Fig. S1 and Fig. S2 are continuations of Figure 1. This work was conducted while David Eriksson was at Uber AI. Figure S2: Randomized SVD relative error at computing In all cases, randomized SVD is unable to achieve a relative error better than about 0. 25. Fig. S3 further demonstrates the effect of preconditioning on msMINRES-CIQ. To further compare msMINRES-CIQ to randomized methods, Fig. S4 plots the empirical covariance Cholesky-based sampling tend to have very similar empirical covariance error. This additional error is due to the randomness in the RFF approximation.

Matrix square roots and their inverses arise frequently in machine learning, e.g.,

LLP, prove generalization error bounds associated to two bag generation models, and establish universal consistency with respect to the balanced error rate (BER).

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees.

This state-of-affairs is often justified by the fact that our analysis of the algorithm is often pessimistic.

The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to its faster empirical convergence and mixing than the standard MH algorithm, its theoretical mixing property is rarely studied in the literature due to its complex proposal scheme.