Saha, A and Shivanna, R and Bhattacharyya, C (2019) How many pairwise preferences do we need to rank a graph consistently? In: 33rd AAAI Conference on Artificial Intelligence, AAAI 2019, 31st Annual Conference on Innovative Applications of Artificial Intelligence, 27 January - 1 February 2019, Hilton Hawaii VillageHonolulu; United States, pp. 4830-4837.
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We consider the problem of optimal recovery of true ranking of n items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of ?(n2) for the purpose. We analyze the problem with an additional structure of relational graph G(n, E) over the n items added with an assumption of locality: Neighboring items are similar in their rankings. Noting the preferential nature of the data, we choose to embed not the graph, but, its strong product to capture the pairwise node relationships. Furthermore, unlike existing literature that uses Laplacian embedding for graph based learning problems, we use a richer class of graph embeddings-orthonormal representations-that includes (normalized) Laplacian as its special case. Our proposed algorithm, Pref-Rank, predicts the underlying ranking using an SVM based approach using the chosen embedding of the product graph, and is the first to provide statistical consistency on two ranking losses: Kendall's tau and Spearman's footrule, with a required sample complexity of O(n2?(G¯)) 23 pairs, ?(G¯) being the chromatic number of the complement graph G¯. Clearly, our sample complexity is smaller for dense graphs, with ?(G¯) characterizing the degree of node connectivity, which is also intuitive due to the locality 4 5 assumption e.g. O(n3) for union of k-cliques, or O(n3) for random and power law graphs etc.-a quantity much smaller than the fundamental limit of ?(n2) for large n. This, for the first time, relates ranking complexity to structural properties of the graph. We also report experimental evaluations on different synthetic and real-world datasets, where our algorithm is shown to outperform the state of the art methods. © 2019, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
| Item Type: | Conference Paper |
|---|---|
| Publication: | 33rd AAAI Conference on Artificial Intelligence, AAAI 2019, 31st Innovative Applications of Artificial Intelligence Conference, IAAI 2019 and the 9th AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019 |
| Publisher: | AAAI Press |
| Additional Information: | The copyright of this article belongs to AAAI Press |
| Keywords: | Embeddings; Graph algorithms; Graphic methods; Laplace transforms; Sampling; Support vector machines, Additional structures; Complement graphs; Experimental evaluation; Graph-based learning; Real-world datasets; Sample complexity; State-of-the-art methods; Statistical consistencies, Graph theory |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems |
| Date Deposited: | 03 Mar 2021 07:41 |
| Last Modified: | 03 Mar 2021 07:41 |
| URI: | http://eprints.iisc.ac.in/id/eprint/66714 |
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