# Statistical physics, networks, machine learning

Statistical physics, statistical inference/learning, statistical optimization

• - equlibrium
• - spin-glass theory
• - message passing
Mézard, M., Parisi, G., & Zecchina, R. (2002). Analytic and algorithmic solution of random satisfiability problems. Science, 297(5582), 812-5.

$P \rightarrow NP \rightarrow PH \rightarrow P^{\sum{P}} \rightarrow PSPACE \rightarrow EXP$

## 正反问题

Ising model, Boltzmann distribution -->

• 正问题 --> combinatorial optimization, hopfield model, SPIN Glasses, potts model, coloring problems, clustering, community detection
• 反问题 --> 从数据中学到模型， Inverse ising, boltzmann machine, RBM, Perception, DNN
$\{J; \beta\} \rightarrow m_i, c_{ij}$

# Statistical Mechanics: Entropy, Order Parameters, and Complexity

## Chapter 1 What is statistical mechanics?

Random walks. The motion of molecules in a gas, and bacteria in a liquid, and photons in the Sun, are described by random walks. Describing the specific trajectory of any given ran- dom walk (left) is not feasible. Describing the statistical properties of a large number of random walks is straightforward (right, showing endpoints of many walks starting at the origin). The deep principle underlying statistical mechanics is that it is often easier to under- stand the behavior of these ensembles of systems.