Control Variates as a Variance Reduction Technique for Random Projections

Control variates are used as a variance reduction technique in Monte Carlo integration, making use of positively correlated variables to bring about a reduction of variance for estimated data. By storing the marginal norms of our data, we can use control variates to reduce the variance of random projection estimates. We demonstrate the use of control variates in estimating the Euclidean distance and inner product between pairs of vectors, and give some insight on our control variate correction. Finally, we demonstrate our variance reduction through experiments on synthetic data and the arcene, colon, kos, nips datasets. We hope that our work provides a starting point for other control variate techniques in further random projection applications.