Topological Attention for Time Series Forecasting
- URL: http://arxiv.org/abs/2107.09031v1
- Date: Mon, 19 Jul 2021 17:24:05 GMT
- Title: Topological Attention for Time Series Forecasting
- Authors: Sebastian Zeng, Florian Graf, Christoph Hofer, Roland Kwitt
- Abstract summary: We study whether $textitlocal topological properties$, as captured via persistent homology, can serve as a reliable signal.
We propose $textittopological attention$, which allows attending to local topological features within a time horizon of historical data.
- Score: 9.14716126400637
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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