261 citations · 836 across the 30 of their papers we have counts for
23 papers · 1 filter
A Study of Performance of Optimal Transport
Yihe Dong, Yu Gao, Richard Peng +2
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite g…
Non-Adaptive Adaptive Sampling on Turnstile Streams
Sepideh Mahabadi, Ilya Razenshteyn, David P. Woodruff +1
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 p…
Scalable Nearest Neighbor Search for Optimal Transport
Arturs Backurs, Yihe Dong, Piotr Indyk +2
The Optimal Transport (a.k.a. Wasserstein) distance is an increasingly popular similarity measure for rich data domains, such as images or text documents. This raises the necessity…
SANNS: Scaling Up Secure Approximate k-Nearest Neighbors Search
Hao Chen, Ilaria Chillotti, Yihe Dong +3
The -Nearest Neighbor Search (-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In…
On Mean Estimation for General Norms with Statistical Queries
Jerry Li, Aleksandar Nikolov, Ilya Razenshteyn +1
We study the problem of mean estimation for high-dimensional distributions, assuming access to a statistical query oracle for the distribution. For a normed space $X = (\mathbb{R}^…
Nonlinear Dimension Reduction via Outer Bi-Lipschitz Extensions
Sepideh Mahabadi, Konstantin Makarychev, Yury Makarychev +1
We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces. The notion is a natural analogue of the notion of a Lipschitz extension of a…
Performance of Johnson-Lindenstrauss Transform for k-Means and k-Medians Clustering
Konstantin Makarychev, Yury Makarychev, Ilya Razenshteyn
Consider an instance of Euclidean -means or -medians clustering. We show that the cost of the optimal solution is preserved up to a factor of under a projec…
Approximate Nearest Neighbor Search in High Dimensions
Alexandr Andoni, Piotr Indyk, Ilya Razenshteyn
The nearest neighbor problem is defined as follows: Given a set of points in some metric space , build a data structure that, given any point , returns a point in…
Practical Data-Dependent Metric Compression with Provable Guarantees
Piotr Indyk, Ilya Razenshteyn, Tal Wagner
We introduce a new distance-preserving compact representation of multi-dimensional point-sets. Given points in a -dimensional space where each coordinate is represented usin…
Approximate Near Neighbors for General Symmetric Norms
Alexandr Andoni, Huy L. Nguyen, Aleksandar Nikolov +2
We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation. Specifically, for every , $d = n^{o(1…
Optimal Hashing-based Time-Space Trade-offs for Approximate Near Neighbors
Alexandr Andoni, Thijs Laarhoven, Ilya Razenshteyn +1
[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the -Approximate Near Neighbor Search problem. For the -dimensional…
Lower Bounds on Time-Space Trade-Offs for Approximate Near Neighbors
Alexandr Andoni, Thijs Laarhoven, Ilya Razenshteyn +1
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of co…
On the Complexity of Inner Product Similarity Join
Thomas D. Ahle, Rasmus Pagh, Ilya Razenshteyn +1
A number of tasks in classification, information retrieval, recommendation systems, and record linkage reduce to the core problem of inner product similarity join (IPS join): ident…
Practical and Optimal LSH for Angular Distance
Alexandr Andoni, Piotr Indyk, Thijs Laarhoven +2
We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optima…
Tight Lower Bounds for Data-Dependent Locality-Sensitive Hashing
Alexandr Andoni, Ilya Razenshteyn
We prove a tight lower bound for the exponent for data-dependent Locality-Sensitive Hashing schemes, recently used to design efficient solutions for the -approximate nearest…
Nearly-optimal bounds for sparse recovery in generic norms, with applications to -median sketching
Arturs Backurs, Piotr Indyk, Eric Price +2
We initiate the study of trade-offs between sparsity and the number of measurements in sparse recovery schemes for generic norms. Specifically, for a norm , sparsity par…
Optimal Data-Dependent Hashing for Approximate Near Neighbors
Alexandr Andoni, Ilya Razenshteyn
We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an -point data set in a -dimensional space our data structure achieves query t…
Sketching and Embedding are Equivalent for Norms
Alexandr Andoni, Robert Krauthgamer, Ilya Razenshteyn
An outstanding open question posed by Guha and Indyk in 2006 asks to characterize metric spaces in which distances can be estimated using efficient sketches. Specifically, we say t…
Restricted Isometry Property for General p-Norms
Zeyuan Allen-Zhu, Rati Gelashvili, Ilya Razenshteyn
The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an matrix satisfies RIP of order for the $\…
Beyond Locality-Sensitive Hashing
Alexandr Andoni, Piotr Indyk, Huy L. Nguyen +1
We present a new data structure for the c-approximate near neighbor problem (ANN) in the Euclidean space. For n points in R^d, our algorithm achieves O(n^ρ + d log n) query time an…
Separating Hierarchical and General Hub Labelings
Andrew V. Goldberg, Ilya Razenshteyn, Ruslan Savchenko
In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An query computes the corresponding distance from the labels of and…
On Model-Based RIP-1 Matrices
Piotr Indyk, Ilya Razenshteyn
The Restricted Isometry Property (RIP) is a fundamental property of a matrix enabling sparse recovery. Informally, an m x n matrix satisfies RIP of order k in the l_p norm if ||Ax|…
On Epsilon-Nets, Distance Oracles, and Metric Embeddings
Ilya Razenshteyn
We give two new applications of an observation from \cite{ADFGW11}. The first is an almost linear sized constant time data structure for reporting very large distances in undirecte…