Selego: robust variate selection for accurate time series forecasting

Abstract

Naïve extensions of uni-variate prediction techniques lead to an unwelcome increase in the cost of multi-variate model learning and significant deteriorations in the model performance. In this paper, we first argue that (a) one can learn a more accurate forecasting model by leveraging temporal alignments among variates to quantify the importance of the recorded variates with respect to a target variate. We further argue that, (b) for this purpose we need to quantify temporal correlation, not in terms of series similarity, but in terms of temporal alignments of key “events” impacting these series. Finally, we argue that (c) while learning a temporal model using recurrence based techniques (such as RNN and LSTM—even when leveraging attention strategies) is difficult and costly, we can achieve better performance by coupling simpler CNNs with an adaptive variate selection strategy. Relying on these arguments, we propose a Selego framework (Selego is a word of latin origin meaning “selection”) for variate selection and experimentally evaluate the performance of the proposed approach on various forecasting models, such as LSTM, RNN, and CNN, for different top-X% variates and different forecasting time in the future (lead) on multiple real-world datasets. Experiments show that the proposed framework can offer significant ($90-98\%$) drops in the number of recorded variates that are needed to train predictive models, while simultaneously boosting accuracy.

Appendix—sample series and feature distributions

Fig. 7

a The target variable NDX (NASDAQ index); b the best 6 series aligned with it (note that alignment of series do not necessarily imply that the series are globally similar – it only means that they show evidence of the same underlying events); c a poorly aligned series; d–k temporal distributions (time and length) of the identified features in these series (here the X-axis denotes the time and the Y-axis identifies the length of the feature identified at a particular point in time)

Fig. 8

a The target variable AAPL (symbol for the Apple stock); b the best 6 series aligned with it(note that alignment of series do not necessarily imply that the series are globally similar – it only means that they show evidence of the same underlying events); c a poorly aligned series; d–k temporal distributions (time and length) of the identified features in these series (here the X-axis denotes the time and the Y-axis identifies the length of the feature identified at a particular point in time)

Fig. 9

a The target variable fuel consumption; b the best 6 series aligned with it (note that alignment of series do not necessarily imply that the series are globally similar—it only means that they show evidence of the same underlying events); c a poorly aligned series; d–k temporal distributions (time and length) of the identified features in these series (here the X-axis denotes the time and the Y-axis identifies the length of the feature identified at a particular point in time)

Figures 7 through 9 provide examples of target variables, the best series aligned based on feature distributions, along with a sample for poorly aligned series. In order to better visualize the feature alignments, consecutive series (e.g. the consecutive days in NASDAQ) have been concatenated and the number of feature layers considered in these charts have been raised from the number of layers considered in the experiments. As we see in these figures, temporal alignment of variates does not mean that they must look similar: instead, alignment only means that the two series show evidence of being impacted from the same underlying events. In Fig. 9b, for example, we see six variates that, together, predict the fuel consumption series 9a well. We also see in the figure that these series used for model training are temporally aligned with the target series but are not necessarily similar to it.