Multi-Scale Heatmap Reconstruction for Differential Privacy
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Solution Overview
Problem
Existing methods for generating heatmaps from private data fail to adequately protect user privacy, as they do not ensure that individual data cannot be recovered from the aggregated heatmaps.
Innovation Solution
A method involving transforming input distributions into multi-scale representations, adding noise dependent on spatial scale, and reconstructing output distributions to approximate the anonymized multi-scale representation while ensuring privacy, with optional sparsification to reduce computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If noise is added to protect privacy in heatmaps, then individual data cannot be recovered, but the accuracy and detail of the heatmap deteriorates
Solution Approach 1:
The patent segments the heatmap generation process into multiple spatial scales (coarse to fine). At each scale, noise is added differentially, with larger noise at coarser scales and smaller noise at finer scales. This segmentation allows the system to protect privacy while preserving local details that are less sensitive to noise, thus resolving the contradiction between privacy protection and heatmap accuracy.
Solution Approach 2:
The patent applies local quality by adding different amounts of noise to different spatial scales rather than uniform noise across the entire heatmap. Coarse-scale structures receive larger noise additions for stronger privacy protection, while fine-scale local details receive smaller noise additions to maintain accuracy. This localized differential noise approach resolves the contradiction by optimizing privacy-protection and accuracy for different spatial regions.
2Reliability
If multi-scale transformation is applied to preserve privacy, then individual data recovery is prevented, but computational complexity increases
Solution Approach 1:
The patent divides the computational domain into multiple scales using a pyramid-like structure, where each level represents a different spatial resolution. This segmentation transforms the single complex computation into multiple simpler computations at different scales, making the overall process more manageable and efficient while maintaining strong privacy guarantees.
Solution Approach 2:
The patent employs dynamic programming techniques to efficiently compute the noisy multi-scale representation. By building solutions from coarser to finer scales and reusing computations across scales, the dynamic approach reduces redundant calculations and optimizes the computational complexity compared to naive multi-scale methods.
3Productivity
If sparsification is applied to reduce computational complexity, then processing speed increases, but information loss increases
Solution Approach 1:
The patent applies sparsification selectively at each spatial scale rather than uniformly across all data. At coarser scales where privacy-protecting noise is larger, more aggressive sparsification is applied. At finer scales where noise is smaller and information is more valuable, less aggressive sparsification is used. This segmented sparsification strategy balances processing speed improvements with information preservation.
Solution Approach 2:
The patent applies partial sparsification by retaining only the most significant non-zero elements above a threshold, rather than processing all elements. This partial action approach achieves sufficient processing speed improvement while minimizing information loss by preserving the most important data elements for reconstruction.
Data Source
AI summary
Improved methods are provided for generating heatmaps or other summary map data from multiple users' data (e.g., probability distributions) in a manner that preserves the privacy of the users' data while also generating heatmaps that are visually similar to the ‘true’ heatmap. These methods include decomposing the average of the users' data (the ‘true’ heatmap) into multiple different spatial scales, injecting random noise into the data at the multiple different spatial scales, and then reconstructing the privacy-preserving heatmap based on the noisy multi-scale representations. The magnitude of the noise injected at each spatial scale is selected to ensure preservation of privacy while also resulting in heatmaps that are visually similar to the ‘true’ heatmap.