This repository accompanies the paper Kian Ming A. Chai and Edwin V. Bonilla. Variational Learning of Fractional Posteriors. ICML 2025. An updated version is also placed here and at arXiv:2603.27488.
The experiments are in two places:
-
- This is self-contained.
- You can probably run it on your laptop. GPU is not required.
- You can only use it as a Jupyter Notebook.
-
Variational autoencoders for MNIST and Fashion-MNIST
- This depends on the inference code and the neural network architectures.
- You will need at least an NVIDIA T4 to run. Possible on free accounts on
- Some results in the paper can be obtained within single time-limited sessions. Some results require multiple such sessions. Saving and loading of partial results are supported in the code. Multi-GPUs are supported via DataParallel, which is useful when run within Kaggle.
- For FID scoring, we use the version by Seitzer.
- Instead of Jupyter Notebook, the code can be converted to pure Python and run from the command line. See the experiments directory for how this is done.
- There is limited testing for CIFAR10, which requires some changes to execute on SageMaker Studio Lab.
- One additional CNN layer (total 3) each for encoder and decoder
- 32-dimensional latent space
- Number of Monte Carlo samples for training reduced to 16
- Number of Monte Carlo samples for validation reduced to 128
- Numer of epoches reduced to 300
- Results using
$\mathcal{L}_\gamma$ , our primary bound:-
$\gamma=1$ (ELBO): train objecture = 1,229; validation objective = 1,172; FID = 141 -
$\gamma=10^{-5}$ (posterior very close to prior): train objective = 1,238; validation objective = 1,184; FID = 135
-
- These results are not fantastic, but they demonstrate that small
$\gamma$ is better. - The study is not extensive. In particular, the 32-dimensional latent space is just to show that the conclusions also hold beyond the 2 and 4 dimensions documented in the paper.