1. Neuroscience
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Likelihood approximation networks (LANs) for fast inference of simulation models in cognitive neuroscience

  1. Alexander Fengler  Is a corresponding author
  2. Lakshmi N Govindarajan
  3. Tony Chen
  4. Michael J Frank  Is a corresponding author
  1. Brown University, United States
  2. Boston College, United States
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Cite this article as: eLife 2021;10:e65074 doi: 10.7554/eLife.65074


In cognitive neuroscience, computational modeling can formally adjudicate between theories and affords quantitative fits to behavioral/brain data. Pragmatically, however, the space of plausible generative models considered is dramatically limited by the set of models with known likelihood functions. For many models, the lack of a closed-form likelihood typically impedes Bayesian inference methods. As a result, standard models are evaluated for convenience, even when other models might be superior. Likelihood-free methods exist but are limited by their computational cost or their restriction to particular inference scenarios. Here, we propose neural networks that learn approximate likelihoods for arbitrary generative models, allowing fast posterior sampling with only a one-off cost for model simulations that is amortized for future inference. We show that these methods can accurately recover posterior parameter distributions for a variety of neurocognitive process models. We provide code allowing users to deploy these methods for arbitrary hierarchical model instantiations without further training.

Data availability

All code is provided freely and is available at the following links: https://github.com/lnccbrown/lans/tree/master/hddmnn-tutorial, https://github.com/lnccbrown/lans/tree/master/al-mlp and https://github.com/lnccbrown/lans/tree/master/al-cnn.

Article and author information

Author details

  1. Alexander Fengler

    Robert J and Nancy D Carney Institute for Brain Science; Cognitive, Linguistic & Psychological Sciences, Brown University, Providence, United States
    For correspondence
    Competing interests
    No competing interests declared.
  2. Lakshmi N Govindarajan

    Robert J and Nancy D Carney Institute for Brain Science; Cognitive, Linguistic & Psychological Sciences, Brown University, Providence, United States
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0936-2919
  3. Tony Chen

    Psychology and Neuroscience, Boston College, Boston, United States
    Competing interests
    No competing interests declared.
  4. Michael J Frank

    Robert J and Nancy D Carney Institute for Brain Science; Cognitive, Linguistic & Psychological Sciences, Brown University, Providence, United States
    For correspondence
    Competing interests
    Michael J Frank, Senior editor, eLife.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8451-0523


National Institute of Mental Health (P50 MH119467-01)

  • Michael J Frank

National Institute of Mental Health (R01 MH084840-08A1)

  • Michael J Frank

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Valentin Wyart, École normale supérieure, PSL University, INSERM, France

Publication history

  1. Received: November 21, 2020
  2. Accepted: April 1, 2021
  3. Accepted Manuscript published: April 6, 2021 (version 1)


© 2021, Fengler et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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