franciscovargas / controlledfollmerdrift Goto Github PK

Move the CSFS method from the notebook into its own module at ControlledFollmerDrift/cfollmer/ . Remove any hard coded elements.

In the paper https://arxiv.org/pdf/2102.06559.pdf by Duvenauds group we want to implement the STL trick in Eq 12 page 5 as an alternative to our current direct KL divergence minimisation

This is a very very simple algo to implement either eq 2.20 or 2.21 in https://arxiv.org/pdf/2106.10880.pdf. We need this as a baseline as our method is the dual formulation of this approach.

Also we would be interested in implementing a bayesian version of the multipmodal examples in Huang et al. with toy generated data to see if our approach has the same nice properties as theirs or if we mode collapse a bit more (which is very possible due to the approximate optimisation).

If time allowing the VarGrad estimator in Niks paper https://arxiv.org/pdf/2005.05409.pdf might be worth implementing although I think stick the landing should be good enough.

This model has an analytic Gaussian Posterior from which we can sample from so we can compare distributions in the 1d setting very easilly

If time allowing the VarGrad estimator in Niks paper https://arxiv.org/pdf/2005.05409.pdf might be worth implementing although I think stick the landing should be good enough.

Look at results table here https://arxiv.org/pdf/2102.06559.pdf .

In the logistic regression notebook we should replace the pyro logreg model and try out PYMC3 so that we can hopefully get a good baseline for this example.

In addition to this we need to double check / code review the CSFS method and make sure its bug free.

• Bayesian Neural Network on MNIST (maybe CIFAR). Pick the gold standard architecture for the HMC model here https://arxiv.org/pdf/2102.06559.pdf.
• Bayesian ICA from the SGLD paper https://www.stats.ox.ac.uk/~teh/research/compstats/WelTeh2011a.pdf (MEG dataset)
• A good Bayesian GMM example (Find a reference from some VI paper)
• What other Bayesian model do practioners care about and use VI for ? Maybe Robust regression ?
• If we had a lot of time we could do a topic model and collapse out the discrete variables
• How do we handle latent variables which are distinct for each data point ? like a VAE , how do we amortise the drift ? By amortising we mean like in VAEs I mean something like \phi_i = NN(x_i) type of thing where \phi_i is the variational parameter for z_i . Its not super clear how this would be done on the drift. It might be possible to do something with Ito's lemma evolve some form of x_i dependant reparametrisation of the SDE instead.
• At the same time all of these x_i are IID so it might just be able to similare the same SDE N times if we decouple things with the log appropiately. This only applies when the z_is are not correlated but the math works out if you assume that optimal drift should depend only on z_i for the ith dimension then this works out. I think it shouldnt be too hard to prove that this is true either. This is a tough example despite being an easier problem than bayesian inference , but it would look very good.