Timezone: »
Poster
On Adaptive Distance Estimation
Yeshwanth Cherapanamjeri · Jelani Nelson
We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data structure with low memory consumption and query time which, when later given any query point $q \in \mathbb{R}^d$, outputs a $(1+\varepsilon)$approximation of $\q  x_i\_p$ with high probability for all $i\in[n]$. The main novelty is our data structure's correctness guarantee holds even when the sequence of queries can be chosen adaptively: an adversary is allowed to choose the $j$th query point $q_j$ in a way that depends on the answers reported by the data structure for $q_1,\ldots,q_{j1}$. Previous randomized Monte Carlo methods do not provide error guarantees in the setting of adaptively chosen queries. Our memory consumption is $\tilde O(nd/\varepsilon^2)$, slightly more than the $O(nd)$ required to store $X$ in memory explicitly, but with the benefit that our time to answer queries is only $\tilde O(\varepsilon^{2}(n + d))$, much faster than the naive $\Theta(nd)$ time obtained from a linear scan in the case of $n$ and $d$ very large. Here $\tilde O$ hides $\log(nd/\varepsilon)$ factors. We discuss applications to nearest neighbor search and nonparametric estimation.
Our method is simple and likely to applicable to other domains: we describe a generic approach for transforming randomized Monte Carlo data structures which do not support adaptive queries to ones that do, and show that for the problem at hand it can be applied to standard nonadaptive solutions to $\ell_p$ norm estimation with negligible overhead in query time and a factor $d$ overhead in memory.
Author Information
Yeshwanth Cherapanamjeri (UC Berkeley)
Jelani Nelson (UC Berkeley)
Jelani Nelson is Professor in the Department of Electrical Engineering and Computer Science at UC Berkeley. His research interests include sketching and streaming algorithms, dimensionality reduction, compressing sensing, and randomized linear algebra. In the past he has been a recipient of the PECASE award, a Sloan Research Fellowship, and an NSF CAREER award. He is also the Founder and President of a 501(c)(3) nonprofit, “AddisCoder Inc.”, which organizes annual summer camps that have provided algorithms training to over 500 high school students in Ethiopia (see addiscoder.com).
Related Events (a corresponding poster, oral, or spotlight)

2020 Spotlight: On Adaptive Distance Estimation »
Thu. Dec 10th 03:00  03:10 AM Room Orals & Spotlights: Learning Theory
More from the Same Authors

2021 Spotlight: A single gradient step finds adversarial examples on random twolayers neural networks »
Sebastien Bubeck · Yeshwanth Cherapanamjeri · Gauthier Gidel · Remi Tachet des Combes 
2021 : Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis 
2021 : Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis 
2022 Poster: Estimation of Entropy in Constant Space with Improved Sample Complexity »
Maryam Aliakbarpour · Andrew McGregor · Jelani Nelson · Erik Waingarten 
2022 Poster: Sketching based Representations for Robust Image Classification with Provable Guarantees »
Nishanth Dikkala · Sankeerth Rao Karingula · Raghu Meka · Jelani Nelson · Rina Panigrahy · Xin Wang 
2021 : Spotlight 4: Estimation of Standard Asymmetric Auction Models »
Yeshwanth Cherapanamjeri · Constantinos Daskalakis · Andrew Ilyas · Emmanouil Zampetakis 
2021 Poster: Adversarial Examples in MultiLayer Random ReLU Networks »
Peter Bartlett · Sebastien Bubeck · Yeshwanth Cherapanamjeri 
2021 Poster: A single gradient step finds adversarial examples on random twolayers neural networks »
Sebastien Bubeck · Yeshwanth Cherapanamjeri · Gauthier Gidel · Remi Tachet des Combes 
2020 Tutorial: (Track1) Sketching and Streaming Algorithms »
Jelani Nelson