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Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST

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Isacchini,  Giulio
Max Planck Research Group Statistical physics of evolving systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Nourmohammad,  Armita
Max Planck Research Group Statistical physics of evolving systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Isacchini, G., Spisak, N., Nourmohammad, A., Mora, T., & Walczak, A. M. (2022). Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST. Physical Review E, 105: 055309. doi:10.1103/PhysRevE.105.055309.


Cite as: https://hdl.handle.net/21.11116/0000-000A-B020-A
Abstract
Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be
computed in practice. One class of methods uses data simulated with different parameters to infer models of
the likelihood-to-evidence ratio, or equivalently the posterior function. Here we frame the inference task as an
estimation of an energy function parametrized with an artificial neural network. We present an intuitive approach,
named MINIMALIST, in which the optimal model of the likelihood-to-evidence ratio is found by maximizing
the likelihood of simulated data. Within this framework, the connection between the task of simulation-based
inference and mutual information maximization is clear, and we show how several known methods of posterior
estimation relate to alternative lower bounds to mutual information. These distinct objective functions aim at
the same optimal energy form and therefore can be directly benchmarked. We compare their accuracy in the
inference of model parameters, focusing on four dynamical systems that encompass common challenges in
time series analysis: dynamics driven by multiplicative noise, nonlinear interactions, chaotic behavior, and highdimensional parameter space.