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Seq2VAR: Multivariate Time Series Representation with Relational Neural Networks and Linear Autoregressive Model

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Advanced Analytics and Learning on Temporal Data (AALTD 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11986))

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Finding understandable and meaningful feature representation of multivariate time series (MTS) is a difficult task, since information is entangled both in temporal and spatial dimensions. In particular, MTS can be seen as the observation of simultaneous causal interactions between dynamical variables. Standard way to model these interactions is the vector linear autoregression (VAR). The parameters of VAR models can be used as MTS feature representation. Yet, VAR cannot generalize on new samples, hence independent VAR models must be trained to represent different MTS. In this paper, we propose to use the inference capacity of neural networks to overpass this limit. We propose to associate a relational neural network to a VAR generative model to form an encoder-decoder of MTS. The model is denoted Seq2VAR for Sequence-to-VAR. We use recent advances in relational neural network to build our MTS encoder by explicitly modeling interactions between variables of MTS samples. We also propose to leverage reparametrization tricks for binomial sampling in neural networks in order to build a sparse version of Seq2VAR and find back the notion of Granger causality defined in sparse VAR models. We illustrate the interest of our approach through experiments on synthetic datasets.

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This work is supported by the company Safran through the CIFRE convention 2017/1317.

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Correspondence to Edouard Pineau .

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A Appendix: Hyperparameters

A Appendix: Hyperparameters

For our Seq2VAR, we used a succession of 2-layers perceptrons for our relational encoder, as in NRI [9]. The parameters to chose concern latent dimension for all layers and the temperature parameter \(\tau \) for the relaxed binary sampling (see Sect. 2.3). They are presented in Table 4.

Table 4. Training parameters.

For NRI, all other parameters are the one of the original paper for the homogeneous springs rigidity except for the dimensionality of the latent space which we set to 64 instead of 256, since in the experimental setup of the original paper, it gives the same results while diminishing computing time and memory needs. For the heterogeneous rigidity, the parameter prediction_steps is set to 5 instead of 10 and \(\tau \) is set to 0.1. These parameters gave the best average results. In fact, due to the highly expressive form of its decoder, NRI was able to build good predictor with not the good graph. We played with parameters to get more stable and better results. For the experiments, we also tried to change the skip first parameter that is set to False or True in the original paper [9], depending on the dataset studied. It did not change the results of the experiments.

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Pineau, E., Razakarivony, S., Bonald, T. (2020). Seq2VAR: Multivariate Time Series Representation with Relational Neural Networks and Linear Autoregressive Model. In: Lemaire, V., Malinowski, S., Bagnall, A., Bondu, A., Guyet, T., Tavenard, R. (eds) Advanced Analytics and Learning on Temporal Data. AALTD 2019. Lecture Notes in Computer Science(), vol 11986. Springer, Cham.

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