2016研读营之统计物理,网络与机器学习
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Statistical Physics that will be used in my lectures
- The Ising model and the maximum entropy distribution
- From dynamics to equilibrium
- Mean-field approximation and the Curie-Weiss model
- Variational approaches
- Random graphs
- Cavity method and belief propagation for the Ising model
- Thouless-Anderson-Palmer equations and the Plefka expansions
统计物理,优化与推断
- 自旋玻璃与组合优化
- Boltzmann分布与贝叶斯统计
- Roudi, Y.; Tyrcha J.& Hertz J., Ising model for neural data: Model quality and approximate methods for extracting functional connectivity Phys. Rev. E, 2009, 79, 051915
- Yedidia J. ; Freeman W. & Weiss Y. ,Understanding belief propagation and its generalizations International Joint Conference on Artificial Intelligence (IJCAI), 2001
- Mezard, M.; Parisi, G. & Zecchina, R. Analytic and algorithmic solution of random satisfiability problems Science, 297, 812 ,2002.
- Mezard, M. & Montanari, A. Information, Physics and Computation Oxford University press, ,2009.
- 周海军,自旋玻璃与消息传递,科学出版社,2015
- Zdeborova, L. & Krzakala, F. Statistical physics of inference: Thresholds and algorithms arXiv preprint arXiv:1511.02476, ,2015.
一些网络中问题的统计物理描述
- 网络中的流行病传播,网络的鲁棒性与Percolation相变
- 从四色地图问题到社区结构探测: Modularity, Stochastic Block Model及可探测相变
- Karrer, B.; Newman, M. E. J. & Zdeborova, L. Percolation on Sparse Networks Phys. Rev. Lett., American Physical Society, 113, 208702 ,2014.
- Zdeborov\'a L. & Krzakala F. Phase transitions in the coloring of random graphs Phys. Rev. E, 2007, 76, 031131
- Fortunato, S. Community detection in graphs Physics Reports, 486, 75 - 174 ,2010.
- Decelle, A.; Krzakala, F.; Moore, C. & Zdeborova, L. Inference and Phase Transitions in the Detection of Modules in Sparse Networks Phys. Rev. Lett., American Physical Society, 107, 065701 ,2011.
网络与随机矩阵
- 邻接矩阵, 随机行走矩阵,Laplacian矩阵及它们的简单谱性质
- Gaussian orthogonal ensemble, 谱密度,Wigner's Semi-cycle, ...
- 统计推断,消息传递与谱方法
- Dan Spielman在Yale开的课程Spectral Graph Theory
- Chung, F. R. Spectral graph theory American Mathematical Soc., 92,1997.
- Luxburg, U. V.; Belkin, M.; Bousquet, O. & Pertinence A tutorial on spectral clustering Stat. Comput, ,2007.
- F. Krzakala et al, Spectral redemption in clustering sparse networks Proc. Natl. Acad. Sci. USA, 2013, 110, 20935-20940
从Ising模型到神经网络
- Ising自旋玻璃模型,平均场方法和副本对称破缺
- Ising模型反问题, Boltzmann Machine及Restricted Boltzmann Machine
- 深度神经网络与重整化群
- Ackley, D. H.; Hinton, G. E. & Sejnowski, T. J. A learning algorithm for boltzmann machines Cognitive Science, 9, 147 - 169 ,1985.
- Kappen, H. & Rodriguez, F. B. Efficient Learning in Boltzmann Machines Using Linear Response Theory Neural Computation, 10, 1137-1156 ,1998.
- Roudi, Y.; Tyrcha, J. & Hertz, J. Ising model for neural data: Model quality and approximate methods for extracting functional connectivity Phys. Rev. E, 79, 051915 ,2009.
- Hinton, G. A practical guide to training restricted Boltzmann machines Momentum, 9, 926 ,2010
- Nielsen, MA. Neural Networks and Deep Learning - URL: http://neuralnetworksanddeeplearning. com
- Gabrie M.;Tramel E. W. & Krzakala F. , Training Restricted Boltzmann Machine via the Thouless-Anderson-Palmer free energy Advances in Neural Information Processing Systems 28, Curran Associates, Inc., 2015, 640-648