Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergence
Authors: Mattes Mollenhauer, Stefan Klus, Christof Schütte, Péter Koltai
JMLR 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition. |
| Researcher Affiliation | Academia | Mattes Mollenhauer1 EMAIL Stefan Klus3 EMAIL Christof Sch utte1,2 EMAIL P eter Koltai1 EMAIL 1Institute of Mathematics, Freie Universit at Berlin Arnimallee 6, D-14195 Berlin 2Zuse Intitute Berlin Takustraße 7, D-14195 Berlin 3School of Mathematical & Computer Sciences, Heriot Watt University Edinburgh, EH14 4AS, UK |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. The content is primarily theoretical derivations and proofs. |
| Open Source Code | No | The paper does not provide any explicit statement about releasing source code or a direct link to a code repository for the described methodology. |
| Open Datasets | No | The paper focuses on theoretical analysis and does not present experimental results using specific datasets, thus no information on open datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments that would involve dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe experiments that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe experiments that would require listing software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup or hyperparameter details. |