency (IDF), ensuring robust performance across varying term distributions.
To evaluate the impact of using BM25 relevance proxy, we rerun certain RankSHAP experiments by comparing results obtained with exact relevance measures to those derived using BM25. We run experiments for BERT and T5 ranking models on the MS MARCO datasets. We report fidelity and weighted fidelity (wFidelity) scores across four ranking value functions: MAP, CG, DCG, and NDCG.
The results of our study can be found in Table For both models, explicit relevance scores consistently yield higher fidelity and weighted fidelity (wFidelity) across all experimental settings (top-10, top-20, top-100). The performance drop when switching from explicit BM25-based scores modest, with fidelity reductions ranging between 6% and 14%, depending on the value function and the number of top documents. Notably, the drop is more pronounced for smaller document sets (e.g., (op-10), where precise relevance judgments likely have greater impact on the accuracy of feature attributions.
With the top-10 10 documents, the fidelity of RankSHAP(NDCG) drops from 0.59 (explicit) to 0.54 (BM25) for BERT, and from 0.56 (explicit) 0.52 (BM25) for T5. These results suggest that BM25 serves as a reasonably effective proxy for relevance, particularly when explicit scores are unavailable, albeit with slight performance degradation. Overall, the findings demonstrate that RankSHAP remains robust with implicit relevance scores, though explicit scores offer tangible advantage, particularly scenarios requiring finer-grained fidelity measures.
It is important to note that limitation of BM25 is its reliance exact keyword matches, which can overlook semantic relationships such as synonyms or paraphrases.
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Table 4: Comparing performance between different feature attribution methods (Random, EXS, RankLIME, RankingSHAP and RankSHAP) for token- based explanations of textual rankers (BM25, BERT, T5 and LLAMA2) based model fidelity (Fidelity) and weighted-fidelity (wFidelity) with ranking models fine tuned on the MS MARCO (MM) and TREC ROBUST 2004 (R04) datasets. Within RankSHAP, we generate feature attributions using 4 different value functions Cumulative Gain (CG), Mean Average Precision (MAP), Discounted Cumulative Gain (DCG) and Normalized Discounted Cumulative Gain (NDCG). For these experiments, we generate feature attributions
for each ranking models with the 10, 20 and 100 most relevant documents for particular query respectively.
Ranker
Top- 10
Top-20
Top- 100
Metric +
Fidelity
wFidelity
Fidelity
wHidelity
Fidelity
wFidelity
Random
0.08
0.04
-0.05
0.01
-0.09
0.00
EXS
0.39
0.34
0.31
0.29
0.24
0.17
RankLIME
0.45
0.37
0.37
0.29
0.26
0.20
RankingSHAP
0.52
0.41
0.45
0.33
0.31
0.24
MM/BM25
RankSHAP(MAP)
0.58
0.41
0.50
0.36
0.41
0.29
RankSHAP(CG)
0.53
0.38
0.47
0.34
0.39
0.26
RankSHAP(DCG)
