We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form, which allows for simple iterative inference algorithms with analytical updates. The variables are: (1) Poisson variables to linearise an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
Inverse Ising inference from high-temperature re-weighting of observations
Keimyung University（启明大学）；Korea Institute for Advanced Study（韩国高等研究院）；Seoul National University（首尔国立大学）；National Institute of Diabetes and Digestive and Kidney Diseases（美国国家糖尿病、消化和肾脏疾病研究所）；National Institutes of Health（美国国立卫生研究院）；Quang Binh University（广平大学）
GenPANIS: A Latent-Variable Generative Framework for Forward and Inverse PDE Problems in Multiphase Media
Technical University of Munich, Professorship of Data-driven Materials Modeling, School of Engineering and Design（慕尼黑技术大学，数据驱动材料建模教授职位，工程与设计学院）；Munich Data Science Institute (MDSI - Core member)（慕尼黑数据科学研究所（MDSI—核心成员））
Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems
ShanghaiTech University（上海科技大学）；Changsha Institute for Computing and Digital Economy, Peking University（北京大学长沙计算与数字经济研究院）；Louisiana State University（路易斯安那州立大学）
