We analyze the convergence of randomized trace estimators. Starting at 1989, several algorithms have been proposed for estimating the trace of a matrix by 1/M∑<sub>i</sub>=1<sup>M</sup>… Expand

We show that by using a high-quality implementation of one of these techniques, we obtain a solver that performs extremely well in the traditional yardsticks of numerical linear algebra: it is significantly faster than high-performance implementations of existing state-of-the-art algorithms, and it is numerically backward stable.Expand

We study the following problem of subset selection for matrices: given a matrix $\mathbf{X} \in \mathbb{R}^{n \times m}$ ($m > n$) and a sampling parameter $k$ ($n \le k \le m$), select a subset of $k$, such that the pseudoinverse of the sampled matrix has as small a norm as possible.Expand

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets.Expand

This article is partially based on preliminary results published in the proceeding of the 32nd International Conference on Machine Learning (ICML 2015).Expand