0.60
0.42
0,51
0.38
0.31
RankSHAP(NDDGG
0.63
0.48
0.54
0.33
Random
0.12
0.02
-0.09
0.01
-0.12
0.00
EXS
0.36
0.21
0.28
0.18
0.11
0.08
MM/BERT
RankLIME
0,41
0.24
0.32
0.24
0.23
0.18
RankingSHAP
0.45
0.29
0.38
0.27
0.28
0.24
RankSHAP(MAP)
0.54
0.42
0.38
0.36
0.33
0.26
RankSHAP(CG)
0.49
0.448
0.35
0.29
0.28
0.24
RankSHAP(DCG)
0.56
0.43
0.40
0.34
0.35
0.28
RankSHAPP(NDGG)
0.59
0.41
0.45
0.38
0.39
0.29
Random
0.05
0.03
-0.04
EXS
0.36
0.21
MM/TS
RankLIME
0.35
0.24
0.35
0.20
0.27
0.17
RankingSHAP
0.41
0.30
0.38
0.32
0.31
0.22
RankSHAP(MAP)
0.50
0.34
0.40
0.33
0.32
0.24
RankSHAP(CG)
0.44
0.32
0.38
0.31
0.30
0.20
RankSHAPPDDG
0.55
0.38
0,43
0.35
0.34
0.27
RankSHAA((NDGG)
0.56
0,39
0.43
0.37
0.36
0.29
Random
0.04
0.01
-0.2
0.0
0.02
0.1
EXS
0.39
0.20
0.32
0.15
0.17
0.05
MM/LLAMA2
RankLIME
0.35
0.24
0.35
0.27
0.17
RankingSHAP
0.44
0.33
0.37
0.23
0.31
0.22
RankSHAP(MAP)
0.55
0.38
0.40
0.33
0.32
RankSHAP(CG)
0.48
0.37
0.36
0.27
0.31
0.24
RankSHAPP(DGG
0.58
0.40
0.43
0.36
0.36
0.28
RankSHAP(NDCG)
0.60
0.42
0.45
0.39
0.39
0.32
Random
0.08
0.04
-0.44
0.00
-0.07
0.00
EXS
0.37
0.33
0.30
0.26
0.22
0.18
R04/BM25
RankLIME
0.43
0.36
0.36
0.25
0.25
0.18
RankingSHAP
0.45
0.35
0.37
0.29
0.26
0.24
RankSHAP(MAP)
0,51
0.37
0.44
0.33
0.32
0.26
RankSHAP(CG)
0.48
0.35
0.36
0.30
0.25
0.25
RankSHAP(DCG)
0.59
0..42
0.52
0.36
0.42
0.29
RankSHAP(NDCG)
0.61
0.44
0.52
0.38
0.45
0.31
Random
0.12
0.02
0.01
-0.12
EXS
0.35
0.20
0.27
0.16
0.10
0.07
R04/BERT
RankLIME
0.40
0.22
0.31
0.23
0.17
RankingSHAP
0.43
0.26
0.36
0.28
RankSHAP(MAP)
0.48
0.35
0.40
0.34
0.37
0.24
RankSHAP(CGG)
0.44
0.28
0.36
0.28
0.29
0.21
RankSHAP/DCG)
0.56
0,41
0,42
0.35
0.37
0.26
RankSHAP(NDCG)
0.59
0.41
0.45
0.38
0.39
0.29
Random
0.05
0.03
-0.11
0.01
-0.04
0.00
EXS
0.38
0.21
0.32
0.17
0.13
0.06
R04/TS
RankLIMM
0.38
0.24
0.35
0.20
0.28
0.17
RankingSHAP
0.41
0.31
0.38
0.24
0.32
0.24
RankSHAPPMMP
0.49
0.34
0.40
0.27
RankSHAP(CG)
0.42
0.30
0.39
0.24
RankSHAPODCG)
0.54
0.37
0.40
0.33
0.35
0.25
RankSHAP(NDCG)
0.56
0.39
0.43
0.37
0.36
0.29
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Table 5: Comparing performance between different feature attribution methods (Random, EXS, Ran,LIME, RankingSHAP) and RankSHAP (with differnt value functions and different methods to model relevance) for token-based explanations of textual rankers (BERT and T5) based model fidelity (Fidelity) and weighted-fided (wFidelity) with ranking models fine tuned on the MS MARCO (MM) dataset. Within RankSHAP, we generate feature attributions using 4 different rank value functions: Cumulative Gain (CG), Mean Average Precision (MAP), Discounted Cumulative Gain (DCG) and Normalized Discounted Cumulative Gain (NDCG) and different methods to compute relevance (Explicit ranking model score vs BM25 score). For these experiments, we generate feature attributions for each ranking models with the 10, 20 and 100 most relevant documents for particular query respectively.
