Analytical estimates of limited sampling biases in different information measures

Measuring the information carried by neuronal activity is made difficult, particularly when recording from mammalian cells, by the limited amount of data usually available, which results in a systematic error. While empirical ad hoc procedures have been used to correct for such error, we have recently proposed a direct procedure consisting of the analytical calculation of the average error, its estimation (up to subleading terms) from the data, and its subtraction from raw information measures to yield unbiased measures. We calculate here the leading correction terms for both the average transmitted information and the conditional information and, since usually one must first regularize the data, we specify the expressions appropriate to different regularizations. Computer simulations indicate a broad range of validity of the analytical results, suggest the effectiveness of regularizing by simple binning and illustrate the advantage of this over the previously used 'bootstrap' procedure.