Characterization of Predictive Behavior of a Retina by Mutual Information

Probing a bullfrog retina with spatially uniform light pulses of correlated stochastic intervals, we calculate the mutual information between the spiking output at the ganglion cells measured with multi-electrode array (MEA) and the interval of the stimulus at a time shift later. The time-integrated information from the output about the future stimulus is maximized when the mean interval of the stimulus is within the dynamic range of the well-established anticipative phenomena of omitted-stimulus responses for the retina. The peak position of the mutual information as a function of the time shift is typically negative considering the processing delay of the retina. However, the peak position can become positive for long enough correlation time of the stimulus when the pulse intervals are generated by a Hidden Markovian model (HMM). This is indicative of a predictive behavior of the retina which is possible only when the hidden variable of the HMM can be recovered from the history of the stimulus for a prediction of its future. We verify that stochastic intervals of the same mean, variance, and correlation time do not result in the same predictive behavior of the retina when they are generated by an Ornstein-Uhlenbeck (OU) process, which is strictly Markovian.