Simulation-Based Inference (SBI) has recently emerged as a powerful framework for Bayesian inference: Neural networks are trained on simulations from a forward model, and learn to rapidly estimate posterior distributions. We here present an SBI framework for parametric spherical deconvolution of diffusion MRI data of the brain. We demonstrate its utility for estimating white matter fibre orientations, mapping uncertainty of voxel-based estimates and performing probabilistic tractography by spatially propagating fibre orientation uncertainty. We conduct an extensive comparison against established Bayesian methods based on Markov-Chain Monte-Carlo (MCMC) and find that: a) in-silico training can lead to calibrated SBI networks with accurate parameter estimates and uncertainty mapping for both single- and multi-shell diffusion MRI, b) SBI allows amortised inference of the posterior distribution of model parameters given unseen observations, which is orders of magnitude faster than MCMC, c) SBI-based tractography yields reconstructions that have a high level of agreement with their MCMC-based counterparts, equal to or higher than scan-rescan reproducibility of estimates. We further demonstrate how SBI design considerations (such as dealing with noise, defining priors and handling model selection) can affect performance, allowing us to identify optimal practices. Taken together, our results show that SBI provides a powerful alternative to classical Bayesian inference approaches for fast and accurate model estimation and uncertainty mapping in MRI.

There is substantial experimental evidence that learning and memory-related behaviours rely on local synaptic changes, but the search for distinct plasticity rules has been driven by human intuition, with limited success for multiple, co-active plasticity rules in biological networks. More recently, automated meta-learning approaches have been used in simplified settings, such as rate networks and small feed-forward spiking networks. Here, we develop a simulation-based inference (SBI) method for sequentially filtering plasticity rules through an increasingly fine mesh of constraints that can be modified on-the-fly. This method, _filter SBI_, allows us to infer entire families of complex and co-active plasticity rules in spiking networks. We first consider flexibly parameterized doublet (Hebbian) rules, and find that the set of inferred rules contains solutions that extend and refine -and also reject- predictions from mean-field theory. Next, we expand the search space of plasticity rules by modelling them as multi-layer perceptrons that combine several plasticity-relevant factors, such as weight, voltage, triplets and co-dependency. Out of the millions of possible rules, we identify thousands of unique rule combinations that satisfy biological constraints like plausible activity and weight dynamics. The resulting rules can be used as a starting point for further investigations into specific network computations, and already suggest refinements and predictions for classical experimental approaches on plasticity. This flexible approach for principled exploration of complex plasticity rules in large recurrent spiking networks presents the most advanced search tool to date for enabling robust predictions and deep insights into the plasticity mechanisms underlying brain function.

Simulation-based inference (SBI) solves statistical inverse problems by repeatedly running a stochastic simulator and inferring posterior distributions from model-simulations. To improve simulation efficiency, several inference methods take a sequential approach and iteratively adapt the proposal distributions from which model simulations are generated. However, many of these sequential methods are difficult to use in practice, both because the resulting optimisation problems can be challenging and efficient diagnostic tools are lacking. To overcome these issues, we present Truncated Sequential Neural Posterior Estimation (TSNPE). TSNPE performs sequential inference with truncated proposals, sidestepping the optimisation issues of alternative approaches. In addition, TSNPE allows to efficiently perform coverage tests that can scale to complex models with many parameters. We demonstrate that TSNPE performs on par with previous methods on established benchmark tasks. We then apply TSNPE to two challenging problems from neuroscience and show that TSNPE can successfully obtain the posterior distributions, whereas previous methods fail. Overall, our results demonstrate that TSNPE is an efficient, accurate, and robust inference method that can scale to challenging scientific models.

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such ’likelihood-free’ algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to fill this gap: We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms including recent approaches employing neural networks and classical Approximate Bayesian Computation methods. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency. Neural network-based approaches generally exhibit better performance, but there is no uniformly best algorithm. We provide practical advice and highlight the potential of the benchmark to diagnose problems and improve algorithms. The results can be explored interactively on a companion website. All code is open source, making it possible to contribute further benchmark tasks and inference algorithms.

During sleep, the brain undergoes dynamic and structural changes. In Drosophila, such changes have been observed in the central complex, a brain area important for sleep control and navigation. The connectivity of the central complex raises the question about how navigation, and specifically the head direction system, can operate in the face of sleep related plasticity. To address this question, we develop a model that integrates sleep homeostasis and head direction. We show that by introducing plasticity, the head direction system can function in a stable way by balancing plasticity in connected circuits that encode sleep pressure. With increasing sleep pressure, the head direction system nevertheless becomes unstable and a sleep phase with a different plasticity mechanism is introduced to reset network connectivity. The proposed integration of sleep homeostasis and head direction circuits captures features of their neural dynamics observed in flies and mice.

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.