Characterizing Retinal Ganglion Cell Responses to Electrical Stimulation Using Generalized Linear Models

The ability to preferentially stimulate different retinal pathways is an important area of research for improving visual prosthetics. Recent work has shown that different classes of retinal ganglion cells (RGCs) have distinct linear electrical input filters for low-amplitude white noise stimulation. The aim of this study is to provide a statistical framework for characterizing how RGCs respond to white-noise electrical stimulation. We used a nested family of Generalized Linear Models (GLMs) to partition neural responses into different components-progressively adding covariates to the GLM which captured non-stationarity in neural activity, a linear dependence on the stimulus, and any remaining non-linear interactions. We found that each of these components resulted in increased model performance, but that even the non-linear model left a substantial fraction of neural variability unexplained. The broad goal of this paper is to provide a much-needed theoretical framework to objectively quantify stimulus paradigms in terms of the types of neural responses that they elicit (linear vs. non-linear vs. stimulus-independent variability). In turn, this aids the prosthetic community in the search for optimal stimulus parameters that avoid indiscriminate retinal activation and adaptation caused by excessively large stimulus pulses, and avoid low fidelity responses (low signal-to-noise ratio) caused by excessively weak stimulus pulses

Modelling multivariate discrete data with latent Gaussian processes

Multivariate count data are common in some fields, such as sports, neuroscience, and text mining. Models that can accurately perform factor analysis are required, especially for structured data, such as time-series count matrices. We present Poisson Factor Analysis using Latent Gaussian Processes, a novel method for analyzing multivariate count data. Our approach allows for non-i.i.d observations, which are linked in the latent space using a Gaussian Process. Due to an exponential non-linearity in the model, there is no closed form solution. Thus, we resort to an expectation maximization approach with a Laplace approximation for tractable inference. We present results on several data sets, both synthetic and real, of a comparison with other factor analysis methods. Our method is both qualitatively and quantitatively superior for non-i.i.d Poisson data, because the assumptions it makes are well suited for the data

Unsupervised methods for large-scale, cell-resolution neural data analysis

In order to keep up with the volume of data, as well as the complexity of experiments and models in modern neuroscience, we need scalable and principled analytic programmes that take into account the scientific goals and the challenges of biological experiments. This work focuses on algorithms that tackle problems throughout the whole data analysis process. I first investigate how to best transform two-photon calcium imaging microscopy recordings – sets of contiguous images – into an easier-to-analyse matrix containing time courses of individual neurons. For this I first estimate how the true fluorescence signal gets transformed by tissue artefacts and the microscope setup, by learning the parameters of a realistic physical model from recorded data. Next, I describe how individual neural cell bodies may be segmented from the images, based on a cost function tailored to neural characteristics. Finally, I describe an interpretable non-linear dynamical model of neural population activity, which provides immediate scientific insight into complex system behaviour, and may spawn a new way of investigating stochastic non-linear dynamical systems. I hope the algorithms described here will not only be integrated into analytic pipelines of neural recordings, but also point out that algorithmic design should be informed by communication with the broader community, understanding and tackling the challenges inherent in experimental biological science