This is the code to reproduce all experiments for the following paper:
@inproceedings{Foong:2021:How_Tight_Can_PAC-Bayes_Be,
title = {How Tight Can {PAC}-{Bayes} Be in the Small Data Regime?},
year = {2021},
author = {Andrew Y. K. Foong and Wessel P. Bruinsma and David R. Burt and Richard E. Turner},
booktitle = {Advances in Neural Information Processing Systems},
volume = {35},
eprint = {https://arxiv.org/abs/2106.03542},
}
Every experiment creates a folder in _experiments.
The names of the files in those folders should be self-explanatory.
First, create and activate a virtual environment for Python 3.8.
virtualenv venv -p python3.8
source venv/bin/activateThen install an appropriate GPU-accelerated version of PyTorch.
Finally, install the requirements for the project.
pip install -e . You should now be able to run the below commands.
In order to generate the synthetic 1D datasets used, run these commands from inside classification_1d:
python gen_data.py --class_scheme balanced --num_context 30 --name 30-context --num_train_batches 5000 --num_test_batches 64
python gen_data.py --class_scheme balanced --num_context 60 --name 60-context --num_train_batches 5000 --num_test_batches 64The generated datasets will be in pacbayes/_data_caches
See Figure 2 in Section 3 and Appendix G.
python theory_experiments.py --setting det1-1
python theory_experiments.py --setting det1-2
python theory_experiments.py --setting det2-1
python theory_experiments.py --setting det2-1
python theory_experiments.py --setting stoch1
python theory_experiments.py --setting stoch2
python theory_experiments.py --setting stoch3
python theory_experiments.py --setting random --random-seed 1 --random-better-bound maurer
python theory_experiments.py --setting random --random-seed 6 --random-better-bound catoniSee Figure 3 and 4 in Section 4 and Appendices I and J.
The numbers from the graphs can be found in eval_metrics_no_post_opt.txt
(without post optimisation) eval_metrics_post_opt.txt (with post optimisation).
MODEL_NONDDP=maurer MODEL_DDP=maurer-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer MODEL_DDP=maurer-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=convex-nonseparable MODEL_DDP=convex-nonseparable-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=convex-nonseparable MODEL_DDP=convex-nonseparable-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-optimistic MODEL_DDP=maurer-optimistic-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-optimistic MODEL_DDP=maurer-optimistic-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-inv MODEL_DDP=maurer-inv-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-inv MODEL_DDP=maurer-inv-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-inv-optimistic MODEL_DDP=maurer-inv-optimistic-ddp NUM_CONTEXT=30 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-inv-optimistic MODEL_DDP=maurer-inv-optimistic-ddp NUM_CONTEXT=30 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer MODEL_DDP=maurer-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer MODEL_DDP=maurer-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=convex-nonseparable MODEL_DDP=convex-nonseparable-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=convex-nonseparable MODEL_DDP=convex-nonseparable-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-optimistic MODEL_DDP=maurer-optimistic-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-optimistic MODEL_DDP=maurer-optimistic-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-inv MODEL_DDP=maurer-inv-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-inv MODEL_DDP=maurer-inv-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.sh
MODEL_NONDDP=maurer-inv-optimistic MODEL_DDP=maurer-inv-optimistic-ddp NUM_CONTEXT=60 ./run_GNP_prop_024.sh
MODEL_NONDDP=maurer-inv-optimistic MODEL_DDP=maurer-inv-optimistic-ddp NUM_CONTEXT=60 ./run_GNP_prop_68.shSee Appendix J.
The numbers from the graphs can be found in eval_metrics_no_post_opt.txt
(without post optimisation) eval_metrics_post_opt.txt (with post optimisation).
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=30 ./run_MLP.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=30 ./run_MLP.sh
MODEL_NONDDP=catoni MODEL_DDP=catoni-ddp NUM_CONTEXT=60 ./run_MLP.sh
MODEL_NONDDP=kl-val MODEL_DDP=kl-val NUM_CONTEXT=60 ./run_MLP.sh