Search Results for author: Ali Vakilian

Found 11 papers, 1 papers with code

(Individual) Fairness for k-Clustering

no code implementations ICML 2020 Sepideh Mahabadi, Ali Vakilian

Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$.

Fairness

Approximating Fair Clustering with Cascaded Norm Objectives

no code implementations8 Nov 2021 Eden Chlamtáč, Yury Makarychev, Ali Vakilian

We utilize convex programming techniques to approximate the $(p, q)$-Fair Clustering problem for different values of $p$ and $q$.

Improved Approximation Algorithms for Individually Fair Clustering

no code implementations26 Jun 2021 Ali Vakilian, Mustafa Yalçıner

We consider the $k$-clustering problem with $\ell_p$-norm cost, which includes $k$-median, $k$-means and $k$-center cost functions, under an individual notion of fairness proposed by Jung et al. [2020]: given a set of points $P$ of size $n$, a set of $k$ centers induces a fair clustering if for every point $v\in P$, $v$ can find a center among its $n/k$ closest neighbors.

Fairness

Approximation Algorithms for Socially Fair Clustering

no code implementations3 Mar 2021 Yury Makarychev, Ali Vakilian

In order to obtain our result, we introduce a strengthened LP relaxation and show that it has an integrality gap of $\Theta(\frac{\log \ell}{\log\log\ell})$ for a fixed $p$.

A framework for learned sparse sketches

no code implementations1 Jan 2021 Simin Liu, Tianrui Liu, Ali Vakilian, Yulin Wan, David Woodruff

In this work, we consider the problem of optimizing sketches to obtain low approximation error over a data distribution.

Learning the Positions in CountSketch

no code implementations20 Jul 2020 Simin Liu, Tianrui Liu, Ali Vakilian, Yulin Wan, David P. Woodruff

Despite the growing body of work on this paradigm, a noticeable omission is that the locations of the non-zero entries of previous algorithms were fixed, and only their values were learned.

Individual Fairness for $k$-Clustering

no code implementations17 Feb 2020 Sepideh Mahabadi, Ali Vakilian

Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$.

Fairness

Learning-Based Low-Rank Approximations

no code implementations NeurIPS 2019 Piotr Indyk, Ali Vakilian, Yang Yuan

Our experiments show that, for multiple types of data sets, a learned sketch matrix can substantially reduce the approximation loss compared to a random matrix $S$, sometimes by one order of magnitude.

Generalization Bounds

Sample-Optimal Low-Rank Approximation of Distance Matrices

no code implementations2 Jun 2019 Piotr Indyk, Ali Vakilian, Tal Wagner, David Woodruff

Recent work by Bakshi and Woodruff (NeurIPS 2018) showed it is possible to compute a rank-$k$ approximation of a distance matrix in time $O((n+m)^{1+\gamma}) \cdot \mathrm{poly}(k, 1/\epsilon)$, where $\epsilon>0$ is an error parameter and $\gamma>0$ is an arbitrarily small constant.

Handwriting Recognition

Learning-Based Frequency Estimation Algorithms

no code implementations ICLR 2019 Chen-Yu Hsu, Piotr Indyk, Dina Katabi, Ali Vakilian

Estimating the frequencies of elements in a data stream is a fundamental task in data analysis and machine learning.

Scalable Fair Clustering

1 code implementation10 Feb 2019 Arturs Backurs, Piotr Indyk, Krzysztof Onak, Baruch Schieber, Ali Vakilian, Tal Wagner

In the fair variant of $k$-median, the points are colored, and the goal is to minimize the same average distance objective while ensuring that all clusters have an "approximately equal" number of points of each color.

Fairness

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