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The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into l1
This paper disproves the non-uniform version of Arora, Rao and Vazirani's Conjecture (2004), asserting that the integrality gap of the sparsest cut SDP, with the triangle inequality constraints, is bounded from above by a constant.
Ranking with Fairness Constraints
This work studies the following variant of the traditional ranking problem when the objective satisfies properties that appear in common ranking metrics such as Discounted Cumulative Gain, Spearman's rho or Bradley-Terry.
Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees
A meta-algorithm for classification that can take as input a general class of fairness constraints with respect to multiple non-disjoint and multi-valued sensitive attributes, and which comes with provable guarantees is proposed.
A local spectral method for graphs: with applications to improving graph partitions and exploring data graphs locally
- Michael W. Mahoney, L. Orecchia, Nisheeth K. Vishnoi
- Computer ScienceJ. Mach. Learn. Res.
- 3 December 2009
This paper introduces a locally-biased analogue of the second eigenvector of the Laplacian matrix, and demonstrates its usefulness at highlighting local properties of data graphs in a semi-supervised manner and shows how it can applied to finding locally- biased sparse cuts around an input vertex seed set in social and information networks.
Integrality gaps for sparsest cut and minimum linear arrangement problems
- Nikhil R. Devanur, Subhash Khot, Rishi Saket, Nisheeth K. Vishnoi
- Mathematics, Computer ScienceSTOC '06
- 21 May 2006
This paper disproves the non-uniform version of the ARV-Conjecture by constructing an Ω(log log n) integrality gap instance for the SDP relaxation of the Minimum Linear Arrangement problem.
Biased normalized cuts
This work presents a modification of “Normalized Cuts” to incorporate priors which can be used for constrained image segmentation and compares the algorithm to other graph cut based algorithms and highlights the advantages.
Fair and Diverse DPP-based Data Summarization
- L. E. Celis, Vijay Keswani, D. Straszak, A. Deshpande, Tarun Kathuria, Nisheeth K. Vishnoi
- Computer ScienceICML
- 12 February 2018
The experimental results on a real-world and an image dataset show that the diversity of the samples produced by adding fairness constraints is not too far from the unconstrained case, and a theoretical explanation of it is provided.
Multiwinner Voting with Fairness Constraints
This work introduces an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be ``fair'' with respect to a given set of attributes and presents simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.
Approximating the exponential, the lanczos method and an Õ(m)-time spectral algorithm for balanced separator
- L. Orecchia, Sushant Sachdeva, Nisheeth K. Vishnoi
- Computer Science, MathematicsSTOC '12
- 7 November 2011
A novel spectral approximation algorithm is given for the balanced (edge-)separator problem that, given a graph G, either finds an Ω(b)-balanced cut of conductance O(√γ) in G, or outputs a certificate that all b-balanced cuts in G have conductance at least γ, and runs in time ~O(m).
Entropy, optimization and counting
It is proved that counting oracles are necessary for computing max-entropy distributions: it is shown how algorithms that compute max-ENTropy distributions can be converted into counting algorithms.