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 geometry of Stein variational gradient descent
Authors: Andrew Duncan, Nikolas Nüsken, Lukasz Szpruch
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performance gains of these in various numerical experiments. |
| Researcher Affiliation | Academia | A. Duncan EMAIL Imperial College London, Department of Mathematics London SW7 2AZ and The Alan Turing Institute, UK N. N usken EMAIL Kings s College London, Department of Mathematics London WC2R 2LS, UK L. Szpruch EMAIL University of Edinburgh School of Mathematics Edinburgh, EH9 3JZ, UK and The Alan Turing Institute, London, UK |
| Pseudocode | No | The paper describes mathematical derivations and methodologies, but it does not contain any explicitly labeled 'Pseudocode' or 'Algorithm' blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing code, nor does it provide a link to a code repository for the methodology described. |
| Open Datasets | Yes | In the first example we consider the one dimensional target distribution π = 1/4N(2, 1) + 1/4N(−2, 1) + 1/4N(6, 1) + 1/4N(−6, 1) on R. ... As a second example, a two-dimensional Gaussian mixture model is considered defined by π = 1/6 ∑6 i=1 N(µi, Σi), where µ1 = (−5, 1)T, µ2 = (−5, −1)T, µ3 = (5, 1)T, µ4 = (5, −1)T, µ5 = (0, 1)T, µ6 = (0, −1)T and Σ1 = Σ2 = Σ3 = Σ4 = 1/5I2×2, and Σ5 = Σ6 = 10 0 0 1/2 . |
| Dataset Splits | No | This paper focuses on simulating particle systems from explicitly defined target distributions, not on experiments using pre-existing datasets with conventional training, validation, and test splits. Therefore, the concept of dataset splits does not directly apply. |
| Hardware Specification | No | The paper mentions numerical experiments and simulations, but it does not specify any particular hardware components such as GPU models, CPU types, or memory specifications used for these experiments. |
| Software Dependencies | No | The paper mentions the use of 'an implicit variable order BDF scheme (Byrne and Hindmarsh, 1975)' for ODE integration and 'the Python Optimal Transport Library (Flamary and Courty, 2017)' for Wasserstein distance computation. However, it does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | The standard SGVD dynamics (1) are simulated for N = 500 particles up to time T = 5000. ... We investigate kernels of the form (4) for different values of p 2. We first consider such kernels with fixed p taking values 2, 1, 1/2, . . .. The behavior of the scheme is strongly dependent on the choice of the bandwidth σ. Following Liu and Wang (2016) and all subsequent works we choose σ according to the median heuristic. ... To this end we consider a form of annealing where we take log p(t) = (1 − t/T) log p0 + t/T log p1, for t ∈ [0, T] and where T = 1000 is the final simulation time. We choose p0 = 2 and p1 = 1/2. |