Ranker
Top-10
Top-20
Top- 100
Metric
Fidelity
WFidelity
Fidelity
wFidelity
Fidelity
wFidelity
Random
0.12
0.02
-0.09
0.01
-0.12
0.00
EXS
0.36
0.21
0.28
0.18
0.11
0.08
MM/BERT
RankLIME
0.41
0.24
0.32
0.24
0.23
0.18
RankingSHAP
0.45
0.29
0.38
0.27
0.28
0.24
RankSHAP(BB225MAAP
0.32
0.31
0.33
0.28
0,22
RankSHAA(BB225/CG)
0.43
0.31
0.26
0.24
0,21
(mnkSHAAPBMM5IDCC)
0.37
0.36
0.30
0.31
0,25
Run:SHAP(BM2SNNDCG
0.38
0.37
0.36
RankSHAP(MAP)
0.54
0.42
0.38
0.36
0.33
0.26
RankSHAP(CG)
0.49
0.48
0.35
0.29
0.28
0.24
RankSHAP(DCG)
0,56
0.43
0.40
0.34
0.35
0.28
RankSHAP(NDDG)
0,59
0.41
0.45
0.38
0.39
0.29
Random
0.05
0.03
-0.11
0.01
-0.04
0.00
EXS
0.36
0.21
0.30
0.17
0.11
0.06
MM/TS
RankLIME
0.35
0.24
0.35
0.20
0.27
0.17
RankingSHAP
0.41
0.30
0.38
0.32
0.31
0.22
RankSHAPFBME5/NAPP
0.45
0.30
0.37
0.29
0.30
0.21
RankSHAP(BM25/CGI
0.41
0.28
0.36
0.27
0.27
0.18
RanSSHAP(BM25/DDGG
0.51
0.35
0.42
0.31
0.31
0.24
RmnkSHAPPBM22/ADDC)
0.52
0.36
0.40
0.34
0.32
0.27
RankSHAP(MAP)
0.50
0.34
0.40
0.33
0.32
0.24
RankSHAP(CG)
0.44
0.32
0.38
0.31
0.30
0.20
RankSHAP(DCG)
0.55
0.38
0.43
0.35
0.34
0.27
RankSHAP(NDCG)
0.56
0.43
0.37
0.36
30


Reviews:
[{"review_id": "CRblfJW1dG", "reviewer": "Reviewer_URTs", "summary": "This paper proposes RankSHAP as a framework for explaining how features contribute to a ranking model's output. The authors extend the classifcal Shapley value concept to the ranking domain by specifying two axioms that a ranking-based feature attribution must satisfy, in additon to the set of four fundamental axioms that Shapely values already satisfy. The authors argue that current methods for explaining ranking models often provide inconsistent or contradictory explanations, making it difficult for users to understand model behavior. These axioms, which are based on game theory and information retrieval principles, ensure the fairness, consistency, and reliability of the explanations. Through extensive experiments, the authors demonstrate that RankSHAP outperforms existing methods in terms of accuracy and alignment with human intuition.", "questions": "- Since the model can be black box, what if the model is itself self-contradictory or inconsistent? For example, a listwise ranking models that ranks documents A and B as A>B>C in the presence of C but as D>B>A in the presence of a document D. Would the explanations provided by RankSHAP in such a scenario inconsistent or unfaithful? Similarly, what happens when the model handles uncertainly or chooses to use stochastic rankings (drawing a different sample from a distribution over permutations), e.g., Singh, Kempe, Joachims. Fairness in Ranking under Uncertainty (2021).\n- Can you explain why the fidelity scores are different for the two datasets? You mention that it is due to the difference in dataset sizes but I am not sure if it is clear if that is the reason.  \n- See weaknesses section too.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Axiomatic Foundation: I appreciate that the authors propose a set of fundamental axioms specifically tailored for ranking feature attributions, drawing inspiration from Shapley values in coalitional game theory. These axioms, namely Rank-Efficiency, Rank-Missingness, Rank-Symmetry, and Rank-Monotonicity, ensure that the attributions are fair, consistent, and meaningful.\n- Generalized Ranking Effectiveness Metric (GREM): The authors introduce GREM, a generalized framework for evaluating the effectiveness of ordered lists. This framework encompasses widely used metrics like NDCG and provides a solid theoretical foundation for assessing the quality of rankings produced by considering feature subsets.\n- Computational Feasibility: Acknowledging the NP-completeness of exact Shapley value calculations, the authors propose an approximate algorithm to leverage a linear model between feature subsets and the ranking effectiveness metric, as well as Kernel-RankSHAP to induce non-linearity into this model. This makes RankSHAP practical for real-world applications.\n- Extensive Empirical Evaluation: The authors conduct comprehensive experiments on two datasets (MS MARCO and Robust04) using multiple ranking models, including BM25, BERT, T5, and LLAMA2. The results demonstrate RankSHAP's superior performance over competing methods like EXS, RankLIME, and RankingSHAP across various metrics like Fidelity and weighted Fidelity.