{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/inverse-ising-problem-in-continuous-time-a","title":"Inverse Ising problem in continuous time: A latent variable approach","arxiv_id":"1709.04495","date":"2017-09-04","proceeding":null,"authors":["Christian Donner","Manfred Opper"],"abstract":"We consider the inverse Ising problem, i.e. the inference of network\ncouplings from observed spin trajectories for a model with continuous time\nGlauber dynamics. By introducing two sets of auxiliary latent random variables\nwe render the likelihood into a form, which allows for simple iterative\ninference algorithms with analytical updates. The variables are: (1) Poisson\nvariables to linearise an exponential term which is typical for point process\nlikelihoods and (2) P\\'olya-Gamma variables, which make the likelihood\nquadratic in the coupling parameters. Using the augmented likelihood, we derive\nan expectation-maximization (EM) algorithm to obtain the maximum likelihood\nestimate of network parameters. Using a third set of latent variables we extend\nthe EM algorithm to sparse couplings via L1 regularization. Finally, we develop\nan efficient approximate Bayesian inference algorithm using a variational\napproach. We demonstrate the performance of our algorithms on data simulated\nfrom an Ising model. For data which are simulated from a more biologically\nplausible network with spiking neurons, we show that the Ising model captures\nwell the low order statistics of the data and how the Ising couplings are\nrelated to the underlying synaptic structure of the simulated network.","url_abs":"http://arxiv.org/abs/1709.04495v3","url_pdf":"http://arxiv.org/pdf/1709.04495v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"inverse-ising-problem-in-continuous-time-a","repo_url":"https://github.com/christiando/dynamic_ising","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}