Biological systems need to process information in real time and must trade off accuracy of presentation and coding costs. Here we operationalize this trade-off and develop an information-theoretic framework that selectively extracts information of the input past that is predictive about the output future, obtaining a generalized eigenvalue problem. Thereby, we unravel the input history in terms of structural phase transitions corresponding to additional dimensions of a state space. We elucidate the relation to canonical correlation analysis and give a numerical example. Altogether, this work relates information-theoretic optimization to the joint problem of system identification and model reduction. Journal: Physical review. E, Statistical, nonlinear, and soft matter physics Custom 1: http://www.ncbi.nlm.nih.gov/pubmed/19518274?dopt=Abstract UPCOMING EVENTS Learn more about our exciting upcoming events! read more Studying at ELSC Our Int'l Ph.D. program provides outstanding students with top-notch courses in computatinal neuroscience. read more The Building The Jerusalem Brain Sciences Building will provide a state-of-the-art research and teaching facility for the Edmond and Lily Safra Center for Brain Sciences. read more ELSC Media Channel Get into our media channel and investigate ELSC's latest videos: seminars, public lectures, courses and video articles. read more Source URL: https://elsc.huji.ac.il/tishby/publications/past-future-information-bottleneck-dynamical-systems
Finally, DCA is related to the Past-Future Information Bottleneck REF (see Appendix F).