Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST.
Giulio Isacchini1,2, Natanael Spisak1, Armita Nourmohammad2,3,4
1Laboratoire de Physique de l'École Normale Supérieure, CNRS, PSL University, Sorbonne Université, and Université Paris Cité, 75005 Paris, France.
Physical Review. E
|June 16, 2022
Summary
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.
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.
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