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Ranking on large-scale graphs plays a fundamental role in many high-impact application domains, ranging from information retrieval, recommender systems, sports team management, biology to neuroscience and many more. PageRank, together with many of its random walk based variants, has become one of the most well-known and widely used algorithms, due to its mathematical elegance and the superior performance across a variety of application domains. Important as it might be, state-of-the-art lacks an intuitive way to explain the ranking results by PageRank (or its variants), e.g., why it thinks the returned top-k webpages are the most important ones in the entire graph; why it gives a higher rank to actor John than actor Smith in terms of their relevance w.r.t. a particular movie? In order to answer these questions, this paper proposes a paradigm shift for PageRank, from identifying which nodes are most important to understanding why the ranking algorithm gives a particular ranking result. We formally define the PageRank auditing problem, whose central idea is to identify a set of key graph elements (e.g., edges, nodes, subgraphs) with the highest influence on the ranking results. We formulate it as an opti-mization problem and propose a family of effective and scalable algorithms (Aurora) to solve it. Our algorithms measure the influence of graph elements and incrementally select influential elements w.r.t. their gradients over the ranking results. We perform extensive empirical evaluations on real-world datasets, which demonstrate that the proposed methods (Aurora) provide intuitive explanations with a linear scalability.
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Why Not Yet: Fixing a Top-k Ranking that is Not Fair to Individuals
This work considers why-not questions in the context of top-k queries and score-based ranking functions. Following the popular linear scalarization approach for multi-objective optimization, we study rankings based on the weighted sum of multiple scores. A given weight choice may be controversial or perceived as unfair to certain individuals or organizations, triggering the question why some entity of interest has not yet shown up in the top-k. We introduce various notions of such why-not-yet queries and formally define them as satisfiability or optimization problems, whose goal is to propose alternative ranking functions that address the placement of the entities of interest. While some why-not-yet problems have linear constraints, others require quantifiers, disjunction, and negation. We propose several optimizations, ranging from a monotonic-core construction that approximates the complex constraints with a conjunction of linear ones, to various techniques that let the user control the tradeoff between running time and approximation quality. Experiments with real and synthetic data demonstrate the practicality and scalability of our technique, showing its superiority compared to the state of the art (SOA).
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- Award ID(s):
- 1956096
- PAR ID:
- 10432220
- Date Published:
- Journal Name:
- Proceedings of the VLDB Endowment
- Volume:
- 16
- Issue:
- 9
- ISSN:
- 2150-8097
- Page Range / eLocation ID:
- 2377 to 2390
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.14778/3598581.3598606
