SlowGuess/NeurIPS_2023_OCR huggingface dataset:
We presented a novel statistical learning framework for learning LTI predictors using trajectories of a dynamical system. The method is rooted in the derivation of a novel RKHS over trajectories, which solely consists of universal functions that have LTI dynamics. Equivalences with function regression in RKHS allow us to provide consistency guarantees not present in previous literature. Another key contribution is a novel rank-independent generalization bound for i.i.d. sampled trajectories that directly describes forecasting performance. The significant implications of the proposed approach are confirmed in experiments, leading to superior performance compared to Koopman operator and sequential data predictors in RKHS. In this work, we confined our forecasts to a non-recurrent domain for a specific length of trajectory data, where the choice of spectra is arbitrary. However, exploring more efficacious spectral sampling schemes is a natural next step for extending our results to asymptotic regimes that include, e.g., periodic and quasi-periodic behavior. It has to be noted that vector-valued kernel methods have limited scalability with a growing number of training data and output dimensionality. Therefore, exploring solutions that improve scalability is an important topic for future work. Furthermore, to enable the use of LTI predictors in safety-critical domains, the quantification of the forecasting error is essential. Hence, deriving uniform prediction error bounds for KKR is of great interest.
The authors acknowledge the financial support of the EU Horizon 2020 research and innovation programme "SeaClear" (ID 871295) and the ERC Consolidator grant "CO-MAN" (ID 864686). Petar Bevanda also thanks Jan Brudigam for feedback, and Vladimir Kostić and Pietro Novelli for useful discussions on operator regression.
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