Search Results for author:
Found 13 papers, 2 papers with code
Individual Fairness for $k$-Clustering
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 $r(x)$.
Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?
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 $q$.
Composable Core-sets for Determinant Maximization Problems via Spectral Spanners
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.
Nonlinear Dimension Reduction via Outer Bi-Lipschitz Extensions
We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces.
Near Neighbor: Who is the Fairest of Them All?
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.
Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm
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.
Non-Adaptive Adaptive Sampling on Turnstile Streams
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.
Streaming Complexity of SVMs
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 $d=1$.
(Individual) Fairness for k-Clustering
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 $r(x)$.
Adaptive Single-Pass Stochastic Gradient Descent in Input Sparsity Time
Moreover, we show that our algorithm can be generalized to approximately sample Hessians and thus provides variance reduction for second-order methods as well.
Adaptive Sketches for Robust Regression with Importance Sampling
In this paper, we introduce an algorithm that approximately samples $T$ gradients of dimension $d$ from nearly the optimal importance sampling distribution for a robust regression problem over $n$ rows.
Approximation Algorithms for Fair Range Clustering
This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick $k$ centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set.
Efficiently Computing Similarities to Private Datasets
We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function $f$ and a large high-dimensional private dataset $X \subset \mathbb{R}^d$, output a differentially private (DP) data structure which approximates $\sum_{x \in X} f(x, y)$ for any query $y$.
