To obtain a bound on the Information Bottleneck Gaussian Process (IB-GP) objective, we use the Markov chain constraint Y X Z and the factorized joint distribution [2]: p(X,Y,Z) = p(Y|X,Z)p(Z|X)p(X) = p(Y|X)p(Z|X)p(X) (1) to expand the mutual information terms in LIB = max I(Z,Y) βI(Z,X) . Henceforth, we use the stochastic encoder pϕ(Z|X)parameterized by ϕas an approximation for p(Z|X). In practice computation of H(Z) might be intractable (even though P(Z)is well defined). Therefore, a variational approximation ρ(Z) is used in place of p(Z) such that KL(p(Z),ρ(Z)) is minimal. In practice computation of p(Y,Z)and p(Y|Z)might be intractable (even though they are well defined).

Intheearly visual system, high dimensional natural stimuli areencoded into the trains of neuronal spikes that transmit the information to the brain to produce perception. However, is all the visual scene information required to explain the neuronal responses?

In the early visual system, high dimensional natural stimuli are encoded into the trains of neuronal spikes that transmit the information to the brain to produce perception. However, is all the visual scene information required to explain the neuronal responses? In this work, we search for answers to this question by developing a joint model of the natural visual input and neuronal responses using the Information Bottleneck (IB) framework that can represent features of the input data into a few latent variables that play a role in the prediction of the outputs. The correlations between data samples acquired from published experiments on ex-vivo retinas are accounted for in the model by a Gaussian Process (GP) prior. The proposed IB-GP model performs competitively to the state-of-the-art feedforward convolutional networks in predicting spike responses to natural stimuli.

In the early visual system, high dimensional natural stimuli are encoded into the trains of neuronal spikes that transmit the information to the brain to produce perception. However, is all the visual scene information required to explain the neuronal responses? In this work, we search for answers to this question by developing a joint model of the natural visual input and neuronal responses using the Information Bottleneck (IB) framework that can represent features of the input data into a few latent variables that play a role in the prediction of the outputs. The correlations between data samples acquired from published experiments on ex-vivo retinas are accounted for in the model by a Gaussian Process (GP) prior. The proposed IB-GP model performs competitively to the state-of-the-art feedforward convolutional networks in predicting spike responses to natural stimuli.