# Differentially Private Multivariate Time Series Forecasting of Aggregated Human Mobility With Deep Learning: Input or Gradient Perturbation?

arXiv: https://arxiv.org/abs/2205.00436 · HTML: https://mlsanity.com/paper/2205.00436/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 64 references that are in the map.
- First posted on arXiv 1 May 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Machine Learning Models that Remember Too Much](https://mlsanity.com/paper/1709.07886/) (2017)
- [A Survey on Deep Learning for Human Mobility](https://mlsanity.com/paper/2012.02825/) (2020)
- [A General Approach to Adding Differential Privacy to Iterative Training Procedures](https://mlsanity.com/paper/1812.06210/) (2018)
- [Local Differential Privacy for Deep Learning](https://mlsanity.com/paper/1908.02997/) (2019)
- [LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale](https://mlsanity.com/paper/2002.05839/) (2020)
- [Trajectory Recovery From Ash: User Privacy Is NOT Preserved in Aggregated Mobility Data](https://mlsanity.com/paper/1702.06270/) (2017)
- [Measuring Membership Privacy on Aggregate Location Time-Series](https://mlsanity.com/paper/1902.07456/) (2019)
- [A survey of results on mobile phone datasets analysis](https://mlsanity.com/paper/1502.03406/) (2015)
- [What Does The Crowd Say About You? Evaluating Aggregation-based Location Privacy](https://mlsanity.com/paper/1703.00366/) (2017)
- [The Influence of Differential Privacy on Short Term Electric Load Forecasting](https://mlsanity.com/paper/1807.02361/) (2018)
- [Toward Evaluating Re-identification Risks in the Local Privacy Model](https://mlsanity.com/paper/2010.08238/) (2020)
- [On the Use of Data from Multiple Mobile Network Operators in Europe to fight COVID-19](https://mlsanity.com/paper/2106.05647/) (2021)

## Built on by (most cited first, 2 of 2)

- [Privacy-Aware Time Series Synthesis via Public Knowledge Distillation](https://mlsanity.com/paper/2511.00700/) (2025)
- [One-Shot Price Forecasting with Covariate-Guided Experts under Privacy Constraints](https://mlsanity.com/paper/2601.11977/) (2026)

## Abstract (arXiv)

This paper investigates the problem of forecasting multivariate aggregated human mobility while preserving the privacy of the individuals concerned. Differential privacy, a state-of-the-art formal notion, has been used as the privacy guarantee in two different and independent steps when training deep learning models. On one hand, we considered textitgradient perturbation, which uses the differentially private stochastic gradient descent algorithm to guarantee the privacy of each time series sample in the learning stage. On the other hand, we considered textitinput perturbation, which adds differential privacy guarantees in each sample of the series before applying any learning. We compared four state-of-the-art recurrent neural networks: Long Short-Term Memory, Gated Recurrent Unit, and their Bidirectional architectures, i.e., Bidirectional-LSTM and Bidirectional-GRU. Extensive experiments were conducted with a real-world multivariate mobility dataset, which we published openly along with this paper. As shown in the results, differentially private deep learning models trained under gradient or input perturbation achieve nearly the same performance as non-private deep learning models, with loss in performance varying between 0.57% to 2.8%. The contribution of this paper is significant for those involved in urban planning and decision-making, providing a solution to the human mobility multivariate forecast problem through differentially private deep learning models.