🧩 Tight Bounds for Jensen’s Gap with Applications to Variational Inference

Official repository for the paper:
Tight Bounds for Jensen’s Gap with Applications to Variational Inference
Accepted for presentation at ACM CIKM 2025
📄 arXiv:2502.03988

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🔗 Related Work

This research builds upon our previous project:
➡️ Bounding Evidence and Estimating Log-Likelihood in VAE (AISTATS 2023)

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📁 Repository Structure

File	Description
bounds.py	Computes tight bounds using pre-generated samples from VAE models (5/10-IWAE).
fig_2.py	Reproduces Figure 2 from the paper.
fig_3-4.py	Reproduces Figures 3 and 4 from the paper.
gamma_20000.csv, lognormal_20000.csv	Sample datasets used in the Figure 3 experiment.

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⚙️ Usage

1. Generate Samples and Compute Components

First, generate samples from VAE models (5/10-IWAE) and compute
$R(x, z) = \frac{p(x|z)p(z)}{q(z|x)}$ — Equation (41) from Struski et al., accepted for AISTATS 2023.

# You can reuse the helper script from our previous repository:
bash calculate_components.sh  # available at:
# https://github.com/gmum/Bounding_Evidence_Estimating_LL/blob/main/calculate_components.sh

2. Compute the Bounds

python bounds.py

3. Reproduce Figures

# Figure 2
python fig_2.py

# Figures 3 and 4 (requires gamma_20000.csv and lognormal_20000.csv)
python fig_3-4.py

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📚 Citation

If you use this code or refer to our results, please cite:

@inproceedings{mazur2025tight,
  title     = {Tight Bounds for Jensen’s Gap with Applications to Variational Inference},
  author    = {Mazur, Marcin and Dziarmaga, Tadeusz and Ko{\'s}cielniak, Piotr and Struski, {\L}ukasz},
  booktitle = {Proceedings of the 34rd ACM International Conference on Information and Knowledge Management (CIKM)},
  year      = {2025}
}