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

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1

    Parker, A.J. & Newsome, W. Sense and the single neuron: probing the physiology of perception. Annu. Rev. Neurosci. 21, 227–277 (1998).

    CAS  Article  Google Scholar 

  2. 2

    Grunewald, A., Bradley, D. & Andersen, R. Neural correlates of structure-from-motion perception in macaque V1 and MT. J. Neurosci. 22, 6195–6207 (2002).

    CAS  Article  Google Scholar 

  3. 3

    Nienborg, H. & Cumming, B. Macaque V2 neurons, but not V1 neurons, show choice-related activity. J. Neurosci. 26, 9567–9578 (2006).

    CAS  Article  Google Scholar 

  4. 4

    Uka, T., Tanabe, S., Watanabe, M. & Fujita, I. Neural correlates of fine depth discrimination in monkey inferior temporal cortex. J. Neurosci. 25, 10796–10802 (2005).

    CAS  Article  Google Scholar 

  5. 5

    Britten, K.H., Newsome, W., Shadlen, M., Celebrini, S. & Movshon, J. A relationship between behavioral choice and the visual responses of neurons in macaque MT. Vis. Neurosci. 13, 87–100 (1996).

    CAS  Article  Google Scholar 

  6. 6

    Dodd, J.V., Krug, K., Cumming, B. & Parker, A. Perceptually bistable three-dimensional figures evoke high choice probabilities in cortical area MT. J. Neurosci. 21, 4809–4821 (2001).

    CAS  Article  Google Scholar 

  7. 7

    Cook, E.P. & Maunsell, J. Dynamics of neuronal responses in macaque MT and VIP during motion detection. Nat. Neurosci. 5, 985–994 (2002).

    CAS  Article  Google Scholar 

  8. 8

    Parker, A.J., Krug, K. & Cumming, B. Neuronal activity and its links with the perception of multi-stable figures. Phil. Trans. R. Soc. Lond. B 357, 1053–1062 (2002).

    Article  Google Scholar 

  9. 9

    Uka, T. & DeAngelis, G. Contribution of area MT to stereoscopic depth perception: choice-related response modulations reflect task strategy. Neuron 42, 297–310 (2004).

    CAS  Article  Google Scholar 

  10. 10

    Liu, J. & Newsome, W. Correlation between speed perception and neural activity in the middle temporal visual area. J. Neurosci. 25, 711–722 (2005).

    CAS  Article  Google Scholar 

  11. 11

    Purushothaman, G. & Bradley, D. Neural population code for fine perceptual decisions in area MT. Nat. Neurosci. 8, 99–106 (2005).

    CAS  Article  Google Scholar 

  12. 12

    Law, C.T. & Gold, J. Neural correlates of perceptual learning in a sensory-motor, but not a sensory, cortical area. Nat. Neurosci. 11, 505–513 (2008).

    CAS  Article  Google Scholar 

  13. 13

    Celebrini, S. & Newsome, W. Neuronal and psychophysical sensitivity to motion signals in extrastriate area MST of the macaque monkey. J. Neurosci. 14, 4109–4124 (1994).

    CAS  Article  Google Scholar 

  14. 14

    Shadlen, M.N., Britten, K., Newsome, W. & Movshon, J. A computational analysis of the relationship between neuronal and behavioral responses to visual motion. J. Neurosci. 16, 1486–1510 (1996).

    CAS  Article  Google Scholar 

  15. 15

    Cohen, M.R. & Newsome, W. Estimates of the contribution of single neurons to perception depend on timescale and noise correlation. J. Neurosci. 29, 6635–6648 (2009).

    CAS  Article  Google Scholar 

  16. 16

    Nienborg, H. & Cumming, B. Correlations between the activity of sensory neurons and behavior: how much do they tell us about a neuron's causality? Curr. Opin. Neurobiol. 20, 376–381 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. 17

    Gold, J.I. & Shadlen, M. The neural basis of decision making. Annu. Rev. Neurosci. 30, 535–574 (2007).

    CAS  Article  Google Scholar 

  18. 18

    Newsome, W.T., Britten, K. & Movshon, J. Neuronal correlates of a perceptual decision. Nature 341, 52–54 (1989).

    CAS  Article  Google Scholar 

  19. 19

    Nienborg, H. & Cumming, B. Decision-related activity in sensory neurons reflects more than a neuron's causal effect. Nature 459, 89–92 (2009).

