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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 $r(x)$.

1 code implementation • 26 Jan 2021 • Martin Aumüller, Sariel Har-Peled, Sepideh Mahabadi, Rasmus Pagh, Francesco Silvestri

Given a set of points $S$ and a radius parameter $r>0$, the $r$-near neighbor ($r$-NN) problem asks for a data structure that, given any query point $q$, returns a point $p$ within distance at most $r$ from $q$.

no code implementations • 1 Jan 2021 • Sepideh Mahabadi, David Woodruff, Samson Zhou

Moreover, we show that our algorithm can be generalized to approximately sample Hessians and thus provides variance reduction for second-order methods as well.

no code implementations • 7 Jul 2020 • Alexandr Andoni, Collin Burns, Yi Li, Sepideh Mahabadi, David P. Woodruff

We show that, for both problems, for dimensions $d=1, 2$, one can obtain streaming algorithms with space polynomially smaller than $\frac{1}{\lambda\epsilon}$, which is the complexity of SGD for strongly convex functions like the bias-regularized SVM, and which is known to be tight in general, even for $d=1$.

no code implementations • 23 Apr 2020 • Sepideh Mahabadi, Ilya Razenshteyn, David P. Woodruff, Samson Zhou

Adaptive sampling is a useful algorithmic tool for data summarization problems in the classical centralized setting, where the entire dataset is available to the single processor performing the computation.

no code implementations • 17 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 $r(x)$.

no code implementations • 6 Jul 2019 • Piotr Indyk, Sepideh Mahabadi, Shayan Oveis Gharan, Alireza Rezaei

In this work, first we provide a theoretical approximation guarantee of $O(C^{k^2})$ for the Greedy algorithm in the context of composable core-sets; Further, we propose to use a Local Search based algorithm that while being still practical, achieves a nearly optimal approximation bound of $O(k)^{2k}$; Finally, we implement all three algorithms and show the effectiveness of our proposed algorithm on standard data sets.

no code implementations • NeurIPS 2019 • Sariel Har-Peled, Sepideh Mahabadi

Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the points, such that given a query point $q$, any point in the $r$-neighborhood of the query, i. e., $\ball(q, r)$, have the same probability of being reported as the near neighbor.

no code implementations • 8 Nov 2018 • Sepideh Mahabadi, Konstantin Makarychev, Yury Makarychev, Ilya Razenshteyn

We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces.

no code implementations • 31 Jul 2018 • Piotr Indyk, Sepideh Mahabadi, Shayan Oveis Gharan, Alireza Rezaei

We show that for many objective functions one can use a spectral spanner, independent of the underlying functions, as a core-set and obtain almost optimal composable core-sets.

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