Related papers: Node Similarities under Random Projections: Limits…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called…
The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the…
This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
Node embedding methods map network nodes to low dimensional vectors that can be subsequently used in a variety of downstream prediction tasks. The popularity of these methods has grown significantly in recent years, yet, their robustness to…
The Johnson-Lindenstrauss (JL) lemma allows subsets of a high-dimensional space to be embedded into a lower-dimensional space while approximately preserving all pairwise Euclidean distances. This important result has inspired an extensive…
A randomized misfit approach is presented for the efficient solution of large-scale PDE-constrained inverse problems with high-dimensional data. The purpose of this paper is to offer a theory-based framework for random projections in this…
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an…
Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse…
We consider a latent space model for random graphs where a node $i$ is associated to a random latent point $X_i$ on the Euclidean unit ball. The probability that an edge exists between two nodes is determined by a ``link'' function, which…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the…