Privacy Amplification by Structured Subsampling for Deep Differentially Private Time Series Forecasting

We analyze why standard DP-SGD amplification assumptions break for forecasting—where batches come from (i) sampling series, (ii) contiguous subsequences, (iii) context/forecast splits—and provide tight event- and user-level guarantees via structured subsampling. We also prove amplification from sequence-model augmentation and validate empirically.

Contribution: I worked on appendix-level optimization/proof pieces:

• Derived a componentwise upper bound (H_\alpha(P,Q)\le\sum_{i,j} w_i v_j\,H_\alpha(p_i,q_j)) under lattice-path constraints on the means.
• Recast the bound as a shallow network with the closed-form “Gaussian hockey-stick” activation (g_\varepsilon(d)=\Phi(d/2-\varepsilon/d)-e^{\varepsilon}\Phi(-d/2-\varepsilon/d)).
• Built a certified SOCP relaxation via a single-tangent affine envelope on (d\in[0,R_{ij}]).

Main writing and experiments were led by the first authors.

WIP (tightening the relaxation).

• Add shared distance coupling via a PSD/Gram-matrix formulation to prevent joint saturation while staying convex.
• Note: multi-segment (SOS-2) envelopes alone still push to the rightmost knot; they don’t fix the degeneracy.