Related papers: Count-Min Tree Sketch: Approximate counting for NL…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Various NLP tasks require a complex hierarchical structure over nodes, where each node is a cluster of items. Examples include generating entailment graphs, hierarchical cross-document coreference resolution, annotating event and subevent…
Sketches are probabilistic data structures that can provide approximate results within mathematically proven error bounds while using orders of magnitude less memory than traditional approaches. They are tailored for streaming data analysis…
The Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap $2$-edge connected subgraphs. This has culminated in a…
We revisit the problem of sketching using approximate leverage scores for matrix least squares problems of the form $\| AX - B \|_F^2$ where the design matrix $A \in \mathbb{R}^{N \times r}$ is tall and skinny with $N \gg r$. We derive the…
Kernel methods provide an elegant framework for developing nonlinear learning algorithms from simple linear methods. Though these methods have superior empirical performance in several real data applications, their usefulness is inhibited…
Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…
Sketch-based streaming algorithms allow efficient processing of big data. These algorithms use small fixed-size storage to store a summary ("sketch") of the input data, and use probabilistic algorithms to estimate the desired quantity.…
We present a new approach for computing compact sketches that can be used to approximate the inner product between pairs of high-dimensional vectors. Based on the Weighted MinHash algorithm, our approach admits strong accuracy guarantees…
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 $(X, Y) \in \mathbb{R}^{n \times p} \times \mathbb{R}^n$,…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of $n$ items from a data universe equipped with a total order, the task is to compute a sketch (data…
Quantile summaries provide a scalable way to estimate the distribution of individual attributes in large datasets that are often distributed across multiple machines or generated by sensor networks. ReqSketch (arXiv:2004.01668) is currently…
Approximate computing trades off accuracy of results for resources such as energy or computing time. There is a large and rapidly growing literature on approximate computing that has focused mostly on showing the benefits of approximation.…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
Incrementally fine-tuning foundational models on new tasks or domains is now the de facto approach in NLP. A known pitfall of this approach is the \emph{catastrophic forgetting} of prior knowledge that happens during fine-tuning. A common…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…