| name | differential-private-optimal-transport-estimation |
| description | Differentially private estimation of smooth optimal transport maps using wavelet density estimators and stability bounds. Privacy-preserving statistical methodology for OT map estimation. Activation: differential privacy, optimal transport, private estimation, wavelet density, minimax estimation. |
Context
Estimating smooth OT maps between probability distributions under differential privacy constraints. Uses wavelet-based density estimators and stability bounds.
Source: arXiv:2606.04683v1
Core Methodology
- Construct wavelet-based density estimators for source/target distributions
- Apply DP noise to wavelet coefficients at appropriate scales
- Leverage stability bounds for smooth OT maps to bound estimation error
- Achieve minimax optimal rates for private OT estimation
- Decompose error into bias, variance, and privacy noise
Implementation
- Choose wavelet basis for distribution smoothness class
- Estimate wavelet coefficients from samples
- Add calibrated Laplace/Gaussian noise for DP
- Reconstruct private density estimates
- Compute OT map between private densities
- Validate against theoretical bounds
Pitfalls
- Privacy budget allocation across scales is critical
- Smoothness assumptions may not hold universally
- Wavelet basis choice affects quality
- High-dimensional OT suffers from curse of dimensionality
Verification
- Verify ε-DP guarantee holds
- Compare error against minimax lower bounds
- Test on synthetic distributions with known OT maps
- Robustness to varying sample sizes and privacy budgets
Activation
differential privacy, optimal transport, private estimation, wavelet density, minimax estimation, smooth OT maps, privacy-preserving statistics
