Flexible statistical inference for mechanistic models of neural dynamics (1711.01861v1)

Abstract: 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.

Flexible Statistical Inference for Mechanistic Models of Neural Dynamics

The paper "Flexible Statistical Inference for Mechanistic Models of Neural Dynamics" presents a novel approach to Bayesian inference for complex, mechanistic models of single-neuron dynamics without tractable likelihood functions. The authors propose a methodology grounded in likelihood-free inference, specifically leveraging Approximate Bayesian Computation (ABC), to bridge the gap between mechanistic modeling and statistical inference.

Methodological Innovation

At the heart of this research is the development of an algorithm termed Sequential Neural Posterior Estimation (SNPE). The SNPE method innovatively combines the strengths of previous ABC approaches by:

1. Mixture-Density Networks (MDNs): Utilizing MDNs to approximate the posterior distributions over model parameters. This allows for handling complex and multi-modal distributions, surpassing the limitations of Gaussian assumptions present in traditional methods.
2. Sequential Design: Implementing a sequential simulation framework where the posterior distribution from one round is used to guide subsequent rounds, thus iteratively refining the proposal distribution.
3. Handling Missing Data and Failures: Introducing mechanisms to efficiently deal with incomplete data features and failed simulations. This is particularly relevant for modeling neural dynamics, where many parameters can lead to unrealistic or undefined behavior of the model.
4. Recurrent Neural Networks (RNNs): Employing RNNs for automatic feature learning from time-series data, allowing the model to learn relevant summaries directly from voltage traces, which is crucial for reducing the manual feature engineering typically required in modeling workflows.

Results and Performance

The paper demonstrates the robustness of the SNPE approach through several experiments:

• Simple Statistical Models: SNPE efficiently recovered posterior distributions for one-dimensional Gaussian mixtures, showing robust performance even in scenarios with unstable behavior where previous methods faltered.
• Generalized Linear Models (GLMs): The approach was validated against GLMs, yielding posterior estimates in strong agreement with those obtained using Particle Gibbs with Ancillary Variables (PG-MCMC), a likelihood-based inference technique.
• Hodgkin-Huxley Models: Applied to both synthetic and real biophysical neuron models, SNPE demonstrated its capability to infer multivariate posteriors over biophysical parameters. On synthetic data, it aligned well with ground truth parameters, and on real data, the mode of the inferred posterior accurately generated voltage traces similar to empirical observations.

Implications and Future Work

This work extends the toolkit available to neuroscientists for performing Bayesian inference on complex neuron models. The ability to recover full posterior distributions without needing explicit likelihoods allows for a quantitative exploration of model robustness and parameter identifiability, significantly contributing to the understanding of neural mechanisms and variability.

Potential future directions include further refinement of the SNPE framework to improve computational efficiency, as well as the application of the method to larger-scale neural circuit models. Additionally, the integration of uncertainty estimates into experimental design could foster more informative datasets, guiding neuroscience experiments to strategically refine model parameters.

Overall, this paper provides a substantial contribution to statistical methodology in computational neuroscience by facilitating a more nuanced exploration of model parameters and their interactions in reproducing biological phenomena.