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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Consistent Kernel Mean Estimation for Functions of Random Variables
Authors: Carl-Johann Simon-Gabriel, Adam Scibior, Ilya O. Tolstikhin, Bernhard Schölkopf
NeurIPS 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We ran experiments on synthetic data to show how accurately ˆµ1, ˆµ2 and ˆµ3 approximate µf(X,Y ) with growing sample size N. We considered three basic arithmetic operations: multiplication X Y , division X/Y , and exponentiation XY , with X N(3; 0.5) and Y N(4; 0.5). As the true embedding µf(X,Y ) is unknown, we approximated it by a U-statistic estimator based on a large sample (125 points). For ˆµ3, we used the simplest possible reduced set method: we randomly sampled subsets of size n = 0.01 N of the xi, and optimized the weights wi and ui to best approximate ˆµX and ˆµY . The results are summarised in Figure 1 and corroborate our expectations: (i) all estimators converge, (ii) ˆµ2 converges fastest and has the lowest variance, and (iii) ˆµ3 is worse than ˆµ2, but much better than the diagonal estimator ˆµ1. |
| Researcher Affiliation | Academia | Department of Empirical Inference, Max Planck Institute for Intelligent Systems Spemanstraße 38, 72076 Tübingen, Germany joint first authors; also with: Engineering Department, Cambridge University |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an explicit statement or link indicating the release of source code for the described methodology. |
| Open Datasets | No | We ran experiments on synthetic data to show how accurately ˆµ1, ˆµ2 and ˆµ3 approximate µf(X,Y ) with growing sample size N. |
| Dataset Splits | No | The paper mentions approximating the true embedding with a large sample, but does not specify train/validation/test splits for their own experiments. It states: 'As the true embedding µf(X,Y ) is unknown, we approximated it by a U-statistic estimator based on a large sample (125 points).' |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | For ˆµ3, we used the simplest possible reduced set method: we randomly sampled subsets of size n = 0.01 N of the xi, and optimized the weights wi and ui to best approximate ˆµX and ˆµY . |