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2 code implementations • 11 Aug 2021 • Alexandr Andoni, Daniel Beaglehole

In this paper, we design an NNS algorithm for the Hamming space that has worst-case guarantees essentially matching that of theoretical algorithms, while optimizing the hashing to the structure of the dataset (think instance-optimal algorithms) for performance on the minimum-performing query.

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 • 26 Jun 2018 • Alexandr Andoni, Piotr Indyk, Ilya Razenshteyn

The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X, D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).

no code implementations • ICML 2018 • Alexandr Andoni, Chengyu Lin, Ying Sheng, Peilin Zhong, Ruiqi Zhong

An Orlicz norm is parameterized by a non-negative convex function $G:\mathbb{R}_+\rightarrow\mathbb{R}_+$ with $G(0)=0$: the Orlicz norm of a vector $x\in\mathbb{R}^n$ is defined as $ \|x\|_G=\inf\left\{\alpha>0\large\mid\sum_{i=1}^n G(|x_i|/\alpha)\leq 1\right\}.

no code implementations • 18 Nov 2016 • Alexandr Andoni, Huy L. Nguyen, Aleksandar Nikolov, Ilya Razenshteyn, Erik Waingarten

We show that every symmetric normed space admits an efficient nearest neighbor search data structure with doubly-logarithmic approximation.

1 code implementation • NeurIPS 2015 • Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig Schmidt

Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

no code implementations • 7 May 2013 • Alexandr Andoni, Rina Panigrahy

To obtain our main result, we show that the optimal payoff functions have to satisfy the Hermite differential equation, and hence are given by the solutions to this equation.

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