Correcting for the Sampling Bias Problem in Spike Train Information Measures (original) (raw)

2007, Journal of Neurophysiology

Panzeri S, Senatore R, Montemurro MA, Petersen RS. Correcting for the sampling bias problem in spike train information measures. Information Theory enables the quantification of how much information a neuronal response carries about external stimuli and is hence a natural analytic framework for studying neural coding. The main difficulty in its practical application to spike train analysis is that estimates of neuronal information from experimental data are prone to a systematic error (called "bias"). This bias is an inevitable consequence of the limited number of stimulusresponse samples that it is possible to record in a real experiment. In this paper, we first explain the origin and the implications of the bias problem in spike train analysis. We then review and evaluate some recent general-purpose methods to correct for sampling bias: the Panzeri-Treves, Quadratic Extrapolation, Best Universal Bound, Nemenman-Shafee-Bialek procedures, and a recently proposed shuffling bias reduction procedure. Finally, we make practical recommendations for the accurate computation of information from spike trains. Our main recommendation is to estimate information using the shuffling bias reduction procedure in combination with one of the other four general purpose bias reduction procedures mentioned in the preceding text. This provides information estimates with acceptable variance and which are unbiased even when the number of trials per stimulus is as small as the number of possible discrete neuronal responses. Abbott LF, Rolls ET, Tovee MJ. Representational capacity of face coding in monkeys. Cereb Cortex 6: 498 -505, 1996. Arabzadeh E, Panzeri S, Diamond ME. Whisker vibration information carried by rat barrel cortex neurons. J Neurosci 24: 6011-6020, 2004. Arabzadeh E, Zorzin E, Diamond ME. Neuronal encoding of texture in the whisker sensory pathway. PLoS Biol 3: e17, 2005. Averbeck BB, Latham PE, Pouget A. Neural correlations, population coding and computation. Nat Rev Neurosci 7: 358 -366, 2006. Borst A, Theunissen FE. Information theory and neural coding. Nat Neurosci 2: 947-957, 1999. de Ruyter van Steveninck R, Lewen GD, Strong SP, Koberle R, Bialek W. Reproducibility and variability in neural spike trains. Science 275: 1805-1808, 1997. Endres D, Foldiak P. Bayesian bin distribution inference and mutual information. IEEE Trans Inform Th 51: 3766 -3779, 2005. Gershon ED, Wiener MC, Latham PE, Richmond BJ. Coding strategies in monkey V1 and inferior temporal cortices.