Inferring decoding strategies from choice probabilities in the presence of correlated variability


The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship that is often quantified by choice probabilities. Although choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. We derive the mathematical relationship between choice probabilities, read-out weights and correlated variability in the standard neural decision-making model. Our solution allowed us to prove and generalize earlier observations on the basis of numerical simulations and to derive new predictions. Notably, our results indicate how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we developed a test to decide whether the decoding weights of individual neurons are optimal for the task, even without knowing the underlying correlations. We confirmed the practicality of our approach using simulated data from a realistic population model. Thus, our findings provide a theoretical foundation for a growing body of experimental results on choice probabilities and correlations.

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Figure 1: Illustration of model setup.
Figure 2: Choice probabilities for example cases.
Figure 3: Correlation structure and its influence on choice probabilities.
Figure 4: Reconstruction of weights from limited data in the case of a heterogenous neuronal population and limited data.
Figure 5: Reliability of reconstruction procedure for the simulated example case across 1,000 repetitions.
Figure 6: Optimality test.


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We thank A. Ecker and P. Berens for stimulating discussions and detailed comments on an earlier version of the manuscript, and H. Nienborg and B.G. Cumming for many helpful conversations. This work was partially supported by the German Ministry of Education, Science, Research and Technology through the Bernstein Award (FKZ 01GQ0601) (M.B.), the Bernstein Center for Computational Neuroscience (FKZ 01GQ1002), the German Excellency Initiative through the Centre for Integrative Neuroscience Tübingen (EXC307) and the European Commission (FP7-ICT-257005). R.M.H. acknowledges the hospitality of the Fiser laboratory at Brandeis University where this study was completed and financial support from the Swartz Foundation. Part of this research was done while J.H.M. was at the Gatsby Computational Neuroscience Unit, University College London.

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R.M.H. conceived the research. R.M.H. and S.G. performed the analytical calculations and R.M.H. performed the simulations. All of the authors discussed the results. R.M.H. wrote the paper with contributions from the other authors. J.H.M. and M.B. advised at all stages.

Corresponding author

Correspondence to Ralf M Haefner.

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The authors declare no competing financial interests.

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Haefner, R., Gerwinn, S., Macke, J. et al. Inferring decoding strategies from choice probabilities in the presence of correlated variability. Nat Neurosci 16, 235–242 (2013).

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