Related papers: On fast bounded locality sensitive hashing
We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for…
We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an…
Locality-sensitive hashing (LSH) is a popular data-independent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of…
Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…
We study the problem of approximating Hamming distance in sublinear time under property-preserving hashing (PPH), where only hashed representations of inputs are available. Building on the threshold evaluation framework of Fleischhacker,…
The approximate nearest neighbor problem ($\epsilon$-ANN) in high dimensional Euclidean space has been mainly addressed by Locality Sensitive Hashing (LSH), which has polynomial dependence in the dimension, sublinear query time, but…
The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…
Random hashing can provide guarantees regarding the performance of data structures such as hash tables---even in an adversarial setting. Many existing families of hash functions are universal: given two data objects, the probability that…
Recently the behavior of operator monotone functions on unbounded intervals with respect to the relation of strictly positivity has been investigated. In this paper we deeply study such behavior not only for operator monotone functions but…
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for univariate approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural…
Learning-based hashing algorithms are ``hot topics" because they can greatly increase the scale at which existing methods operate. In this paper, we propose a new learning-based hashing method called ``fast supervised discrete hashing"…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…
Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…
Inspired by applications in weighted polynomial approximation problems, we study an optimal mass distribution problem. Given a gauge function $h$ and a positive "roof" function $R$ compactly supported in $\mathbb{R}^n$, we are interested in…
We find probability error bounds for approximations of functions $f$ in a separable reproducing kernel Hilbert space $\mathcal{H}$ with reproducing kernel $K$ on a base space $X$, firstly in terms of finite linear combinations of functions…
The "extremal function" $c(H)$ of a graph $H$ is the supremum of densities of graphs not containing $H$ as a minor, where the "density" of a graph $G$ is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005),…