Flexible statistical inference for mechanistic models of neural dynamics

By Jan-Matthis Lueckmann, Pedro J. Gonçalves, Giacomo Bassetto, Kaan Öcal, Marcel Nonnenmacher, Jakob H. Macke. 2017

334 citations recorded by the source corpus.

Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome this limitation by using likelihood-free inference approaches (also known as Approximate Bayesian Computation, ABC) to perform full Bayesian inference on single-neuron models. Our approach builds on recent advances in ABC by learning a neural network which maps features of the observed data to the posterior distribution over parameters. We learn a Bayesian mixture-density network approximating the posterior over multiple rounds of adaptively chosen simulations. Furthermore, we propose an efficient approach for handling missing features and parameter settings for which the simulator fails, as well as a strategy for automatically learning relevant features using recurrent neural networks. On synthetic data, our approach efficiently estimates posterior distributions and recovers ground-truth parameters. On in-vitro recordings of membrane voltages, we recover multivariate posteriors over biophysical parameters, which yield model-predicted voltage traces that accurately match empirical data. Our approach will enable neuroscientists to perform Bayesian inference on complex neuron models without having to design model-specific algorithms, closing the gap between mechanistic and statistical approaches to single-neuron modelling.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Statistics and Probability, Probabilistic & Bayesian Methods, Neuroscience

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Citations in the corpus

BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks (2020, methodology): “More efficient methods for approximate inference, such as sequential Monte Carlo (ABC-SMC), Markov-Chain Monte Carlo variants [48], or neural density estimation methods [18, 41, 33], optimize sampling from a proposal distribution in order to balance the speed-accuracy trade-off of vanilla ABC method”
ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations (2018, methodology): “Recent neural mixture density networks that directly estimate posteriors for complex data (Papamakarios and Murray 2016; Lueckmann et al. 2017) also fit into this ABC– CDE framework, and are especially promising for image data.”
Mining gold from implicit models to improve likelihood-free inference (2018, methodology): “They can be used to train a surrogate for the likelihood p(x|θ) [17, 19, 34] or, in a Bayesian setting, the posterior p(θ|x) [29, 33, 37].”
Likelihood-free inference with emulator networks (2018, background): “A complementary use of density-estimation in ABC is to directly target the posterior distribution [6, 37, 38, 39].”
Mining for Dark Matter Substructure: Inferring Subhalo Population Properties from Strong Lenses with Machine Learning (2019, background): “…& Murray 2016; Thomas et al. 2016; Uria et al. 2016; van den Oord et al. 2016b, 2016c, 2016a; Gutmann et al. 2017; Louppe & Cranmer 2017; Lueckmann et al. 2017; Papamakarios et al. 2017; Tran et al. 2017; Chen et al. 2018; Dinev & Gutmann 2018; Grathwohl et al. 2018; Huang et al. 2018;…”
Likelihood-free MCMC with Amortized Approximate Ratio Estimators (2019, methodology): “imize a parameterized prior. This work lends itself naturally to a likelihood-free setting, but only provides point-estimates. Similarly, approaches like Sequential Neural Posterior Estimation (SNPE) [10] borrow ideas from VI literature and iteratively adjusts a parameterized posterior deﬁned as a M”
Automatic Posterior Transformation for Likelihood-Free Inference (2019, methodology): “SNPE-B has MoG proposals, but its importance weights can lead to slow learning: here it fails to capture the crescent shapes.”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “Recent methods [8, 9, 10] address this by modeling an approximate density ˆ p ( x | θ ) and use ˆ p ( x | θ ) as a proxy in the likelihood ratio.”
Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows (2018, methodology): “We followed the setup of Lueck-mann et al. [43], and we used 18 features extracted from the timeseries as data x .”
sbi: A toolkit for simulation-based inference (2020, background): “…experience accumulated developing delfi (mackelab.org, 2017), which it succeeds. delfi was based on theano (Al-Rfou et al., 2016) (development discontinued) and developed both for SBI research (Greenberg et al., 2019; Lueckmann et al., 2017) and for scientific applications (Gonçalves et al., 2019).”
Sequential Neural Methods for Likelihood-free Inference (2018, methodology): “Here we use the particular method by Lueckmann et al. [15], which we denote SNPE-B.”
Autoregressive Energy Machines (2019, methodology): “Work in progress. models have seen use as surrogate likelihoods (Papamakar-ios et al., 2019) and approximate posterior distributions (Papamakarios & Murray, 2016; Lueckmann et al., 2017) for likelihood-free inference.”