Forward-Backward Gaussian Variational Inference via JKO in the Bures-Wasserstein Space
Authors: Michael Ziyang Diao, Krishna Balasubramanian, Sinho Chewi, Adil Salim
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, via elementary simulations, we demonstrate that FBGVI is implementable, practical and competitive with the Bures Wasserstein gradient descent (BWGD) method of (Lambert et al., 2022b). We consider two examples: Gaussian targets. For the first experiment, we consider a scenario where the target density is π(x) exp( 1 2 (x µ), Σ 1 (x µ) ), where µ Unif([0, 1]10) and Σ 1 = U diag 10 9 10 8 1 U T, with U R10 10 chosen as a uniformly random orthogonal matrix. |
| Researcher Affiliation | Collaboration | 1Massachusetts Institute of Technology 2University of California, Davis 3Microsoft Research. |
| Pseudocode | Yes | Algorithm 1 FB GVI and Stochastic FB GVI |
| Open Source Code | Yes | A Jupyter notebook containing code for our experiments can be found at https://github.com/mzydiao/FBGVI/ blob/main/FBGVI-Experiments.ipynb. |
| Open Datasets | No | The paper describes synthetic data generation for 'Gaussian targets' and a generative model for 'Bayesian logistic regression', but does not provide concrete access information (link, DOI, formal citation with authors/year) for a publicly available or open dataset. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, or detailed splitting methodology) for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | We run FB GVI and stochastic FB GVI with target potential π exp( V ) initialized at p0 = N(0, I10), where I10 is the 10 10 identity matrix. The step size η is varied, and the resulting plots of log KL(pk π) for different choices of η are displayed in Figure 1. |