Learning Theory for Distribution Regression

Authors: Zoltán Szabó, Bharath K. Sriperumbudur, Barnabás Póczos, Arthur Gretton

JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical Our main contribution is to prove that this scheme is consistent in the two-stage sampled setup under mild conditions (on separable topological domains enriched with kernels): we present an exact computational-statistical efficiency trade-off analysis showing that our estimator is able to match the one-stage sampled minimax optimal rate (Caponnetto and De Vito, 2007; Steinwart et al., 2009). This result answers a 17-year-old open question, establishing the consistency of the classical set kernel (Haussler, 1999; G artner et al., 2002) in regression.
Researcher Affiliation Academia Zolt an Szab o EMAIL ORCID 0000-0001-6183-7603 Gatsby Unit, University College London Sainsbury Wellcome Centre, 25 Howland Street London W1T 4JG, UK Bharath K. Sriperumbudur EMAIL Department of Statistics Pennsylvania State University University Park, PA 16802, USA Barnab as P oczos EMAIL Machine Learning Department School of Computer Science Carnegie Mellon University 5000 Forbes Avenue Pittsburgh PA 15213 USA Arthur Gretton EMAIL ORCID 0000-0003-3169-7624 Gatsby Unit, University College London Sainsbury Wellcome Centre, 25 Howland Street London W1T 4JG, UK
Pseudocode No The paper describes mathematical derivations, theorems, and proofs related to learning theory for distribution regression. It does not contain any clearly labeled 'Pseudocode' or 'Algorithm' blocks, nor does it present structured steps formatted like code.
Open Source Code Yes Finally, we note that although the primary focus of the current paper was theoretical, we have applied the MERR method (Szab o et al., 2015, Section A.2) to supervised entropy learning and aerosol prediction based on multispectral satellite images.18 For code, see https://bitbucket.org/szzoli/ite/.
Open Datasets No The paper mentions using 'multispectral satellite images' for an application of the MERR method but does not provide any specific link, DOI, repository name, or formal citation with author attribution for accessing this dataset.
Dataset Splits No The paper is theoretical in nature, focusing on proving consistency and deriving computational-statistical efficiency trade-offs. It does not describe any experimental setup with dataset splits (e.g., training, validation, test sets).
Hardware Specification No The paper is primarily theoretical and does not describe experimental results or the hardware used to obtain them. Therefore, no specific hardware specifications are provided.
Software Dependencies No The paper is theoretical and focuses on mathematical proofs and learning theory. It does not describe specific software dependencies with version numbers for experimental reproduction.
Experiment Setup No The paper is theoretical, presenting mathematical analysis, theorems, and proofs. It does not detail any experimental setup, hyperparameters, or training configurations.