Statistical physics and statistical inference

There is a deep analogy between Bayesian inference and statistical physics. Combining this analogy with tools from spin glass theory gives fast algorithms, based on “message-passing” or belief propagation, for inference on sparse, high-dimensional data. It also reveals phase transitions in our ability to detect structure in data, as a function of its sparsity and the strength of the structure. I will give a friendly introduction to this analogy — designed for those who are not experts in either field — using community detection in social and biological networks as an example.