no code implementations • 18 Mar 2024 • Gregory Dexter, Christos Boutsikas, Linkai Ma, Ilse C. F. Ipsen, Petros Drineas
Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows than columns.
no code implementations • 24 Mar 2023 • Gregory Dexter, Rajiv Khanna, Jawad Raheel, Petros Drineas
We present novel bounds for coreset construction, feature selection, and dimensionality reduction for logistic regression.
no code implementations • 31 Jan 2022 • Shany Shumeli, Petros Drineas, Haim Avron
Given a low rank perturbation to a matrix, we argue that a low-rank approximate correction to the (inverse) square root exists.
no code implementations • NeurIPS 2020 • Agniva Chowdhury, Palma London, Haim Avron, Petros Drineas
Linear programming (LP) is used in many machine learning applications, such as $\ell_1$-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc.
no code implementations • 23 Jun 2020 • Agniva Chowdhury, Petros Drineas, David P. Woodruff, Samson Zhou
To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have been proposed, which are termed Sparse Principal Component Analysis (SPCA).
no code implementations • 9 Sep 2018 • Agniva Chowdhury, Jiasen Yang, Petros Drineas
When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA).
no code implementations • ICML 2018 • Agniva Chowdhury, Jiasen Yang, Petros Drineas
Ridge regression is a variant of regularized least squares regression that is particularly suitable in settings where the number of predictor variables greatly exceeds the number of observations.
no code implementations • 22 May 2018 • Vikram Ravindra, Petros Drineas, Ananth Grama
Recent neuroimaging studies have shown that functional connectomes are unique to individuals, i. e., two distinct fMRIs taken over different sessions of the same subject are more similar in terms of their connectomes than those from two different subjects.
1 code implementation • 24 Dec 2017 • Petros Drineas, Michael W. Mahoney
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
no code implementations • 29 May 2017 • Agniva Chowdhury, Jiasen Yang, Petros Drineas
Projection-cost preservation is a low-rank approximation guarantee which ensures that the cost of any rank-$k$ projection can be preserved using a smaller sketch of the original data matrix.
no code implementations • 13 Aug 2015 • Kimon Fountoulakis, Abhisek Kundu, Eugenia-Maria Kontopoulou, Petros Drineas
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem.
no code implementations • 17 Jun 2015 • Saurabh Paul, Petros Drineas
We introduce single-set spectral sparsification as a deterministic sampling based feature selection technique for regularized least squares classification, which is the classification analogue to ridge regression.
no code implementations • NeurIPS 2015 • Abhisek Kundu, Petros Drineas, Malik Magdon-Ismail
We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch.
no code implementations • 2 Mar 2015 • Abhisek Kundu, Petros Drineas, Malik Magdon-Ismail
This paper addresses how well we can recover a data matrix when only given a few of its elements.
no code implementations • 1 Jun 2014 • Saurabh Paul, Malik Magdon-Ismail, Petros Drineas
In the unsupervised setting, we also provide worst-case guarantees of the radius of the minimum enclosing ball, thereby ensuring comparable generalization as in the full feature space and resolving an open problem posed in Dasgupta et al. We present extensive experiments on real-world datasets to support our theory and to demonstrate that our method is competitive and often better than prior state-of-the-art, for which there are no known provable guarantees.
no code implementations • 14 Oct 2013 • Abhisek Kundu, Srinivas Nambirajan, Petros Drineas
For any matrix A in R^(m x n) of rank \rho, we present a probability distribution over the entries of A (the element-wise leverage scores of equation (2)) that reveals the most influential entries in the matrix.
no code implementations • 26 Nov 2012 • Saurabh Paul, Christos Boutsidis, Malik Magdon-Ismail, Petros Drineas
Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space.
no code implementations • 19 Jul 2012 • Kenneth L. Clarkson, Petros Drineas, Malik Magdon-Ismail, Michael W. Mahoney, Xiangrui Meng, David P. Woodruff
We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to the same problem with input matrix $\tilde A$ of dimension $s \times d$ and corresponding $\tilde b$ of dimension $s\times 1$.
no code implementations • 16 Feb 2012 • Christos Boutsidis, Petros Drineas, Malik Magdon-Ismail
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression.
no code implementations • NeurIPS 2011 • Christos Boutsidis, Petros Drineas, Malik Magdon-Ismail
Principal Components Analysis~(PCA) is often used as a feature extraction procedure.
no code implementations • 13 Oct 2011 • Christos Boutsidis, Anastasios Zouzias, Michael W. Mahoney, Petros Drineas
On the other hand, two provably accurate feature extraction methods for $k$-means clustering are known in the literature; one is based on random projections and the other is based on the singular value decomposition (SVD).
no code implementations • NeurIPS 2010 • Christos Boutsidis, Anastasios Zouzias, Petros Drineas
This paper discusses the topic of dimensionality reduction for $k$-means clustering.
1 code implementation • 18 May 2010 • Petros Drineas, Michael W. Mahoney
Our first and main result is a simple algorithm to approximate the solution to a set of linear equations defined by a Laplacian (for a graph $G$ with $n$ nodes and $m \le n^2$ edges) constraint matrix.
Numerical Analysis
no code implementations • NeurIPS 2009 • Christos Boutsidis, Petros Drineas, Michael W. Mahoney
We present a novel feature selection algorithm for the $k$-means clustering problem.