\n- User Study Validation: The paper includes a user study to assess the alignment of RankSHAP with human intuition. This is an interesting study that tasks participants with re-ordering documents and inferring queries based on feature attributions. The results show that RankSHAP significantly improves user understanding of ranking decisions.", "weaknesses": "- User study caveats: (a) Preconceived Notions: The authors observed that randomly generated feature attributions achieved a higher concordance score in the re-ordering task than expected based on their metric evaluation. This suggests that participants might have relied on pre-existing assumptions or biases about the topics, potentially influencing their judgments throughout the experiment. Is that a drawback of the setup that also impacts rest of the observations?\n(b) Subjectivity: The authors noted significant variance in the queries estimated by participants for the same document set and feature attributions. This probably highlights the inherent subjectivity in interpreting feature attributions and formulating queries, which can lead to diverse responses and impact the evaluation's reliability. \nDespite limitations, it is indeed on interesting study to include in the paper since progress in the field of interpretability requires human subjects to be involved. \n- Dependence on Relevance Scores: The effectiveness of RankSHAP relies on the availability of accurate relevance scores for each query-document pair. Obtaining these scores often necessitates ground truth labels, which can be scarce or unavailable. The paper proposes using implicit measures like click-through rates to infer relevance when explicit labels are absent.\n-", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "r4KfGKHVuZ", "reviewer": "Reviewer_ExvH", "summary": "The paper introduces a Shapley-value-based feature attribution method tailored specifically for ranking tasks. Traditional feature attribution methods, mostly developed for regression or classification, often produce conflicting results when adapted to ranking, which can lead to confusion among end-users. RankSHAP addresses this by adhering to a set of axioms tailored for ranking. Extensive experiments demonstrate that RankSHAP aligns well with human intuition and outperforms existing methods in fidelity and weighted fidelity. Additionally, a user study confirms its practical value in helping users understand model decisions.", "questions": "How does RankSHAP perform when features are highly interdependent? Are there adjustments made for such cases?\n\nHow does the RankSHAP framework handle scenarios where relevance scores are subjective or unavailable?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The introduction of axioms specific to ranking provides a robust framework, distinguishing RankSHAP from other feature attribution methods.\n\nThe authors incorporate a user study to validate that RankSHAP explanations align with human understanding, which adds practical value.", "weaknesses": "RankSHAP’s reliance on relevance scores for accurate NDCG calculations could be a limitation in scenarios where relevance is difficult to quantify or subjective.\n\nAlthough RankSHAP was tested in a user study, the evaluation might have limited generalizability due to sample size.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YedJgqUKtS", "reviewer": "Reviewer_TGSB", "summary": "This paper presents RankSHAP, an extension of SHAP value tailored to interpret learning-to-rank models. The authors reinterpreted the Shapley value axioms (Rank-Efficiency, Rank-Missingness, Rank-Symmetry, and Rank-Monotonicity), and defined new properties (Relevance Sensitivity and Position Sensitivity) to better capture the unique requirements of ranking models in feature attribution. To demonstrate practicality, they integrated the NDCG metric into KernelSHAP and validated their method through experiments.", "questions": "Are there experiments with GREM metrics other than NDCG? While the choice of NDCG is understandable (appendix C), experiments with other metrics are needed to demonstrate the validity of the proposed method across different metrics, which would strengthen its generality.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- The paper introduces a thoughtful adaptation of the Shapley value for the ranking domain, defining new ranking-specific properties that enhance SHAP's applicability in ranking contexts.