Related papers: Matrix sketching for supervised classification wit…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…
Fairness is a fundamental requirement for trustworthy and human-centered Artificial Intelligence (AI) system. However, deep neural networks (DNNs) tend to make unfair predictions when the training data are collected from different…
In last few years there are major changes and evolution has been done on classification of data. As the application area of technology is increases the size of data also increases. Classification of data becomes difficult because of…
Sketching is a powerful dimensionality reduction technique for accelerating algorithms for data analysis. A crucial step in sketching methods is to compute a subspace embedding (SE) for a large matrix $\mathbf{A} \in \mathbb{R}^{N \times…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As…
We introduce a technique for estimating a structured covariance matrix from observations of a random vector which have been sketched. Each observed random vector $\boldsymbol{x}_t$ is reduced to a single number by taking its inner product…
For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where…
Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this…
Matrices have become essential data representations for many large-scale problems in data analytics, and hence matrix sketching is a critical task. Although much research has focused on improving the error/size tradeoff under various…
In this work, we study distributed sketching methods for large scale regression problems. We leverage multiple randomized sketches for reducing the problem dimensions as well as preserving privacy and improving straggler resilience in…
We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…
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,…
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…
Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can…
Many real-world applications reveal difficulties in learning classifiers from imbalanced data. The rising big data era has been witnessing more classification tasks with large-scale but extremely imbalance and low-quality datasets. Most of…
We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…