Abstract
Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that lead to beneficial and detrimental effects of noise correlation on decoding. Further, the proposed framework sheds light on the contribution of neuronal noise, highlighting cases where, counter-intuitively, increased noise may lead to improved decoding performance. Finally, we examined the impact of dynamical parameters, including neuronal leak and integration time constant, on decoding. Overall, this work presents a fruitful approach to the study of decoding using a comprehensive theoretical framework that merges dynamical parameters with estimates of readout error.
Highlights
In recent years, neuronal decoding has emerged as a key aspect of understanding the neural code [1]
We formally analyze the optimal decoding error of a linear decoder based on Fisher linear discriminant analysis (LDA)
The above results show that, depending upon the structure of the input delivered to the two neural populations, noise correlations produce widely different effects on classification error
Summary
Neuronal decoding has emerged as a key aspect of understanding the neural code [1]. We verified the analytical solution by comparing it to numerical estimates of the error rate as a function of noise correlation These numerical estimates were obtained with Eq (1), where populations x and y both received inputs ν1 = 11 and ν2 = 14 in order for the model to mimick a scenario where the two populations have identical tuning properties. The above results show that, depending upon the structure of the input delivered to the two neural populations, noise correlations produce widely different effects on classification error While insights into these results can be obtained without the full formalism described here [34], such formalism becomes pivotal when examining the effect of specific network parameters, as described
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