    CAS  Article  Google Scholar 

  20. 20

    Nienborg, H., Cohen, M. & Cumming, B.G. Decision-related activity in sensory neurons: correlations among neurons and with behavior. Annu. Rev. Neurosci. 35, 463–483 (2012).

    CAS  Article  Google Scholar 

  21. 21

    Wang, X.J. Decision making in recurrent neuronal circuits. Neuron 60, 215–234 (2008).

    CAS  Article  Google Scholar 

  22. 22

    Gu, Y., Angelaki, D. & DeAngelis, G. Neural correlates of multisensory cue integration in macaque MSTd. Nat. Neurosci. 11, 1201–1210 (2008).

    CAS  Article  Google Scholar 

  23. 23

    Nienborg, H. & Cumming, B. Psychophysically measured task strategy for disparity discrimination is reflected in V2 neurons. Nat. Neurosci. 10, 1608–1614 (2007).

    CAS  Article  Google Scholar 

  24. 24

    Abbott, L.F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999).

    CAS  Article  Google Scholar 

  25. 25

    Chen, Y., Geisler, W. & Seidemann, E. Optimal decoding of correlated neural population responses in the primate visual cortex. Nat. Neurosci. 9, 1412–1420 (2006).

    CAS  Article  Google Scholar 

  26. 26

    Cohen, M.R. & Newsome, W. Context-dependent changes in functional circuitry in visual area MT. Neuron 60, 162–173 (2008).

    CAS  Article  Google Scholar 

  27. 27

    Law, C.T. & Gold, J. Reinforcement learning can account for associative and perceptual learning on a visual-decision task. Nat. Neurosci. 12, 655–663 (2009).

    CAS  Article  Google Scholar 

  28. 28

    Bishop, C. Pattern Recognition and Machine Learning (Springer, New York, 2006).

  29. 29

    Averbeck, B.B., Latham, P. & Pouget, A. Neural correlations, population coding and computation. Nat. Rev. Neurosci. 7, 358–366 (2006).

    CAS  Article  Google Scholar 

  30. 30

    Cohen, M.R. & Kohn, A. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14, 811–819 (2011).

    CAS  Article  Google Scholar 

  31. 31

    Gu, Y. et al. Perceptual learning reduces interneuronal correlations in macaque visual cortex. Neuron 71, 750–761 (2011).

    CAS  Article  Google Scholar 

  32. 32

    Buzsáki, G. Large-scale recording of neuronal ensembles. Nat. Neurosci. 7, 446–451 (2004).

    Article  Google Scholar 

  33. 33

    Kerr, J.N. & Denk, W. Imaging in vivo: watching the brain in action. Nat. Rev. Neurosci. 9, 195–205 (2008).

    CAS  Article  Google Scholar 

  34. 34

    Stevenson, I.H. & Kording, K. How advances in neural recording affect data analysis. Nat. Neurosci. 14, 139–142 (2011).

    CAS  Article  Google Scholar 

  35. 35

    Shadlen, M.N. & Newsome, W. The variable discharge of cortical neurons: implications for connectivity, computation and information coding. J. Neurosci. 18, 3870–3896 (1998).

    CAS  Article  Google Scholar 

  36. 36

    Liu, J. & Newsome, W. T. Local field potential in cortical area MT: stimulus tuning and behavioral correlations. J. Neurosci. 26, 7779–7790 (2006).

    CAS  Article  Google Scholar 

  37. 37

    Marder, E. Variability, compensation, and modulation in neurons and circuits. Proc. Natl. Acad. Sci. USA 108 (suppl. 3): 15542–15548 (2011).

    CAS  Article  Google Scholar 

  38. 38

    Padmanabhan, K. & Urban, N. Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content. Nat. Neurosci. 13, 1276–1282 (2010).

    CAS  Article  Google Scholar 

  39. 39

    Ecker, A.S., Berens, P., Tolias, A. & Bethge, M. The effect of noise correlations in populations of diversely tuned neurons. J. Neurosci. 31, 14272–14283 (2011).

    CAS  Article  Google Scholar 

  40. 40

    Churchland, M.M. & Shenoy, K. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. J. Neurophysiol. 97, 4235–4257 (2007).

    Article  Google Scholar 

  41. 41

    Jazayeri, M. Probabilistic sensory recoding. Curr. Opin. Neurobiol. 18, 431–437 (2008).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Contributions

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.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Note, Supplementary Figures 1–11 (PDF 3416 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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). https://doi.org/10.1038/nn.3309

Download citation

Further reading

Search

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing