  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 \textit{gradient 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 \textit{input 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.
