Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting
This addresses forecasting in hierarchical time series, which is important for domains like retail or finance, but it is incremental as it builds on existing graph-based and deep learning approaches.
The paper tackles the problem of forecasting hierarchical time series by proposing a graph-based method that unifies relational and hierarchical inductive biases, using trainable graph pooling to learn the hierarchy from data and incorporating differentiable reconciliation; simulation results show it compares favorably against state-of-the-art methods.
Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on the predicted values. In this paper, we propose a graph-based methodology to unify relational and hierarchical inductive biases in the context of deep learning for time series forecasting. In particular, we model both types of relationships as dependencies in a pyramidal graph structure, with each pyramidal layer corresponding to a level of the hierarchy. By exploiting modern - trainable - graph pooling operators we show that the hierarchical structure, if not available as a prior, can be learned directly from data, thus obtaining cluster assignments aligned with the forecasting objective. A differentiable reconciliation stage is incorporated into the processing architecture, allowing hierarchical constraints to act both as an architectural bias as well as a regularization element for predictions. Simulation results on representative datasets show that the proposed method compares favorably against the state of the art.