The Importance of Parameters in Ranking Functions
Christoph Standke, Nikolaos Tziavelis, Wolfgang Gatterbauer, Benny Kimelfeld

TL;DR
This paper investigates the computation of SHAP scores for column weights in ranking functions, analyzing their complexity and proposing approximation schemes across various ranking and effect functions.
Contribution
It provides a comprehensive complexity analysis of SHAP score computation for different ranking functions and effect measures, extending to Shapley value calculations.
Findings
All cases admit an additive FPRAS for approximation.
Exact computation is polynomial-time solvable or #P-hard depending on the case.
Complexity results extend to computing Shapley values for columns.
Abstract
How important is the weight of a given column in determining the ranking of tuples in a table? To address such an explanation question about a ranking function, we investigate the computation of SHAP scores for column weights, adopting a recent framework by Grohe et al.[ICDT'24]. The exact definition of this score depends on three key components: (1) the ranking function in use, (2) an effect function that quantifies the impact of using alternative weights on the ranking, and (3) an underlying weight distribution. We analyze the computational complexity of different instantiations of this framework for a range of fundamental ranking and effect functions, focusing on probabilistically independent finite distributions for individual columns. For the ranking functions, we examine lexicographic orders and score-based orders defined by the summation, minimum, and maximum functions. For the…
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Taxonomy
TopicsGame Theory and Voting Systems · History and advancements in chemistry · Information Retrieval and Search Behavior
