Related papers: On Sketching Trimmed Statistics
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
Space-efficient streaming estimation of quantiles in massive datasets is a fundamental problem with numerous applications in data monitoring and analysis. While theoretical research led to optimal algorithms, such as the Greenwald-Khanna…
We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed…
In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h…
We consider massive distributed datasets that consist of elements modeled as key-value pairs and the task of computing statistics or aggregates where the contribution of each key is weighted by a function of its frequency (sum of values of…
Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$,…
Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods…
We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…
Sketching is a powerful dimensionality reduction technique for accelerating algorithms for data analysis. A crucial step in sketching methods is to compute a subspace embedding (SE) for a large matrix $\mathbf{A} \in \mathbb{R}^{N \times…
We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices…
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…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
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 study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
The metric sketching problem is defined as follows. Given a metric on $n$ points, and $\epsilon>0$, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up…
We consider the problem of high-dimensional heavy-tailed statistical estimation in the streaming setting, which is much harder than the traditional batch setting due to memory constraints. We cast this problem as stochastic convex…
As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference…