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Abstract

Many models in neuroscience, such as networks of spiking neurons or complex biophysical models, are defined as
numerical simulators. This means one can simulate data from the model, but calculating the likelihoods associated
with specific observations is hard or intractable, which in turn makes statistical inference challenging. So-called
Approximate Bayesian Computation (ABC) aims to make Bayesian inference possible for likelihood-free models.
However, standard ABC algorithms do not scale to high-dimensional observations, e.g. inference of receptive
fields from high-dimensional stimuli.
Here, we develop an approach to likelihood-free inference for high-dimensional data, where we train a neural
network to perform statistical inference given adaptively simulated data sets. The network is composed of layers
performing non-linear feature extraction, and fully connected layers for non-linear density estimation. Feature extraction layers are either convolutional or recurrent in structure, depending on whether the data is high-dimensional
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in space or time, respectively. This approach makes it possible to scale ABC to problems with high-dimensional
inputs.
We illustrate this method in two canonical examples in neuroscience. First, we infer receptive field parameters of
a V1 simple cell model from neural activity resulting from white-noise stimulation, a high-dimensional stimulus in
the space domain. Second, we perform Bayesian inference on a Hodgkin-Huxley model of a single neuron, given
full voltage traces resulting from intracellular current stimulation. On both applications, we retrieve the posterior
distribution over the parameters, i.e. the manifold of parameters for which the model exhibits the same behaviour
as the observations. Our approach will allow neuroscientists to leverage the power of deep neural networks to
link high-dimensional data to complex simulations of neural dynamics.