Tight Data-Robust Bounds to Mutual Information Combining Shuffling and Model Selection Techniques

The estimation of the information carried by spike times is crucial for a quantitative understanding of brain function, but it is difficult because of an upward bias due to limited experimental sampling. We present new progress, based on two basic insights, on reducing the bias problem. First, we show that by means of a careful application of data-shuffling techniques, it is possible to cancel almost entirely the bias of the noise entropy, the most biased part of information. This procedure provides a new information estimator that is much less biased than the standard direct one and has similar variance. Second, we use a nonparametric test to determine whether all the information encoded by the spike train can be decoded assuming a low-dimensional response model. If this is the case, the complexity of response space can be fully captured by a small number of easily sampled parameters. Combining these two different procedures, we obtain a new class of precise estimators of information quantities, which can provide data-robust upper and lower bounds to the mutual information. These bounds are tight even when the number of trials per stimulus available is one order of magnitude smaller than the number of possible responses. The effectiveness and the usefulness of the methods are tested through applications to simulated data and recordings from somatosensory cortex. This application shows that even in the presence of strong correlations, our methods constrain precisely the amount of information encoded by real spike trains recorded in vivo.