Related papers: Harmonic Decomposition in Data Sketches
Similarity-preserving hashing is a core technique for fast similarity searches, and it randomly maps data points in a metric space to strings of discrete symbols (i.e., sketches) in the Hamming space. While traditional hashing techniques…
Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…
Frequency estimation is one of the most fundamental problems in streaming algorithms. Given a stream $S$ of elements from some universe $U=\{1 \ldots n\}$, the goal is to compute, in a single pass, a short sketch of $S$ so that for any…
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…
We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian…
Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors…
Many real-world matrix datasets arrive as high-throughput vector streams, making it impractical to store or process them in their entirety. To enable real-time analytics under limited computational, memory, and communication resources,…
We consider a basic problem in the general data streaming model, namely, to estimate a vector $f \in \Z^n$ that is arbitrarily updated (i.e., incremented or decremented) coordinate-wise. The estimate $\hat{f} \in \Z^n$ must satisfy…
Given a stream with frequencies $f_d$, for $d\in[n]$, we characterize the space necessary for approximating the frequency negative moments $F_p=\sum |f_d|^p$, where $p<0$ and the sum is taken over all items $d\in[n]$ with nonzero frequency,…
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
In rapid and massive data streams, it is often not possible to estimate the frequency of items with complete accuracy. To perform the operation in a reasonable amount of space and with sufficiently low latency, approximated methods are…
The sliding window model of computation captures scenarios in which data are continually arriving in the form of a stream, and only the most recent $w$ items are used for analysis. In this setting, an algorithm needs to accurately track…
Recently there has been increased interest in using machine learning techniques to improve classical algorithms. In this paper we study when it is possible to construct compact, composable sketches for weighted sampling and statistics…
Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-\epsilon)$-approximation for Max-Cut must use $n^{1-O(\epsilon)}$ space; moreover,…
We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying…
We introduce and study a new data sketch for processing massive datasets. It addresses two common problems: 1) computing a sum given arbitrary filter conditions and 2) identifying the frequent items or heavy hitters in a data set. For the…
The turnstile data stream model offers the most flexible framework where data can be manipulated dynamically, i.e., rows, columns, and even single entries of an input matrix can be added, deleted, or updated multiple times in a data stream.…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…