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The problem of (point) forecasting 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 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 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 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 recent techniques 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.
Author Information
Sebastian Zeng (University of Salzburg)
Florian Graf (University of Salzburg)
Christoph Hofer (University of Salzburg)
Roland Kwitt (University of Salzburg)
More from the Same Authors
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2022 Poster: On Measuring Excess Capacity in Neural Networks »
Florian Graf · Sebastian Zeng · Bastian Rieck · Marc Niethammer · Roland Kwitt -
2017 Poster: Deep Learning with Topological Signatures »
Christoph Hofer · Roland Kwitt · Marc Niethammer · Andreas Uhl -
2015 Poster: Statistical Topological Data Analysis - A Kernel Perspective »
Roland Kwitt · Stefan Huber · Marc Niethammer · Weili Lin · Ulrich Bauer