Schatztheoretische Analyse Neuronaler Codierungsstrategien

This dissertation deals with the application of estimation theory to the analysis of neural codes. Neural systems that represent stimulus information presumably optimize their response characteristics by minimizing the error achievable when reconstructing the stimulus from the activity. By calculating this minimal reconstruction error either for theoretical models of neural encoding systems or from empirically measured activity, estimation theory serves to quantify the encoding accuracy achievable by a given coding scheme. Following an introduction of the basic concepts of classical estimation theory and a discussion of the ideas behind its application to neural coding, this thesis contains two worked-out examples that tackle major problems inThis dissertation deals with the application of estimation theory to the analysis of neural codes. Neural systems that represent stimulus information presumably optimize their response characteristics by minimizing the error achievable when reconstructing the stimulus from the activity. By calculating this minimal reconstruction error either for theoretical models of neural encoding systems or from empirically measured activity, estimation theory serves to quantify the encoding accuracy achievable by a given coding scheme. Following an introduction of the basic concepts of classical estimation theory and a discussion of the ideas behind its application to neural coding, this thesis contains two worked-out examples that tackle major problems in the corresponding areas of computational neuroscience. The first application involves a Fisher information analysis of the representational accuracy achieved by a population of stochastically spiking neurons that encode a stimulus with their spike counts during some fixed time interval. The obtained results lead to three main conclusions. First, the structure of neuronal noise can substantially modify the encoding properties of neural systems. In particular, the claim that limited-range correlations impose an upper limit on this capacity was shown to be correct only for the biologically implausible case of fixed-variance noise. This shows that choosing the correct neuronal noise model can be critical for theoretical analysis. Second, considerations on parameter variability lead to the hypothesis that the great variability observed empirically may not simply be a byproduct of neuronal diversity, but could be exploited by the neural system to achieve better encoding performance. Finally, it is demonstrated that neural populations can choose from a wide variety of strategies to optimize their tuning properties. Hence, the question of optimal tuning properties may not be reduced to a simple "broad or narrow"-dichotomy. Second, a linear reconstruction approach (the Wiener-Kolmogorov filter) was used to analyze coding strategies for time-varying stimuli. In an application to motion representation in H1-neurons, it turned out that, as shown above for static stimuli, the exact type of noise (e.g. Poissonian, additive, or multiplicative) is also important in the context of coding of dynamic stimuli. Moreover, it was shown that biphasic filters allow the best reconstruction if their time scale corresponds to the stimulus autocorrelation time, while the performance of single-phase filters always improves with decreasing time scale. A second application of the Wiener-Kolmogorov filter to a more sophisticated model of contrast coding in retinal activity suggested that non-linear contrast gain control does not improve the encoding of temporal contrast patterns in the normal physiological regime of retinal function. However, this example also demonstrated that the application of estimation theory to complex, real-world biological systems is not as straightforward as it may seem from purely theoretical studies. In conclusion, this thesis demonstrates that estimation theory provides a unified framework for the study of neural codes for both static and time-varying stimuli. In addition, it has successfully applied this framework to aspects of neural coding and derived results of general importance for our current picture of neural representation of stimulus information. It is hoped that this work is of value for both experimental and theoretical neuroscientists the corresponding areas of computational neuroscience. The first application involves a Fisher information analysis of the representational accuracy achieved by a population of stochastically spiking neurons that encode a stimulus with their spike counts during some fixed time interval. The obtained results lead to three main conclusions. First, the structure of neuronal noise can substantially modify the encoding properties of neural systems. In particular, the claim that limited-range correlations impose an upper limit on this capacity was shown to be correct only for the biologically implausible case of fixed-variance noise. This shows that choosing the correct neuronal noise model can be critical for theoretical analysis. Second, considerations on parameter variability lead to the hypothesis that the great variability observed empirically may not simply be a byproduct of neuronal diversity, but could be exploited by the neural system to achieve better encoding performance. Finally, it is demonstrated that neural populations can choose from a wide variety of strategies to optimize their tuning properties. Hence, the question of optimal tuning properties may not be reduced to a simple "broad or narrow"-dichotomy. Second, a linear reconstruction approach (the Wiener-Kolmogorov filter) was used to analyze coding strategies for time-varying stimuli. In an application to motion representation in H1-neurons, it turned out that, as shown above for static stimuli, the exact type of noise (e.g. Poissonian, additive, or multiplicative) is also important in the context of coding of dynamic stimuli. Moreover, it was shown that biphasic filters allow the best reconstruction if the