Related papers: Constructing Linear-Sized Spectral Sparsification …
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We derive a new proof to show that the incremental resparsification algorithm proposed by Kelner and Levin (2013) produces a spectral sparsifier in high probability. We rigorously take into account the dependencies across subsequent…
We provide an algorithm that, given an $n$-vertex $m$-edge Eulerian graph with polynomially bounded weights, computes an $\breve{O}(n\log^{2} n \cdot \varepsilon^{-2})$-edge $\varepsilon$-approximate Eulerian sparsifier with high…
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…
We study differentially private algorithms for graph cut sparsification, a fundamental problem in algorithms, privacy, and machine learning. While significant progress has been made, the best-known private and efficient cut sparsifiers on…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA'12) that has since found numerous applications in streaming, distributed computing, and massively…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by…
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
Expander decompositions form the basis of one of the most flexible paradigms for close-to-linear-time graph algorithms. Length-constrained expander decompositions generalize this paradigm to better work for problems with lengths, distances…
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only…
We show that the problem of recovering the topology and admittance of an electrical network from power and voltage data at all vertices is often ill-posed, and sometimes it even has multiple solutions. We reformulate the problem to seek for…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data, improving upon the previous best algorithm whose sampling complexity has at least cubic dependence on…