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].
On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests
Authors: Krishnakumar Balasubramanian, Tong Li, Ming Yuan
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments are presented to further demonstrate the merits of our approach. Keywords: Adaptation, goodness of fit, maximum mean discrepancy, optimal rates of Convergence, reproducing kernel Hilbert space. 6. Numerical Experiments To complement the earlier theoretical development, we also performed several sets of simulation experiments to demonstrate the merits of the proposed adaptive test. |
| Researcher Affiliation | Academia | Krishnakumar Balasubramanian EMAIL Department of Statistics University of California, Davis Davis, CA 95616, USA Tong Li EMAIL Ming Yuan EMAIL Department of Statistics Columbia University New York, NY 10027, USA |
| Pseudocode | No | The paper describes mathematical frameworks and theoretical proofs. It does not include any explicit pseudocode blocks or algorithms. |
| Open Source Code | No | The paper refers to an open license (CC-BY 4.0) for the paper itself and mentions using the 'chebfun framework in Matlab', which is a third-party tool. However, it does not explicitly state that the authors' own implementation code for the described methodology is released or provide a link to a code repository. |
| Open Datasets | Yes | For the case of Euclidean data, we used the MNIST digits data set from the following webpage: http://yann.lecun.com/exdb/mnist/. ... For the case of directional data, we used the Human Fibroblasts dataset from Iyer et al. (1999); Dhillon et al. (2003) and the Yeast Cell Cycle dataset from Spellman et al. (1998). |
| Dataset Splits | Yes | As a compromise, we first use 50% of the total dataset first to get an estimate of the parameter of P0. We then use the rest of the data to do the goodness of fit test to the simple hypothesis P0 defined with the estimated parameter. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments, such as CPU or GPU models, memory, or cloud instance specifications. |
| Software Dependencies | No | The paper mentions the 'chebfun framework in Matlab' but does not specify version numbers for Matlab or the chebfun library. |
| Experiment Setup | Yes | We repeated for each case 200 runs and estimated the 95% quantile of Tn under H0 by the corresponding sample quantile. ... The value of α was set to 0.05. The sample size n varied from 200 to 1000 (in steps of 200) and for each value of sample size 100 simulations were conducted to estimate the probability of rejecting H0. ... The number of eigenvalues used for kernel approximation (denoted by N) is given in Table 1. Sample size 200 400 600 800 1000 N 15 22 25 28 36 |