Topological Attention for Time Series Forecasting
This work addresses forecasting accuracy for time series analysis, offering an incremental improvement by adding topological features to existing models.
The authors tackled the problem of univariate time series forecasting by incorporating local topological properties from persistent homology as a complementary signal, and their topological attention method, integrated with N-BEATS, achieved state-of-the-art performance on the M4 benchmark dataset of 100,000 time series.
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.