Minimax Estimation of Kernel Mean Embeddings
Authors: Ilya Tolstikhin, Bharath K. Sriperumbudur, Krikamol Muandet
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The main contribution of the paper is in showing that the above mentioned rate of n 1/2 is minimax in Hk and L2(Rd)-norms over the class of discrete measures and the class of measures that has an infinitely differentiable density, with k being a continuous translation-invariant kernel on Rd. The interesting aspect of this result is that the minimax rate is independent of the smoothness of the kernel and the density of P (if it exists). Keywords: Bochner integral, Bochner s theorem, kernel mean embeddings, minimax lower bounds, reproducing kernel Hilbert space, translation invariant kernel. Therefore the goal of this work is to obtain minimax rates for the estimation of µP in Hk and L2(Rd). |
| Researcher Affiliation | Academia | Ilya Tolstikhin EMAIL Department of Empirical Inference Max Planck Institute for Intelligent Systems Spemanstraße 38, T ubingen 72076, Germany; Bharath K. Sriperumbudur EMAIL Department of Statistics Pennsylvania State University University Park, PA 16802, USA; Krikamol Muandet EMAIL Department of Mathematics Faculty of Science, Mahidol University 272 Rama VI Rd. Rajchathevi, Bangkok 10400, Thailand. |
| Pseudocode | No | The paper describes its methodology through mathematical formulations, theorems, and proofs. There are no explicitly labeled pseudocode blocks or algorithm sections with structured steps. |
| Open Source Code | No | The paper states 'License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v18/17-032.html.' This refers to the licensing of the paper itself, not the release of any source code for the methodology described. No other statements or links for code release are found. |
| Open Datasets | No | The paper is theoretical, focusing on minimax estimation for kernel mean embeddings based on 'random samples X1, . . . , Xn drawn i.i.d. from P.' It discusses 'discrete measures' and 'measures that has an infinitely differentiable density' without referring to any specific, named datasets or providing access information for publicly available data. |
| Dataset Splits | No | As this is a theoretical paper that does not conduct experiments on specific datasets, there is no mention of training/test/validation dataset splits. |
| Hardware Specification | No | This is a theoretical paper focused on mathematical proofs and derivations. It does not describe any experiments that would require specific hardware, and no hardware specifications are mentioned. |
| Software Dependencies | No | The paper focuses on theoretical contributions and does not describe any computational implementation or experimental setup that would involve specific software dependencies or version numbers. |
| Experiment Setup | No | As a theoretical paper, it does not describe any experimental setup, hyperparameters, or training configurations. The content consists of mathematical analysis and proofs. |