Estimation of information in neuronal responses.

The article by Buracas and Albright1xBuracas, G.T. and Albright, T.D. Trends Neurosci. 1999; 22: 303–309Abstract | Full Text | Full Text PDF | PubMed | Scopus (50)See all References1 provides an excellent review of recent progress concerning the neural representation of sensory stimuli. The authors outline clearly the potential pitfalls of the ‘direct’2xBuracas, G.T. et al. Neuron. 1998; 20: 959–969Abstract | Full Text | Full Text PDF | PubMed | Scopus (228)See all References, 3xde Ruyter van Steveninck, R.R. et al. Science. 1997; 275: 1805–1808CrossRef | PubMed | Scopus (402)See all References and ‘reconstruction’4xBialek, W. et al. Science. 1991; 252: 1854–1857CrossRef | PubMedSee all References, 5xBialek, W. and Rieke, F. Trends Neurosci. 1992; 15: 428–434Abstract | Full Text PDF | PubMed | Scopus (102)See all References, 6xOram, M.W. et al. Trends Neurosci. 1998; 21: 259–265Abstract | Full Text | Full Text PDF | PubMed | Scopus (146)See all References methods for estimation of mutual information (namely, the need to estimate a probability distribution of spike trains, which are considered as vectors in what could be a very large space), but the naive reader might be left with the belief that there are no good alternatives.However, such alternatives do exist. We recently developed an approach to the analysis of information in spike trains that encompasses dynamics, but does not require a vector-space embedding nor the estimate of a multivariate probability distribution7xVictor, J.D. and Purpura, K.P. Network. 1997; 8: 127–164CrossRefSee all References7. This method has been applied in mammalian visual cortex by us8xVictor, J.D. and Purpura, K.P. J. Neurophysiol. 1996; 76: 1310–1326PubMedSee all References, 9xMechler, F. et al. J. Neurosci. 1998; 18: 6583–6598PubMedSee all References, 10xVictor, J.D. and Purpura, K.P. J. Neurophysiol. 1998; 80: 554–571PubMedSee all References, and in the insect olfactory system by Laurent and colleagues11xMacLeod, K., Backer, A., and Laurent, G. Nature. 1998; 395: 693–698CrossRef | PubMed | Scopus (166)See all References11.Any method for estimation of information in spike trains requires making assumptions about the nature of the code. The accuracy of the information estimate depends on both the correctness and the breadth of the assumptions. Fewer assumptions about the nature of the neural code are made by the metric-space methods than by vector-space methods (such as the direct and reconstruction methods). However, this broader scope necessarily incurs a penalty in terms of the amount of mutual information that can be identified. A rough estimate of this penalty can be determined by comparing information calculations based on model data in which the vector-space assumptions are known to be appropriate. This comparison indicates a penalty of about 25% paid by the metric-space methods in return for their broader scope. Conversely, assumptions concerning the nature of the code that are overly narrow could also lead to underestimates of information, as the aspects of the spike train that carry the information might be overlooked.As discussed by Buracas and Albright1xBuracas, G.T. and Albright, T.D. Trends Neurosci. 1999; 22: 303–309Abstract | Full Text | Full Text PDF | PubMed | Scopus (50)See all References1, even the most efficient neuronal representations are only about 50% efficient, when efficiency is determined by the reconstruction and direct methods. Residual inefficiency is generally attributed to neuronal noise. However, some of this ‘inefficiency’ might be only apparent, representing instead a contribution from forms of coding beyond the scope of the analysis method. Moreover, theoretical considerations have raised the possibility that the structure of central neuronal representations has the abstract properties of a metric space, rather than a vector space12xHopfield, J.J. Nature. 1995; 376: 33–36CrossRef | PubMedSee all References, 13xEdelman, S. Behav. Brain Sci. 1998; 21: 449–467PubMedSee all References. For these reasons, as information-theoretic analyses are pursued in a wider variety of settings, the neurophysiologist should be prepared to use a wide range of techniques for information analysis, with both narrow and broad prior assumptions.