Paper:
Flexible statistical inference for mechanistic models of neural dynamics
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.

Review:
The authors present an Approximate Bayesian Computation approach to fitting dynamical systems models of single neuron dynamics. This is an interesting paper that aims to bring ABC to the neuroscience community. The authors introduce some tricks to handle the specifics of neuron models (handling bad simulations and bad features), and since fitting nonlinear single neuron models is typically quite painful, this could be a valuable tool. Overall, this paper is a real gem.
My biggest issue is that, in its current form, many of the proposed improvements over [19] are a bit unclear in practice. Sections 2.2-2.3 were difficult to parse for someone less familiar with ABC/MDNs. Since these are the main improvements, it would help to add/clarify here. Additionally, the classifier for bad simulations, the imputation for bad features, and the recurrent network for learning features need to be included in the algorithm in the appendix.
Additionally, the value of imputation for missing features in neural models is plausible, but completely theoretical in the paper’s current form. For the HH model, for instance, latency is not a feature and it seems there aren’t good simulations with bad features. Is there a clear example where imputation would be necessary for inference?
Minor issues:
In section 2. “could” should be replaced with “here we do.” One challenge in reading the paper is that many of the improvements seem to be purely hypothetical, until you get to the results.
It would be helpful to have a more complete description of the features used in the main text, and also to clarify at the beginning of section 2.1 that x=f(s).
Using a recurrent neural network for learning features seems like an interesting direction, but the results here are more of a teaser than anything else. Completely unpacking this could likely be a paper by itself.
For the GLM simulation -- what features are used? Also, the data augmentation scheme could be more clear in the appendix. If I understand correctly it isn’t necessary for the generative model, but just for getting the true posteriors and in PG-MCMC.