title: Anthropic Correction of Information Estimates and Its Application to Neural Coding.
abstract: Information theory has been used as an organizing principle in neuroscience for several decades. Estimates of the mutual information (MI) between signals acquired in neurophysiological experiments are believed to yield insights into the structure of the underlying information processing architectures. With the pervasive availability of recordings from many neurons, several information and redundancy measures have been proposed in the recent literature. A typical scenario is that only a small number of stimuli can be tested, while ample response data may be available for each of the tested stimuli. The resulting asymmetric information estimation problem is considered. It is shown that the direct plug-in information estimate has anegativebias. Ananthropiccorrection is introduced that has apositivebias. These two complementary estimators and their combinations are natural candidates for information estimation in neuroscience. Tail and variance bounds are given for both estimates. The proposed information estimates are applied to the analysis of neural discrimination and redundancy in the avian auditory system.
authors.affiliation: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720 USA.
authors.forename: Michael C
authors.initials: MC
authors.lastname: Gastpar
authors.affiliation: School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853 USA ( prg56@cornell.edu ).
authors.forename: Patrick R
authors.initials: PR
authors.lastname: Gill
authors.affiliation: Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94720 USA ( alex.huth@berkeley.edu ).
authors.forename: Alexander G
authors.initials: AG
authors.lastname: Huth
authors.affiliation: Helen Wills Neuroscience Institute and the Department of Psychology, University of California, Berkeley, CA 94720 USA ( theunissen@berkeley.edu ).
authors.forename: Frédéric E
authors.initials: FE
authors.lastname: Theunissen
keywords: Anthropic principle; information estimation; neural coding; neuron; redundancy