There is a deep analogy between statistical inference and statistical physics; I will give a friendly introduction to both of these fields. I will then discuss phase transitions in two problems of interest to a broad range of data sciences: community detection in social and biological networks, and clustering of sparse high-dimensional data. In both cases, if our data becomes too sparse or too noisy, it suddenly becomes impossible to find the underlying pattern, or even tell if there is one. Physics both helps us locate these phase transitions, and design optimal algorithms that succeed all the way up to this point. Along the way, I will visit ideas from computational complexity, random graphs, random matrices, and spin glass theory.

Is this perspective actually useful?

See Igor Carron’s “phase diagram” list, and stuff like this Weng et al “Overcoming The Limitations of Phase Transition by Higher Order Analysis of Regularization Techniques” (WeMZ16)

## Refs

- Barb15
- Barbier, J. (2015) Statistical physics and approximate message-passing algorithms for sparse linear estimation problems in signal processing and coding theory.
*ArXiv:1511.01650 [Cs, Math]*. - OyTr15
- Oymak, S., & Tropp, J. A.(2015) Universality laws for randomized dimension reduction, with applications.
*ArXiv:1511.09433 [Cs, Math, Stat]*. - WeMZ16
- Weng, H., Maleki, A., & Zheng, L. (2016) Overcoming The Limitations of Phase Transition by Higher Order Analysis of Regularization Techniques.
*ArXiv:1603.07377 [Cs, Math, Stat]*.