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

Giulio Isacchini1,2, Natanael Spisak1, Armita Nourmohammad2,3,4

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This study introduces MINIMALIST, a novel simulation-based inference method using artificial neural networks to estimate energy functions. It benchmarks various posterior estimation techniques, enhancing parameter inference for complex dynamical systems.

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Area of Science:

  • Computational Statistics
  • Machine Learning
  • Dynamical Systems

Background:

  • Simulation-based inference (SBI) is crucial for parameter learning when model likelihoods are intractable.
  • Existing SBI methods infer likelihood-to-evidence ratios or posterior functions using simulated data.
  • Framing inference as energy function estimation offers a unified perspective.

Purpose of the Study:

  • To present MINIMALIST, an intuitive simulation-based inference approach.
  • To connect SBI with mutual information maximization.
  • To benchmark different posterior estimation methods within a unified framework.

Main Methods:

  • Parametrized an energy function using artificial neural networks for inference.
  • Developed the MINIMALIST approach by maximizing the likelihood of simulated data.
  • Analyzed the relationship between SBI and mutual information lower bounds.

Main Results:

  • Established a clear link between simulation-based inference and mutual information maximization.
  • Demonstrated how existing posterior estimation methods relate to mutual information lower bounds.
  • Benchmarked accuracy across four dynamical systems with common time series challenges.

Conclusions:

  • MINIMALIST provides an intuitive framework for simulation-based inference.
  • The unified approach allows direct benchmarking of diverse posterior estimation techniques.
  • The study highlights challenges in parameter inference for complex dynamical systems.