\n- The authors have conducted both performance evaluations and a user study to validate their method.", "weaknesses": "The proposed method, RankSHAP, heavily relies on the KernelSHAP method [1] with modifications to incorporate NDCG for ranking applications. Rather than introducing a fundamentally new method, the paper adapts an existing approach specifically for ranking tasks. While the axiomatic reformulation is valuable, the technical novelty beyond extending KernelSHAP with NDCG remains limited.\n\n[1] Scott M Lundberg and Su-In Lee, A Unified Approach to Interpreting Model Predictions, in NeurIPS, 2017.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qrkgVbjZAr", "reviewer": "Reviewer_UYR5", "summary": "The RankSHAP method leverages Shapley values, considering all possible feature combinations and their interactions (or approximations thereof), to provide a detailed, interaction-aware explanation of feature contributions in ranking models. This approach aligns well with the feature importance analysis used in regression models, making the methodology intuitive.", "questions": "I think RankSHAP is a nice contribution to ranking explainability, but improving the handling of bias, refining its reliance on averages, and clarifying its application scope could elevate its impact further.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The paper provides a good motivation for RankSHAP by discussing the limitations of simpler ranking explanation methods, like LIME, which lack consideration for full feature interaction and listwise ranking structure. By addressing these limitations, RankSHAP presents a more nuanced and comprehensive approach to ranking explainability.\n\n2. RankSHAP's performance is evaluated using fidelity metrics, which assess how accurately RankSHAP captures feature contributions in line with the model’s scoring function. This fidelity-based evaluation aligns RankSHAP’s explanations with the ranking model’s actual logic, resulting in explanations that are reflective of the ranker's structure rather than arbitrary feature importance.\n\n3. The method is flexible since RankSHAP can work with a range of ranking models, from traditional learning-to-rank approaches to neural ranking models. This makes RankSHAP’s applicable to many fields, including search, recommendation, and information retrieval.", "weaknesses": "1. **Correlation, Not Causation**: While RankSHAP provides insight into feature importance, the explanations are inherently correlational, not causal. Therefore, while RankSHAP can reveal which features push an item up in ranking, this does not imply that these features are directly causing higher ranks. I'm not saying the authors claim causality, but in terms of doing \"better\" at explaining ranking, they're explaining correlations between the rank and the features better, and not want causally drives a higher ranking. \n\n2. **Model Dependency and Bias**: The effectiveness of RankSHAP is fundamentally dependent on the quality and calibration of the ranker itself (correct?). If the scoring function is miscalibrated or biased (e.g., favoring higher-ranked items based solely on position), RankSHAP’s explanations may reinforce these biases instead of offering corrective insights. The authors could discuss how potential biases (position, selection, algorithmic biases) within the ranker affect the usefulness of RankSHAP’s explanations to be truly meaningful.\n\n3. **Limitations in Simple Averages for Shapley Values**: The reliance on simple averages in traditional Shapley values means that RankSHAP does not consider the number of interactions (N) or the variance in a feature’s impact across different contexts. This averaging could dilute the significance of features with occasional strong influence, potentially overlooking context-dependent importance and limiting RankSHAP’s insights.\n\n4. **Reinforcement of Potentially Polarized Content**: Because RankSHAP's explanations reflect the ranker’s scoring function, any inherent polarization or bias in the model could be echoed in the explanations. This could inadvertently support polarized content if the ranking model favors certain types of data, raising concerns for applications in content moderation and recommendation.\n\n5. **Redundancy in Presentation and Scope of Rankers**: The paper does not clearly specify the types of ranking models used in its evaluation, which, I think could and maybe should matter? Or at least will help elucidate where it's particularly useful (I imagine the more non linear the ranker the more useful?)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)