Random projections with control variates**

Random projections are used to estimate parameters of interest in large scale data sets by projecting data into a lower dimensional space. Some parameters of interest between pairs of vectors are the Euclidean distance and the inner product, while parameters of interest for the whole data set could be its singular values or singular vectors. We show how we can borrow an idea from Monte Carlo integration by using control variates to reduce the variance of the estimates of Euclidean distances and inner products by storing marginal information of our data set. We demonstrate this variance reduction through experiments on synthetic data as well as the colon and kos datasets. We hope that this inspires future work which incorporates control variates in further random projection applications.