On the Robustness of Kernel Goodness-of-Fit Tests
Authors: Xing Liu, François-Xavier Briol
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We will now evaluate the proposed GOF tests using both synthetic and real data. |
| Researcher Affiliation | Collaboration | Xing Liu EMAIL Quant Co François-Xavier Briol EMAIL Department of Statistical Science University College London |
| Pseudocode | Yes | Algorithm 1 Robust-KSD (R-KSD) test for goodness-of-fit evaluation. |
| Open Source Code | Yes | Code for reproducing all experiments can be found at github.com/Xing LLiu/robust-kernel-test. |
| Open Datasets | Yes | We use the data set as Matsubara et al. (2022); Key et al. (2025), which is a 1-dimensional data set of 82 galaxy velocities (Postman et al., 1986; Roeder, 1990). |
| Dataset Splits | Yes | To avoid using the same data for model training and testing, we randomly split the data into equal halves, each containing ndata = 41 data points. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used, only mentioning execution times without specifying the processor, GPU, or memory. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | Unless otherwise mentioned, all standard KSD tests are based on an IMQ kernel k(x, x ) = h IMQ(x x ) where h IMQ(u) = (1 + u 2 2/λ2) 1/2 with a bandwidth λ2 > 0 selected via the median heuristic, i.e., λmed = Median Xi Xj 2 : 1 i < j n . All tilted-KSD and robust-KSD tests are based on a tilted IMQ kernel with weight w(x) = (1 + x a 2 2/c) b, where a Rd and c > 0. We fix a = 0 and c = 1 in all experiments, as all data will always be centered and on a suitable scale. More generally, we could replace x a 2 2/c by a weighted norm of the form (x a) C(x a), where C Rd d is a pre-conditioning matrix, chosen possibly as the empirical covariance matrix or robust estimates of it. Since our experiments will focus on sub-Gaussian models, we choose b = 1/2. This ensures the Stein kernel is bounded. All tests have nominal level α = 0.05. The probability of rejection is computed by averaging over 100 repetitions, and the 95% confidence intervals are reported. |