Universal Model-free Information Extraction
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Bayesian approaches have been used extensively in scientific and engineering research to quantify uncertainty and extract information. However, its model-dependent nature means that when the a priori model is incomplete or unavailable, there is a severe risk that Bayesian approaches will yield misleading results. Here, we propose a universal model-free information extraction approach, capable of reliably recovering target signals from complex responses. This breakthrough leverages on a data-centric approach, whereby measured data is reconfigured to create an enriched observable space, which in turn is mapped to a well-adapted manifold, thereby detecting crucial information via a reconstructed low-rank phase-space. A Koopman operator is used to transform hidden and complex nonlinear dynamics to linear one, which enables us to detect hidden event of interest from rapidly evolving systems, and relate it to either unobservable stimulus or anomalous behaviour. Thanks to its data-driven nature, our method excludes completely any prior knowledge on governing dynamics. We benchmark the astonishing accuracy of our method on three diverse and challenging problems in: biology, medicine, and engineering. In all cases, our approach outperforms existing state-of-the-art methods, of both Bayesian and non-Bayesian type. By creating a new reliable information analysis paradigm, it is suitable for ubiquitous nonlinear dynamical systems or end-users with little expertise, which permits the unbiased understanding of various mechanisms in the real world.
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