# MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories

arXiv: https://arxiv.org/abs/2106.01808 · HTML: https://mlsanity.com/paper/2106.01808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Exploring the Limits of Language Modeling](https://mlsanity.com/paper/1602.02410/) (2016)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Noise Contrastive Estimation and Negative Sampling for Conditional Models: Consistency and Statistical Efficiency](https://mlsanity.com/paper/1809.01812/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [CCMI : Classifier based Conditional Mutual Information Estimation](https://mlsanity.com/paper/1906.01824/) (2019)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Edward: A library for probabilistic modeling, inference, and criticism](https://mlsanity.com/paper/1610.09787/) (2016)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Sequential Bayesian Experimental Design for Implicit Models via Mutual Information](https://mlsanity.com/paper/2003.09379/) (2020)
- [Overview of Approximate Bayesian Computation](https://mlsanity.com/paper/1802.09720/) (2018)

## Built on by (most cited first, 1 of 1)

- [Identifying parameter couplings and uncertainties of mixed-noise stochastic systems via full-covariance Gaussian mixture network](https://mlsanity.com/paper/2608.15198/) (2026)

## Abstract (arXiv)

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 where 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 high-dimensional parameter space.