Recurrent generalized linear models with correlated Poisson observations
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چکیده
We introduce the Recurrent Generalized Linear Model (R-GLM), an extension of GLMs based on a compact representation of the spiking history through a linear recurrent neural network. R-GLMs match the predictive likelihood of Linear Dynamical Systems (LDS) with linear-Gaussian observations. We also address a disadvantage of GLMs, including the R-GLM, that they cannot model instantaneous correlations. The LDS however allows for extra correlated variability through the new innovation in the latent space. To improve GLMs we introduce a class of correlated output distributions which can be used with any type of multivariate data: binary, counts or continuous. The correlated Bernoulli distribution matches the predictive likelihood of Ising models for static binarized spike data. The correlated Poisson distribution offers significant improvements in predictive likelihood for GLMs and R-GLMs. We evaluate the performance of the models on a dataset recorded from a Utah array implanted into motor areas of a macaque monkey during a delayed reaching task. We report that the R-GLM consistently finds long timescales (of up to several seconds) of correlated activity similar to those found by LDS and longer than the timescales learnt by standard GLMs (up to 400 ms). Like all GLMs, the proposed model can be used with any link function and any output distribution. This is unlike models based on LDS which require careful approximations to be trained with Poisson outputs.
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تاریخ انتشار 2012