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HRNet: Differentially Private Hierarchical and Multi-Resolution Network for Human Mobility Data Synthesization

Shun Takagi, Li Xiong, Fumiyuki Kato, Yang Cao, Masatoshi Yoshikawa

TL;DR

This work presents HRNet, a differentially private generator for human mobility data that achieves strong utility under DP by combining a hierarchical location encoding via a 2D quad deconvolutional network, multi-resolution multi-task learning, and private pre-training based on a DP transition matrix. The method addresses two DP bottlenecks—model size and learning complexity for large POI vocabularies—by parameterizing location with logarithmic growth and distributing learning across resolutions. Empirical results across multiple real and synthetic datasets show HRNet outperforms state-of-the-art DP methods on key trajectory statistics, while providing a principled DP budget allocation between pre-training and DP-SGD. The approach delivers privacy-preserving synthetic mobility data with practical utility for tasks such as next-location prediction, trajectory classification, and commuting analysis, enabling safer urban analytics and public health research.

Abstract

Human mobility data offers valuable insights for many applications such as urban planning and pandemic response, but its use also raises privacy concerns. In this paper, we introduce the Hierarchical and Multi-Resolution Network (HRNet), a novel deep generative model specifically designed to synthesize realistic human mobility data while guaranteeing differential privacy. We first identify the key difficulties inherent in learning human mobility data under differential privacy. In response to these challenges, HRNet integrates three components: a hierarchical location encoding mechanism, multi-task learning across multiple resolutions, and private pre-training. These elements collectively enhance the model's ability under the constraints of differential privacy. Through extensive comparative experiments utilizing a real-world dataset, HRNet demonstrates a marked improvement over existing methods in balancing the utility-privacy trade-off.

HRNet: Differentially Private Hierarchical and Multi-Resolution Network for Human Mobility Data Synthesization

TL;DR

This work presents HRNet, a differentially private generator for human mobility data that achieves strong utility under DP by combining a hierarchical location encoding via a 2D quad deconvolutional network, multi-resolution multi-task learning, and private pre-training based on a DP transition matrix. The method addresses two DP bottlenecks—model size and learning complexity for large POI vocabularies—by parameterizing location with logarithmic growth and distributing learning across resolutions. Empirical results across multiple real and synthetic datasets show HRNet outperforms state-of-the-art DP methods on key trajectory statistics, while providing a principled DP budget allocation between pre-training and DP-SGD. The approach delivers privacy-preserving synthetic mobility data with practical utility for tasks such as next-location prediction, trajectory classification, and commuting analysis, enabling safer urban analytics and public health research.

Abstract

Human mobility data offers valuable insights for many applications such as urban planning and pandemic response, but its use also raises privacy concerns. In this paper, we introduce the Hierarchical and Multi-Resolution Network (HRNet), a novel deep generative model specifically designed to synthesize realistic human mobility data while guaranteeing differential privacy. We first identify the key difficulties inherent in learning human mobility data under differential privacy. In response to these challenges, HRNet integrates three components: a hierarchical location encoding mechanism, multi-task learning across multiple resolutions, and private pre-training. These elements collectively enhance the model's ability under the constraints of differential privacy. Through extensive comparative experiments utilizing a real-world dataset, HRNet demonstrates a marked improvement over existing methods in balancing the utility-privacy trade-off.
Paper Structure (69 sections, 1 theorem, 30 equations, 14 figures, 3 tables)

This paper contains 69 sections, 1 theorem, 30 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Differential Privacy
  4. Problem Formulation
  5. Trajectory:
  6. Generator:
  7. Evaluation:
  8. The Baseline Generator
  9. The baseline generator
  10. The objective function:
  11. The sequential generation:
  12. The two bottlenecks
  13. The number of parameters $|\theta|$
  14. The number of labels
  15. Discussion: impact of the discretization parameter
  16. ...and 54 more sections

Key Result

theorem 1

Given a dataset $D$, privacy parameters $\varepsilon_1, \varepsilon_2\in\mathbb{R}^+$ and $\delta\in[0,1]$, and initial parameters of HRNet $\theta$, the pre-training and training process for HRNet is as follows: Here, ${\rm dptran}(D,\varepsilon_2)$ refers to the computation of Equation (eq:dptran) and pretrain is the standard training with loss function (eq:loss). DPSGD is the private training

Figures (14)

  • Figure 1: HRNet utilizes three novel components to address the bottlenecks of applying DP-SGD in human mobility generation: 1) a hierarchical location encoding mechanism using deconvolution networks, 2) multi-task learning across multiple resolutions, and 3) private pre-training using a DP coarse transition matrix.
  • Figure 2: Overview of multi-task training with hierarchical location encoding. In this example, we assume that $w=4$, so we have 4*4 POIs at resolution 2 and 2*2 regions at resolution 1 due to the hierarchical location encoding. Given prefix $(1,2,6)$, the model learns to infer grid cell $10$ at resolution $2$, as well as grid cell $3$ at resolution $1$.
  • Figure 3: The discrepancy of destination on Peopleflow dataset ($w=64$) for each $\varepsilon\in [0,3.0]$.
  • Figure 4: The discrepancy of transition on Geolife dataset ($w=32$) for each $\varepsilon\in [0,3.0]$.
  • Figure 5: The discrepancy of destination on Didi dataset ($w=32$) for each $\varepsilon$ and $\delta=10^{-5}$.
  • ...and 9 more figures

Theorems & Definitions (2)

  • definition 1: ($\varepsilon, \delta$)-Differential Privacy
  • theorem 1