Topological Attention for Time Series Forecasting

Abstract: The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether $\textit{local topological properties}$, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose $\textit{topological attention}$, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as $\texttt{N-BEATS}$, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.