convgp

Code for running Gaussian processes with convolutional and symmetric structures. The code is currently being cleaned up and will be continuously published over the next week or so. Things that you can expect to come:

• stored trained models,
• code to replicate the figures in the paper,
• detailed commands to replicate the exact experiments in the paper.

Paper

The accompanying paper can be found on arXiv.

Setup

GPflow with inter-domain support

In order to run the examples here, you need to have a branch of GPflow installed that supports inter-domain inducing variables. The branch located here and can be installed following the usual GPflow instructions. You can either use your favourite virtualenv to install the branch in, or switch back and forth between the main and customised versions of GPflow by running their setup script.

Datasets

You will also need to setup the datasets. In /datasets, run:

python process_cifar10.py
python process_rectangles.py

Running tests

Tests to check the correct functioning of most of the code is included. To run the tests use one of the two following:

python -m unittest
nosetests testing --nologcapture --with-coverage --cover-package=convgp --cover-html

The test coverage includes everything except the class MultiOutputInducingSVGP.

Experiments

Speed considerations

Running on the GPU is possible, and often significantly faster when using float32 data. This reduced precision is fine when using stochastic optimisation, but often problematic when using (variants of) BFGS. We recommend float32 to be used only with stochastic optimisation, and float64 otherwise. This has to be adjusted manually in the gpflowrcfile.

Running experiments

We have the following experiments:

• rectangles.py: Rectangles dataset (rbf, conv, and weighted conv kernels).
• mnist01.py: Zeros vs ones MNIST (rbf, conv, and weighted conv kernels).
• mnist.py: Full multiclass MNIST (rbf, conv, and weighted conv kernels).
• sumkern_mnist.py: Full multiclass MNIST (rbf + conv / wconv, rbf + poly + conv / wconv).

Many experiments have several command line options that can be used to modify a run. All have --name, which determines the name of the file in ./results/ that stores the optimisation trace. Experiments are resumed if a file of the correct name exists. Other options change the learning rate or minibatch size. See below for example experiments.

Optimisation traces can be displayed using display.py. The results files are passed as a positional argument, e.g.:

python display.py ./results/fullmnist*

Rectangles

python rectangles.py -k conv -M 16 --minibatch-size 100 -l 0.01 -n rectangles-paper  # Paper
python rectangles.py -k fullgp-rbf --optimiser l-bfgs-b -M 0  # Optimal RBF
python rectangles.py -k wconv -M 16 --minibatch-size 100 -l 0.01  # Full solution
python rectangles.py -k conv -M 35 --minibatch-size 100 -l 0.01  # Full support on the GP
python rectangles.py -k wconv -M 35 --minibatch-size 100 -l 0.01  # Idem
python rectangles.py -k wconv -M 200 --minibatch-size 100 -l 0.01 --dataset rectangles-image --Zinit patches

The results for the rectangles-image dataset aren't super impressive. Need to play around with the learning rate, and perhaps other kernels (possibly additive).

Mnist 0 vs 1

python mnist01.py -k rbf -M 100
python mnist01.py -k conv -M 50
python mnist01.py -k wconv -M 50

Mnist

python mnist.py -k rbf -M 750 --learning-rate-block-iters=60000 --learning-rate "0.001 * 10**-(i // b / 3)" --minibatch-size 200
python mnist.py -k conv -M 750 --learning-rate-block-iters=30000 --learning-rate "0.001 * 10**-(i // b / 3)" --minibatch-size 200
python mnist.py -k wconv -M 750 --learning-rate-block-iters=30000 --learning-rate "0.001 * 10**-(i // b / 3)" --minibatch-size 200
python sumkern_mnist.py -k1 wconv -k2 rbf -M 750 --vardist full --learning-rate-block-iters=20000 --learning-rate "0.001 * 10**-(i // b / 3) --minibatch-size 200

The learning rate decay of the sum kernel experiment is set too aggressively for convergence of the variational objective function. However, this rate was chosen as it repeatably converges to the (near-optimal) performance reported in the paper with 24 hours of time on a GTX1080. We also ran the experiment for several times longer, which showed little improvement in performance and no signs of over-fitting.

CIFAR-10

python cifar.py -k wconv -M 1000 --minibatch-size 50
python cifar.py -k multi -M 1000 --minibatch-size 30
python cifar.py -k addwconv -M 1000 --minibatch-size 30

Reproducing the plots from the paper

For reference, you can download the pickled optimisation histories for the results in the paper for full MNIST (223 MB) and for CIFAR-10 (408 MB). SHA checksums can be found in./results/.

After running the above experiments, you can run python paper-plots.py to recreate the figures from the paper.

Notes on the code

While the repositories for gpflow-inter-domain and convgp are separate, they rely on some modifications in each other. The most non-elegant adaptation to GPflow is to allow variables internal to the TensorFlow optimiser to be restored through opt_tools. The whole set up is a bit less than ideal, it would probably be better to use the internal TensorFlow loading and storing mechanisms, but this would require larger edits to GPflow.