As time series data is collected and used in a variety of fields, the importance of preserving privacy on time series is also on the increase. This paper is a preliminary study of the Diferential Privacy (DP) algorithm specially designed to provide privacy to time series data by integrating the time series decomposition technique. In particular, this study extends the Fourier Perturbation Algorithm (FPA) with Seasonal and Trend decomposition using LOESS (STL). In this work, we propose STL-DP, which first performs STL decomposition to the original data. Then we apply the FPA only to the core part of the time series, particularly trend or seasonal components, to provide privacy. In this preliminary study, we show that our approach consistently outperforms other baselines in terms of utility according to the experimental results. Our code is available at
https://github.com/Privacy-DASH/STL-DP.
Recently the need for providing data privacy has
significantly increased, as the quantity of data is growing at an
unprecedented speed, and a trend to make such large data
accessible to the public is also growing. To share data
and use them for multiple tasks, ensuring data privacy is
crucial. Therefore, many privacy protection techniques
have been proposed and researched, such as Diferential
Privacy (DP) [
However, despite the vulnerability of time series data due to their widespread application in various fields, privacy-preserving mechanisms on time series data have not been extensively investigated yet [4]. In this paper, we consider and propose a DP mechanism specially designed to protect the privacy on time series data. One of the unique characteristics of time series is that it exhibits a strong correlation among successive values. Accordingly, if the adversary knows the approximate time information, information leakage can occur through contextual understanding, as shown by other research works [5, 6]. However, existing perturbation methods such as Gaussian Perturbation Algorithm (GPA) [7], and Laplace Perturbation Algorithm (LPA) [8] do not consider nEvelop-O characteristics of time series to provide the most suitable privacy protection method for time series. • We show that STL-DP efectively protects the core parts of the time series data under the same privacy budget, thereby significantly improving utility over the existing methods. lowing Eq. (1):
[ () ∈ ] ≤ each , comes [12].
× [ ( ′ ) ∈ ], ∀ ∈ ( ) (1)
DP mechanism aims to keep the query response for
′ the same, despite having one or fewer non- There are various time series decomposition methods overlapping individuals. Specifically, the smaller the such as classical decomposition [14], X11 [15], and is, the higher the privacy protection of the data be- STL [9]. The classical method is simple to implement using LOESS (STL)
2.1. - Diferential Privacy
Diferential Privacy [
′ Definition. There are two databases , isfy || − vidual users, i.e., = ∪ =1 , and the data of any single ||1 ≤ 1. D denotes composed data of indiuser can be put as . Let us denote and as some randomized function and a privacy budget, respectively. guarantees -privacy if and only if it satisfies the fol′ which sat
LPA [8]
adds independent noise generated from the Laplace
distribution [
compression-based method that first applies the Discrete Fourier Transform (DFT) to the true query answers, then performs LPA to Fourier coeficients [ 8]. The perturbed coeficients undergo the inverse DFT (IDFT) to obtain the resulting perturbed sequence. The entire process can be expressed as perturbed f(D) = ( ( ( ())) , where is a function that maps each individual 1, 2, … , to numbers. The DFT and IDFT for the ℎ element of the series is defined as ( 2): ( ()) ( ()) =
= ∑ =1 ∑ 1 =1 2 √−1
− 2 √−1 () As compression methods convert the series from time to frequency domain, noises injected in the frequency domain are no longer independent but are correlated. For this reason, FPA is better suited for perturbing time series [13], and we extend the FPA-based method in our work. but is inapplicable since some data from both ends of the sequence are lost. X11 successfully tackled the problem of data loss but is still limited in use as it can only handle monthly or quarterly data. On the other hand, STL effectively handles the problems mentioned above. STL is a flexible and robust time series decomposition method that leverages local regression (LOESS).
We propose STL-DP to protect core information of the time series while improving utility within a predefined privacy budget. Refer to Figure 1 for a glance at our proposed STL-DP.
The main diference of STL-DP with the existing methods is the integration of STL decomposition. First, by incorporating the decomposition phase, we can identify the core components, such as the trend and seasonality of time series data, which may contain critical information and are prone to attacks. One of the STL-DP mechanisms is referred to as sFPA, which is a method that injects noises only to the seasonal part of the decomposed series. Similarly, the approach of performing perturbations only on the trend is named tFPA. Lastly, the perturbed components from the seasonal or trend parts are combined with the rest of the unperturbed components to reconstruct the form of the sequence.
Methods. We demonstrate the efectiveness of the proposed STL-DP by comparing the utility of our sFPA and tFPA with two baselines, LPA and FPA. Herein, we introduce two diferent metrics to quantify utility. The first metric is the Euclidean distance between the original and the perturbed series. Nextly, the original and the perturbed data are each fed into the forecasting model to evaluate the respective Mean Absolute Percentage Error (MAPE), and the diference between the two MAPEs is used as the second metric.
Dataset. We used the power consumption data from 2017-01-01 to 2017-12-31 of three zones of Tetouan city located in northern Morocco [16]. The properties of the dataset are summarized as follows: • Prediction variables : Power consumption of zone 1, 2, and 3 of Tetouan city with additional information, including temperature, humidity, wind speed, general difuse flows, and difuse flows. • Data information : Aggregated from 550,374 inhabitants according to Morocco Census [16].
Throughout the experiment, we set the privacy budget 1 − 4 as 0.48, 2.4, 4.8, and 24, respectively, and the sensitivity as 48, which are experimental settings taken from Günther, et al. [17].
Euclidean distance results. The degree of closeness between the original and the perturbed series under the same privacy budget can be interpreted as the level of utility. As shown in Table 1, LPA yields a greater distance than other methods, confirming that FPA-based methods are better than LPA. Furthermore, our tFPA and sFPA are consistently ranked as the best algorithm in terms of Euclidean distance. These results indicate the superiority of STL-DP over the baselines.
that our objective is to generate noise-injected series that minimize the performance drop of the forecasting model.
As shown in Table 2, we used four models, from a simple feed-forward neural network to advanced models such as LSTM and Transformer as our forecasting model. The models were trained to predict the upcoming 20 timesteps given the past 60 timesteps. In most cases, as grew, the forecasting error diference ( △MAPE) decreased. Not surprisingly, both sFPA and tFPA outperformed other DP Generative adversarial nets, Advances in neural mechanisms for a majority of models in terms of △MAPE. information processing systems 27 (2014). [4] S. Papadimitriou, F. Li, G. Kollios, P. S. Yu, Time series compressibility and privacy, in: Proceedings 5. Conclusion and Future Work of the 33rd international conference on Very large data bases, Citeseer, 2007, pp. 459–470.
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