Optimal Control Variates for Survey Sampling and Causal Inference

What the math gives to ML

The paper's transferable asset is a design-aware control-variate construction: instead of choosing a baseline heuristically, it selects basis directions that optimally explain covariance induced by sampling or exposure mechanisms and outcome uncertainty. In neural-network training, the same principle can reduce minibatch gradient noise by projecting per-example gradients onto a small set of known, cheap feature directions and subtracting the predictable component. The most promising implementation is an optimizer-side control variate with online covariance estimates and spectral truncation to control computational and numerical costs.