Related papers: Lifting Linear Sketches: Optimal Bounds and Advers…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…
In federated contextual linear bandits, high data dimensionality incurs prohibitive computation and communication costs: local agents perform $O(d^3)$-time determinant computation and upload $O(d^2)$ parameters, making existing algorithms…
CountSketch and Feature Hashing (the "hashing trick") are popular randomized dimensionality reduction methods that support recovery of $\ell_2$-heavy hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and approximate inner…
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…
This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$…
Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of…
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…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
In this work we propose a new paradigm for designing efficient deep unrolling networks using operator sketching. The deep unrolling networks are currently the state-of-the-art solutions for imaging inverse problems. However, for…
We study matrix sketching methods for regularized variants of linear regression, low rank approximation, and canonical correlation analysis. Our main focus is on sketching techniques which preserve the objective function value for…
To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…
Consider the following "local" cut-detection problem in a directed graph: We are given a starting vertex $s$ and need to detect whether there is a cut with at most $k$ edges crossing the cut such that the side of the cut containing $s$ has…
Graph streams represent data interactions in real applications. The mining of graph streams plays an important role in network security, social network analysis, and traffic control, among others. However, the sheer volume and high dynamics…
We improve upon previous oblivious sketching and turnstile streaming results for $\ell_1$ and logistic regression, giving a much smaller sketching dimension achieving $O(1)$-approximation and yielding an efficient optimization problem in…
We give the first L_1-sketching algorithm for integer vectors which produces nearly optimal sized sketches in nearly linear time. This answers the first open problem in the list of open problems from the 2006 IITK Workshop on Algorithms for…
We derive optimal statistical and computational complexity bounds for exp-concave stochastic minimization in terms of the effective dimension. For common eigendecay patterns of the population covariance matrix, this quantity is…
The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic…
The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…
Randomized sketching accelerates large-scale numerical linear algebra by reducing computational complexity. While the traditional sketch-and-solve approach reduces the problem size directly through sketching, the sketch-and-precondition…
Sketching is a dimensionality reduction technique where one compresses a matrix by linear combinations that are chosen at random. A line of work has shown how to sketch the Hessian to speed up each iteration in a second order method, but…