Ising Model Statistical Test Implementation

This is an implementation of the paper "Concentration of Multilinear Functions of the Ising Model with Applications to Network Data". This is a submission for Nurture.ai's Global NIPS Paper Implementation Challenge.

For a description of the submission, please see this blog post: https://medium.com/@nurtureai/marianne-hoogeveen-from-physics-via-mathematics-to-machine-learning-c1b92f1c6b58

The implementation can be found in this notebook.

Summary of results

The notebook contains code that

• Generates samples of Ising lattices with nearest-neighbor interaction under zero magnetization using MCMC
• Generates samples that depart from an Ising model in the high-temperature limit, with the departure parameterized by a variable τ
• Performs a hypothesis test on these samples using a statistic introduced in the paper, where the null hypothesis is that the sample is an Ising lattice in the high-temperature limit
• Plots the percentage of successful rejections of the null hypothesis is plotted against τ (see plot below)