Extracting information from neuronal populations: information theory and decoding approaches

Key Points

  • To understand complex brain processes, there is a clear need to shift from traditional single-cell studies of trial-averaged responses to single-trial analyses of multiple neurons. In this respect, the decoding and information-theory formalisms offer a powerful framework to study how the brain computes information from the single-trial activity of neuronal populations.

  • Compared with single-cell studies, population analysis with decoding and information theory has several advantages: the information of the neuronal population is considered as a whole; information is extracted from single-trial occurrences; it is possible to discover which stimulus features are encoded by the neural responses; it is possible to evaluate which features of the neural responses carry relevant information; and it is possible to combine information from different types of neural signals.

  • Several studies have shown how much more knowledge can be extracted using the decoding and information-theory methodologies and how, in some cases, information that it is ambiguous at the single-cell level can be clearly interpreted when considering the whole population.

  • Decoding has the advantage of being similar to real behavioural calculations, but it may lose information contained in the neural responses. Information theory considers all the information in the neural response, but it is more difficult to compute for large populations and its values may not be biologically relevant.

  • The complementary knowledge offered by decoding and information theory has not been exploited enough in neuroscience. A joint application of both approaches may offer additional insights into how neuronal populations encode information.


To a large extent, progress in neuroscience has been driven by the study of single-cell responses averaged over several repetitions of stimuli or behaviours. However,the brain typically makes decisions based on single events by evaluating the activity of large neuronal populations. Therefore, to further understand how the brain processes information, it is important to shift from a single-neuron, multiple-trial framework to multiple-neuron, single-trial methodologies. Two related approaches — decoding and information theory — can be used to extract single-trial information from the activity of neuronal populations. Such population analysis can give us more information about how neurons encode stimulus features than traditional single-cell studies.

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Figure 1: Three main steps for the population analysis of neural recordings.
Figure 2: Decoding analysis.
Figure 3: Sources of information loss.
Figure 4: Decoding arm reaches and saccades to eight different directions.
Figure 5: Encoding of information by the local field potential phase.


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We are very thankful to F. Montani, K. Whittingstall, J. Csicsvari, A. Mazzoni and G. Kreiman for comments, to P. Dayan for interesting discussions about uncertainty and decoding, and to all our brilliant colleagues that collaborated with us on these topics: R. Andersen, M. Diamond, I. Fried, C. Koch, N. Logothetis, C. Kayser, M. Montemurro, R. Petersen and A. Treves. We acknowledge support from the Engineering and Physical Sciences Research Council, the Medical Research Council, the Royal Society and the Italian Institute of Technology.

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Correspondence to Rodrigo Quian Quiroga.

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Spike sorting

The grouping of spikes into clusters based on the similarity of their shapes. Given that, in principle, each neuron tends to fire spikes of a particular shape, the resulting clusters correspond to the activity of different putative neurons. The end result of spike sorting is determining which spike corresponds to which of these neurons.


Predicting the most likely stimulus or behaviour eliciting an observed neural response.

Information theory

A mathematical theory that deals with measures of information and their application to the study of communication systems. In neuroscience it is used to establish the amount of information about a stimulus or behaviour that is contained in the neural responses.

Local field potential

(LFP). A neurophysiological signal that is obtained by low-pass filtering extracellular recordings. It represents the mean field potential generated by the slow components of synaptic and neural events in the vicinity of the recording electrode.

Posterior probability

The posterior probability of a random variable is the conditional probability assigned to the variable given some event. For example, the posterior probability P(s|r) is the conditional probability that stimulus s was presented, given that a response r was observed.

Shannon entropy

A measure of the uncertainty about the value that might be taken by a random variable.


The unit used to measure reduction of uncertainty. One bit corresponds to a reduction of uncertainty by a factor of two (for example, a correct answer to a yes/no question).

Unbiased decoder

A decoder is said to be unbiased if the expected value of its decoding error (the difference between the true and the estimated stimulus values) is zero.

Brain–machine interface

A direct communication link between a brain (human or animal) and an external device, such as a prosthetic limb or a sensing device.

Principal-component analysis

A linear transformation that projects the data on to an orthogonal base, in which the greatest variance of the data lies on the first coordinate (the first principal component), the second greatest variance on the second coordinate, and so on. It is usually used to reduce the dimensionality of complex data.

Spike afterpotential

A transient hyperpolarization of a neuron following the firing of an action potential. It is caused by K+ channels, which open during the spike and close a few milliseconds after the neural membrane potential goes back to its resting value.


In MRI research, a voxel refers to the smallest measured volume unit, analogous to a three-dimensional pixel. In functional MRI studies these are typically of the order of 30 mm3, although much smaller voxel volumes have been achieved in more recent work.

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Quian Quiroga, R., Panzeri, S. Extracting information from neuronal populations: information theory and decoding approaches. Nat Rev Neurosci 10, 173–185 (2009). https://doi.org/10.1038/nrn2578

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