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Time series data in the retail world are particularly rich in terms of dimensionality, and these dimensions can be aggregated in groups or hierarchies. Valuable information is nested in these complex structures, which helps to predict the aggregated time series data. From a portfolio of brands under HUUBs monitoring, we selected two to explore their sales behaviour, leveraging the grouping properties of their product structure. Using statistical models, namely SARIMA, to forecast each level of the hierarchy, an optimal combination approach was used to generate more consistent forecasts in the higher levels. Our results show that the proposed methods can indeed capture nested information in the more granular series, helping to improve the forecast accuracy of the aggregated series. The Weighted Least Squares (WLS) method surpasses all other methods proposed in the study, including the Minimum Trace (MinT) reconciliation.
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator mapping a Hi
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data,
Multi-omics data, that is, datasets containing different types of high-dimensional molecular variables (often in addition to classical clinical variables), are increasingly generated for the investigation of various diseases. Nevertheless, questions
Recently proposed consistency-based Semi-Supervised Learning (SSL) methods such as the $Pi$-model, temporal ensembling, the mean teacher, or the virtual adversarial training, have advanced the state of the art in several SSL tasks. These methods can
It is important to estimate the local average treatment effect (LATE) when compliance with a treatment assignment is incomplete. The previously proposed methods for LATE estimation required all relevant variables to be jointly observed in a single da