On the privacy cost for dependent Gaussian data: spectral density estimation under local differential privacy

What the math gives to ML

The paper identifies a dependence-specific privacy phenomenon: for locally privatized stationary Gaussian observations, the high-privacy effective sample size is N alpha^4, rather than the N alpha^2 rate familiar from independent data. Its transferable asset is the spectral representation of temporal dependence together with a sharp way to quantify how privacy noise interacts with correlated sequences. A practical neural-network use is to privately estimate the spectrum of sequence inputs or intermediate activations, construct a regularized inverse spectral filter, and feed approximately whitened sequences to a Transformer or state-space model. The filter may reduce redundant temporal information and improve private training stability.