aiqbench analysis
This paper advances hierarchical time series forecasting by embedding coherence constraints directly into the hypothesis space via operator-valued kernels, eliminating the need for post-hoc reconciliation steps. By deriving excess risk bounds within a vector-valued reproducing kernel Hilbert space, the authors provide theoretical guarantees for generalization performance that are often missing in standard end-to-end models. The approach represents a significant methodological improvement for statistical machine learning applications requiring consistent predictions across multiple aggregation levels.
Hierarchical Time Series Forecasting with Operator-Valued Kernels
arXiv:2610.18196v1 Announce Type: cross Abstract: Hierarchical time series forecasting requires generating accurate predictions that are coherent across multiple levels of aggregation. Existing methods either rely on two-stage pipelines with post-hoc reconciliation or on end-to-end models that often lack statistical guarantees. We introduce a unified framework that formulates hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space. By designing structured operator-valued kernels, our approach enforces coherence directly within the hypothesis space, ensuring that all predictions satisfy hierarchical constraints by construction. We further propose tailored kernel constructions for hierarchical data and derive excess risk bounds that characterize generalization performance. Empirical results on synthetic and real-world datasets demonstrate the relevance of the proposed method.
Abstract:Hierarchical time series forecasting requires generating accurate predictions that are coherent across multiple levels of aggregation. Existing methods either rely on two-stage pipelines with post-hoc reconciliation or on end-to-end models that often lack statistical guarantees. We introduce a unified framework that formulates hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space. By designing structured operator-valued kernels, our approach enforces coherence directly within the hypothesis space, ensuring that all predictions satisfy hierarchical constraints by construction. We further propose tailored kernel constructions for hierarchical data and derive excess risk bounds that characterize generalization performance. Empirical results on synthetic and real-world datasets demonstrate the relevance of the proposed method.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.18196 [stat.ML]
(or arXiv:2610.18196v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.18196 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 208 words
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