Related papers: A High Performance GPU CountSketch Implementation …
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…
Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality…
Sketching uses randomized Hash functions for dimensionality reduction and acceleration. The existing sketching methods, such as count sketch (CS), tensor sketch (TS), and higher-order count sketch (HCS), either suffer from low accuracy or…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
Splotch is a rendering algorithm for exploration and visual discovery in particle-based datasets coming from astronomical observations or numerical simulations. The strengths of the approach are production of high quality imagery and…
Given a symmetric matrix $A$, we show from the simple sketch $GAG^T$, where $G$ is a Gaussian matrix with $k = O(1/\epsilon^2)$ rows, that there is a procedure for approximating all eigenvalues of $A$ simultaneously to within $\epsilon…
We propose OverSketch, an approximate algorithm for distributed matrix multiplication in serverless computing. OverSketch leverages ideas from matrix sketching and high-performance computing to enable cost-efficient multiplication that is…
In this paper, we revisit the classic CountSketch method, which is a sparse, random projection that transforms a (high-dimensional) Euclidean vector $v$ to a vector of dimension $(2t-1) s$, where $t, s > 0$ are integer parameters. It is…
Iterative sketching and sketch-and-precondition are randomized algorithms used for solving overdetermined linear least-squares problems. When implemented in exact arithmetic, these algorithms produce high-accuracy solutions to least-squares…
Sketch-based algorithms for network traffic monitoring have drawn increasing interest in recent years due to their sub-linear memory efficiency and high accuracy. As the volume of network traffic grows, software-based sketch implementations…
Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…
We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data $(X, Y) \in \mathbb{R}^{n \times p} \times \mathbb{R}^n$,…
A litany of theoretical and numerical results have established the sketch-and-precondition paradigm as a powerful approach to solving large linear regression problems in standard computing environments. Perhaps surprisingly, much less work…
Count-Min Sketch is a widely adopted algorithm for approximate event counting in large scale processing. However, the original version of the Count-Min-Sketch (CMS) suffers of some deficiences, especially if one is interested by the…
We propose new variants of the sketch-and-project method for solving large scale ridge regression problems. Firstly, we propose a new momentum alternative and provide a theorem showing it can speed up the convergence of sketch-and-project,…
The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
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…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…