Binless strategies for estimation of information from neural data.

We present an approach to estimate information carried by experimentally observed neural spike trains elicited by known stimuli. This approach makes use of an embedding of the observed spike trains into a set of vector spaces, and entropy estimates based on the nearest-neighbor Euclidean distances within these vector spaces [L. F. Kozachenko and N. N. Leonenko, Probl. Peredachi Inf. 23, 9 (1987)]. Using numerical examples, we show that this approach can be dramatically more efficient than standard bin-based approaches such as the "direct" method [S. P. Strong, R. Koberle, R. R. de Ruyter van Steveninck, and W. Bialek, Phys. Rev. Lett. 80, 197 (1998)] for amounts of data typically available from laboratory experiments.

[1]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[2]  H. Quastler.  Information theory in psychology : problems and methods , 1955 .

[3]  Ga Miller,et al.  Note on the bias of information estimates , 1955 .

[4]  R. FitzHugh.  THE STATISTICAL DETECTION OF THRESHOLD SIGNALS IN THE RETINA , 1957, The Journal of general physiology.

[5]  V. Mountcastle,et al.  NEURAL ACTIVITY IN MECHANORECEPTIVE CUTANEOUS AFFERENTS: STIMULUS-RESPONSE RELATIONS, WEBER FUNCTIONS, AND INFORMATION TRANSMISSION. , 1965, Journal of neurophysiology.

[6]  J. McFadden.  The Entropy of a Point Process , 1965 .

[7]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[8]  A. Carlton.  On the bias of information estimates. , 1969 .

[9]  P. Grassberger.  Finite sample corrections to entropy and dimension estimates , 1988 .

[10]  William Bialek,et al.  Reading a Neural Code , 1991, NIPS.

[11]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[12]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[13]  A. Tsybakov,et al.  Root-N consistent estimators of entropy for densities with unbounded support , 1994, Proceedings of 1994 Workshop on Information Theory and Statistics.

[14]  William R. Softky,et al.  Sub-millisecond coincidence detection in active dendritic trees , 1994, Neuroscience.

[15]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[16]  D. Baylor,et al.  Concerted Signaling by Retinal Ganglion Cells , 1995, Science.

[17]  T. Sejnowski,et al.  Reliability of spike timing in neocortical neurons. , 1995, Science.

[18]  Stefano Panzeri,et al.  The Upward Bias in Measures of Information Derived from Limited Data Samples , 1995, Neural Computation.

[19]  E. Marder,et al.  Decoding Synapses , 1996, The Journal of Neuroscience.

[20]  William Bialek,et al.  Spikes: Exploring the Neural Code , 1996 .

[21]  William Bialek,et al.  Entropy and Information in Neural Spike Trains , 1996, cond-mat/9603127.

[22]  L. Györfi,et al.  Nonparametric entropy estimation. An overview , 1997 .

[23]  Jonathan D. Victor,et al.  Metric-space analysis of spike trains: theory, algorithms and application , 1998, q-bio/0309031.

[24]  B. Knight,et al.  Response variability and timing precision of neuronal spike trains in vivo. , 1997, Journal of neurophysiology.

[25]  Rob R. de Ruyter van Steveninck,et al.  The metabolic cost of neural information , 1998, Nature Neuroscience.

[26]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[27]  B J Richmond,et al.  Stochastic nature of precisely timed spike patterns in visual system neuronal responses. , 1999, Journal of neurophysiology.

[28]  Jonathan D. Victor,et al.  Asymptotic Bias in Information Estimates and the Exponential (Bell) Polynomials , 2000, Neural Computation.

[29]  T. Gawne.  The simultaneous coding of orientation and contrast in the responses of V1 complex cells , 2000, Experimental Brain Research.

[30]  G. Gestri.  Dynamics of a model for the variability of the interspike intervals in a retinal neuron , 2004, Biological Cybernetics.

[31]  John P. Miller,et al.  Temporal encoding in nervous systems: A rigorous definition , 1995, Journal of Computational Neuroscience.