This is contains some of my work for the summer project 2018 under supervision by Luigi del Debbio. The focus was on learning, and eventually I attempted to help a research group out with the (now) published research in https://arxiv.org/abs/1810.11503.

Accompyning this work, I also implemented my own package for RBMs at https://github.com/torfjelde/ml.

Unfortunately there were no good reason to finish the reports, thus many of them are still in an unfinished state.

• 01-maxent: A "paper-like" attempt resulting from a deep-dive into maximum entropy.
• 02-rbms: A "paper-like" attempt resulting from a deep-dive into RBMs.
• 03-rbm-cumulants-numerical: This is probably the most (or only) noteworthy of the reports. Here I derive an upper-bound for the terms in the Taylor expansion of the RBM cumulants. This helped to show that extracting the learned couplings of the RBM numerically was not possible, further strengthening the necessity of the analytical expression obtained in https://arxiv.org/abs/1810.11503.

• 01-MCMC: From the very beginning of the project. Simple implementations of Metropolis-Hastings and Gibbs sampling.
• 02-RBMs: First attempt at implementing RBMs. Includes simple implementation of RBMs and application to Ising model.
• 03-toyproblems: Replicated experiments some experiments the research group focused on using my own RBM package https://github.com/torfjelde/ml. I was also trying to explore the some peculiarities seen when attempting to learn a discrete Ising model using a continuous (Gaussian) RBM. This was of interest due to the final application (which I cannot discuss here as the group is still working on this).
• 04-upper-bounding-kappa and 05-upper-bounding-kappa-improved: Presents failure of the numerical approximation to the Taylor expansion of the RBM cumulants. Work related to 03-rbm-cumulatns-numerical report. First notebook is the one where the derived upper-bound is broken, and second notebook is with more careful type-conversions leading to upper-bound being satisfied. Both uses the RBM implementation from https://github.com/coppolachan/rbm_ising since this was the package used and implemented by the research group.